Calculating Climate Effects on Birds and Mammals: Impacts on Biodiversity, Conservation, Population...

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Calculating Climate Effects on Birds and Mammals Impacts on BiodiversityConservation Population Parameters and Global Community StructureAuthor(s) Warren P Porter Srinivas Budaraju Warren E Stewart and Navin RamankuttySource American Zoologist 40(4)597-630 2000Published By The Society for Integrative and Comparative BiologyDOI httpdxdoiorg1016680003-1569(2000)040[0597CCEOBA]20CO2URL httpwwwbiooneorgdoifull1016680003-1569282000290405B05973ACCEOBA5D20CO3B2

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597

AMER ZOOL 40597ndash630 (2000)

Calculating Climate Effects on Birds and MammalsImpacts on Biodiversity Conservation Population Parameters and

Global Community Structure1

WARREN P PORTER2 SRINIVAS BUDARAJU3dagger WARREN E STEWARTdagger AND

NAVIN RAMANKUTTYDaggerDepartment of Zoology University of Wisconsin 250 N Mills St

Madison Wisconsin 53706daggerDepartment of Chemical Engineering University of Wisconsin 1415 Johnson Drive

Madison Wisconsin 53706DaggerInstitute for Environmental Studies 1225 West Dayton Street

Madison Wisconsin 53706

SYNOPSIS This paper describes how climate variation in time and space canconstrain community structure on a global scale We explore body size scaling andthe energetic consequences in terms of absorbed mass and energy and expendedmass and energy We explain how morphology specific physiological propertiesand temperature dependent behaviors are key variables that link individual en-ergetics to population dynamics and community structure

This paper describes an integrated basic principles model for mammal energeticsand extends the model to bird energetics The model additions include molar bal-ance models for the lungs and gut The gut model couples food ingested to respi-ratory gas exchanges and evaporative water loss from the respiratory system Weincorporate a novel thermoregulatory model that yields metabolic calculations asa function of temperature The calculations mimic empirical data without regres-sion We explore the differences in the quality of insulation between hair andfeathers with our porous media model for insulation

For mammals ranging in size from mice to elephants we show that calculatedmetabolic costs are in agreement with experimental data We also demonstratehow we can do the same for birds ranging in size from hummingbirds to ostrichesWe show the impact of changing posture and changing air temperatures on en-ergetic costs for birds and mammals We demonstrate how optimal body size thatmaximizes the potential for growth and reproduction changes with changing cli-matic conditions and with diet quality Climate and diet may play important rolesin constraining community structure (collection of functional types of differentbody sizes) at local and global scales Thus multiple functional types may coexistin a locality in part because of the temporal and spatial variation in climate andseasonal food variation We illustrate how the models can be applied in a conser-vation and biodiversity context to a rare and endangered species of parrot theOrange-bellied Parrot of Australia and Tasmania

INTRODUCTION

A brief history

Ever since the era of Charles Darwin bi-ologists have been intrigued by how and

1 From the Symposium Evolutionary Origin ofFeathers presented at the Annual Meeting of the So-ciety for Integrative and Comparative Biology 6ndash10January 1999 at Denver Colorado

2 E-mail wportermhubzoologywiscedu3 Current address West Vaco Laurel Research Lab-

oratory 11101 Johnrsquos Hopkins Road Laurel MD20723

why animals live where they do and whatis it about their properties that makes themappear where they do and appear in thespecies associations that they form Hutch-inson (1959) defined the concept of theniche MacArthur et al (1966) Roughgar-den (1974) and many others explored as-pects of how size and habitat may influencecommunity structure Norris (1967) andBartlett and Gates (1967) were the first tocalculate explicitly how climate affects an-imal heat and mass balance and the conse-quences for body temperature in outdoor

598 W P PORTER ET AL

environments The climate space conceptemerged from steady state heat and massbalance calculations and was used to ex-plore how climates might constrain animalsurvival outdoors (Porter and Gates 1969)

Those early animal models of the 1960swere limited by the lack of models for dis-tributed heat generation internally distrib-uted evaporative water loss internally anda first principles model of gut functionBatch reactor plug flow and other modelswere already in existence in the chemicalengineering literature (Bird et al 1960)and it would take time for the biologicalcommunity to rediscover them Also miss-ing were a first principles model of porousinsulation for fur or feathers an appendagemodel and a general microclimate modelthat could use local macroclimate data tocalculate the range of local microenviron-ments above and below ground It becamepossible to estimate convection heat trans-fer properties knowing only the volume ofan animal (Mitchell 1976) Another usefuldevelopment was the appearance of a coun-tercurrent heat exchange model for append-ages (Mitchell and Myers 1968) and themeasurement of heat transfer characteristicsfrom animal appendage shapes (Wathen etal 1971 1974) It also became possible todeal with outdoor turbulence effects onconvective heat transport (Kowalski andMitchell 1976) A general-purpose micro-climate model emerged in the early 1970s(Beckman et al 1971 Porter et al 1973Mitchell et al 1975) that calculated aboveand below ground microclimates The abil-ity to deal with local environmental hetero-geneity and calculate percent of thermallyavailable habitat came later (Grant and Por-ter 1992) Over time general-purpose con-ductionndashradiation porous media models forfur appeared in the biological literature(Kowalski 1978) and it became possible torefine and test them in a variety of habitatsand on many species (Porter et al 1994)The extension of the models to radial in-stead of Cartesian coordinates and the im-plementation of first principles fluid me-chanics in the porous media (Stewart et al1993 Budaraju et al 1994 1997) addedimportant new dimensions to the modelswhich could now calculate temperature and

velocity profiles and therefore heat andmass transfer within the fur from basic prin-ciples A test of the ectotherm and micro-climate models to estimate a speciesrsquo sur-vivorship growth and reproduction at acontinental scale appeared in the mid 1990s(Adolph and Porter 1993 1996)

Thanks to these developments and theones reported in this paper such as the tem-perature dependent behavior linked to thenew thermoregulatory model it is now pos-sible to ask lsquolsquoHow does climate affect in-dividual animalsrsquo temperature dependentbehavior and physiology and what role(s)does it play in population dynamics andcommunity structurersquorsquo This paper attemptsto address some of these questions

We approach the problem from the per-spective of a combination of heat and masstransfer engineering and specific aspects ofmorphology physiology and temperaturedependent behavior of individuals Weshow how this interactive combination isessential to calculate preferred activity timethat minimizes size specific heatwaterstress

Preferred activity time is a key link be-tween individual energetics and populationlevel variables of survivorship growth andreproduction since it impacts all three pop-ulation variables Both individual and pop-ulation level effects may place constraintson community structure At the individuallevel climate at any given time and foodtype and quality affect the optimal bodysize that maximizes discretionary mass andenergy the resources needed for growthand reproduction Climate also affects com-munity structure by affecting individualsurvivorship directly (heat balancemeta-bolic costs) and indirectly (activity timeoverlap of predator and prey) Climate af-fects seasonal food availability distributionof food in space and time and the cost offoraging for that food at different times dur-ing a day Survivorship is affected by tem-perature dependent behavior changes thatallow animals to move to less costly micro-environments at any time For small mam-mals underground burrows or under snowtunnels provide temperatures that never staybelow 08C due to local heating effects ofthe animalrsquos metabolic heat production

599CLIMATEndashANIMAL INTERACTIONS

At the population level climate plays avery important role in population numbersEach species interacts in its own way withclimate affecting its abundance and com-munity structure As Ives et al (1999 p546) have pointed out

Our main result is that interspecific com-petition and species number have littleinfluence on community-level variancesthe variance in total community biomassdepends only on how species respond toenvironmental fluctuations This con-trasts with arguments (Tilman andDowning 1994 Lawton and Brown1993) that interspecific competition maydecrease community-level variances bydriving negative covariances betweenspecies abundances We show that nega-tive covariances are counteracted by in-creased species-level variances createdby interspecific competition

Consequently assessing the effect ofbiodiversity on community variabilityshould emphasize species-environmentinteractions and differences in speciesrsquosensitivities to environmental fluctuations(for example drought-tolerant speciesand phosphorus-limited species) (Mc-Naughton 1977 1985 Frost et al1994) Competitive interactions are rela-tively unimportant except through theireffects on mean abundances We have fo-cused on competitive communities be-cause much current experimental workhas addressed competition among plantsNonetheless the same results can beshown to hold for more complex modelswith multiple trophic levels

Exactly how climate variation vegetationdifferences animal morphology and for-aging behavior all interact to constrain mul-tiple functional typesrsquo existence as a com-munity is still largely unknown Very littleis known about temperature dependent for-aging in mammals although this has beenwell studied in reptiles and insects Quan-titative consequences of functional mor-phology on encounter probability and foodhandling time also are relatively unexploredas yet in mammals

Temporal climate variation in a localitycreates the opportunity for multiple optimal

body sizes over annual cycles The spatiallocal variation in topography and vegetationcreates multiple local climates Thus tem-poral and spatial variation in climate createsopportunities for multiple functional types(sizes) to coexist as communities becauseas we shall see below different body sizesinteract differently with climate Qualita-tively this idea is not new However withlikely major shifts in global climates andthe rapid global changes in land use thereis urgent need to move these qualitativeideas to a quantitative framework for pro-tection of biodiversity conservation biolo-gy and a number of other applications Wefocus in this paper on applications to mam-mals and birds

An overview of this paper

The structure of the paper begins with anoverview of how macroclimate drives mi-croclimates which in turn impact individ-ual animal properties We then show howkey individual properties determine popu-lation level parameters that can be used tocalculate population dynamics variablesWe then illustrate how individual propertiesalso impact on community structure that inturn feed back to temperature dependent an-imal properties of individuals

The initial overview provides a contextfor an analysis of the model componentsand their interactions in hierarchical con-texts We start with the model componentsfrom the core to the skin then from the skinthrough the insulation to the environmentWe demonstrate how these components col-lectively can define the metabolic cost tomammals ranging in size from mice to el-ephants We show how the empiricalmouse-to-elephant metabolic regressionline for animals of different sizes changesdepending upon the animalrsquos climate andposture

Then we explore how changing mammalbody size affects discretionary energyacross all climates Once the mammal mod-el is explored we repeat the process for thebird model We demonstrate how we canestimate metabolic cost across bird sizesranging from hummingbirds to ostrichesWe show how postural changes and air tem-


FIG 1 Flow diagram illustrating the interconnections between climate individual properties population dy-namics and community structure

perature can alter metabolic cost estimatesfor birds

Once sensitivity analyses are completedwe explore how temporal and spatial vari-ation in global climate impact body size de-pendent discretionary energy assuming nofood limitation and thereby place con-straints on the potential combinations ofbody sizes (community structure) of mam-mals at the global scale

Finally we show how these models canbe applied to estimate for the first time frombasic principles the metabolic costs andfood requirements of an endangered speciesof bird the Orange-bellied Parrot of Tas-mania and Australia We show these resultsfor body sizes ranging from hatchling tofully mature adult for a wide range of en-vironmental conditions

MATERIALS AND METHODS

The modelsOverview Figure 1 is a flow diagram that

shows qualitatively how we connect mac-

roclimate microclimates individual prop-erties population level effects and com-munity attributes The macroclimatendashmi-croclimate connection is achieved in partby general climate data available throughthe National Oceanic and Atmospheric Ad-ministration (NOAA) The microclimatemodel has been described for a variety ofhabitats that range from southwestern des-erts (Mitchell et al 1975 Porter et al1973) to Santa Fe Island in the Galapagos(Christian et al 1983) to Michigan bogs(Kingsolver 1979) It is a one-dimensionalfinite difference model that simultaneouslysolves the heat and mass balance equationsfor the ground surface and below It alsocalculates wind speed and temperature pro-files from the ground surface to two meterreference height where meteorological dataare typically measured Clear sky solar ra-diation is calculated from basic principles(McCullough and Porter 1971)

Microclimate calculations for heteroge-


neous environments can determine percentof thermally available habitat and temper-ature dependent feeding frequency (Grantand Porter 1992) Grant and Porter showedthat item feeding frequency was a linearfunction of the thermally available percentof the habitat (the percentage that allowsthe animal to stay within its preferred tem-perature range thereby avoiding significantthermoregulatory heat stress costs) A sum-mation of a dayrsquos preferred activity timesover a month and over the year yields totalannual activity time

Total annual activity time is a key vari-able linking individual energetics with pop-ulation and community level phenomenaAnnual activity time for a terrestrial verte-brate was first calculated from basic prin-ciples in 1973 (Porter et al 1973) By lsquolsquoba-sic principlesrsquorsquo we mean equations derivedfrom thermodynamic principles that do notinvolve regression equations Total annualactivity time can be used to calculate keylife history variables such as survivorshipgrowth and reproductive potential (Adolphand Porter 1993 Adolph and Porter 1996)that are used to calculate population dy-namics

Survivorship (mortality) probabilityhouris affected by activity time which is af-fected by temperature dependent habitat se-lection Climate change may affect survi-vorship partly by modifying predationprobabilities that change with seasonalchanges in overlap of predator and preypreferred activity time (Porter et al 1973Porter and James 1979) and partly due toclimate stress (Porter and Gates 1969)

Growth and reproduction potential de-pend on mass and energy intake and expen-ditures The difference between intake andexpenditure is the capital available forgrowth or reproduction We are in a strongposition to calculate massenergy expendi-tures Intake of mass and energy is morechallenging Intake depends on item feed-ing frequency and handling time Handlingtime depends on the size of food lsquolsquopack-agesrsquorsquo and morphology of the feeding ap-paratus Calculations in this paper assumedno shortage of food and that the mass flowthrough the gut scales with mass (Calder1984) and meets the body sizeclimate im-

posed metabolic demand The mass flowabsorbed over a day is assumed sufficientto meet basic thermoregulatory require-ments for the day plus a user defined mul-tiplier (up to 7) above the minimal metab-olism needed to maintain core temperaturein the current climate This was done to tryto establish an upper bound for absorbedmass for different sizes of animals

Different sizes of animals may representdifferent trophic levels in the communityOnly some of the connections between aspeciesrsquo individual energetics populationdynamics and community attributes areshown in Figure 1 Other species within thehabitat may influence temperature depen-dent behavior by competing with the arbi-trarily chosen animal species representedhere thereby affecting their numbers (Iveset al 1999) The reader may imagine mul-tiple layers of this graph for individual spe-cies interconnected vertically to allow forexplicit multiple species descriptions

Model cross section

Figure 2 represents a diagrammatic crosssection through an arbitrarily chosen part ofan animal This could represent a torsowhose geometry may be approximated bya cylinder sphere or ellipsoid or even across section through an appendage if theheat loss by respiration is removed Theremay or may not be a porous insulation be-yond the skin Figure 2 shows what wouldbe needed for heat and mass transfer cal-culations Data needed are the mean lengthof the fibers (hair or hair-like elements infeathers) fiber density as a function ofdepth fiber diameter and the depth of theinsulation Length and depth of the fibersare usually different unless the fibers extendoutward normal to the skin Solar reflectiv-ity and transmissivity of the fibers also mustbe known if the animal is diurnal and ex-posed to sunlight The environmental con-ditions that specify the climate boundaryconditions for an individual include solarradiation infrared fluxes from the sky andground air temperature wind speed andrelative humidity of the air passing over theanimal These values are calculated basedon the animalrsquos average height above


FIG 2 Diagram of a cross-section of an animal with porous insulation and heat fluxes including uniform heatgeneration and uniform heat dissipation by respiration See abbreviations list for definitions of terms

ground and the microclimate calculationsfor environment conditions above groundThe microclimate equations have been de-scribed (Mitchell et al 1975 Porter et al1973)

Most of the equations describing porousmedia heat flux without convection throughthe fur are described (Conley and Porter1986 Porter et al 1994) Heat and massflux equations describing flow through furare complex (Stewart et al 1993 Budarajuet al 1994 1997) Solar radiation was in-corporated in the model used here by as-suming that solar radiation is absorbedvery close to the furfeatherndashair interfacewhich is usually the case for bird feathersand dark dense fur (Porter unpublisheddata) Absorbed solar radiation heats the fi-ber elements which then emit infrared ra-diation outward toward the sky and inwardthrough the porous insulation The watts ofabsorbed solar radiation were treated as anadditional source of thermal radiation fromthe sky for the half of the animal exposed

to the sky Thus the diffuse infrared radi-ation equations already in model were alsoused for incorporating absorbed solar radi-ation in the model

The porous media model is only part ofthe animal model used to calculate meta-bolic heat production that will maintaincore temperature given the internal and ex-ternal morphology of the animal includingits insulation (Porter et al 1994) The ra-dial dimension of an animal is calculatedfrom its weight and geometry An iterativesearching routine named Zbrent guesses themetabolic heat production needed to main-tain any specified core temperature (Presset al 1986) Zbrent finds the unique met-abolic heat production that satisfies the heatand mass balance equations (AppendixPorter et al 1994) given the body allom-etry dimensions specified core tempera-ture insulation properties and environmen-tal conditions Because the equations are in-terconnected relatively few variables deter-mine these solutions (Porter et al 1994)


FIG 3 Temperature profiles in the body for modelsof uniform heat generation vs heat generation in acentral region with radial conduction only

Inside the body

The type of food in the gut determinesthe relative proportions of carbohydratesproteins and lipids that are absorbed by thebody A healthy body will utilize these ab-sorbed molecules as substrates The de-mand for energy and the substrates beingoxidized determine the amount of oxygenneeded The oxygen consumption is asso-ciated with heat generation The proportionof the substrates oxidized determines theamount of carbon dioxide produced andhence the respiratory quotient The oxygendemand specifies the moles of air that mustpass through the respiratory system to meetthe demand Thus the type of food in thegut affects indirectly the amount of incom-ing respiratory air which in turn affects thewater balance in the respiratory system inthe heat generation-ventilation-gut coupledmodel described below

Heat generation models Figure 3 showshow the current model of distributed heatgeneration throughout the body creates aparabolic temperature profile from the bodycore to skin The equations describing uni-form heat generation for rectangular (slab)cylindrical spherical and ellipsoid geome-try (Porter et al 1994) all show that the

internal heat generation and the temperaturegradient from core to skin are functions ofthe body radius squared The model solvesthe heat and mass balance equations (Porteret al 1994) for heat generation needed tomaintain core temperature by iterativeguessing the solution for each hour of sim-ulation throughout a 24 hr daily cycle Thecoupled equations of heat and mass transfersimultaneously yield solutions for waterbalance gut absorbed food requirementshours of activity time and discretionarymass and energy available for growth or re-production or fat deposition as describedbelow

Earlier metabolic heat generation modelssuch as a slab approximation assumed aheat source only at the center of the animal(Porter and Gates 1969 Porter et al1973) This assumption creates a simple lin-ear temperature profile from core to skin(Fig 3 Porter et al 1994) but not shownhere This type of construct frequently usesthe term lsquolsquothermal conductancersquorsquo the recip-rocal ofrsquorsquo thermal resistancersquorsquo Thermalconductance is a linear model of heat trans-fer commonly used in many biological pub-lications referring to animal heat transferUnfortunately it is only relevant in the con-text of non-heat generating materials

A cylindrical geometry with a heatsource only at the center (axis) does notmathematically allow for the heat sourceonly at the axis since it is undefined there(Bird et al 1960) A central heated regionis required Simple conduction (but notadded heat generation by the conductingtissues) of heat radially from the perimeterof the core region yields a logarithmic tem-perature profile This logarithmic profilehas different heat generation requirementsto maintain a specified core temperature inthe center region than a model using dis-tributed heat production from the core tothe skin

Respiration An important addition to thecurrent model is the distributed respiratorywater loss which represents lungs that spanmost of the body cavity This innovationgives much better agreement of predictedmetabolic rates with measured values

Figure 4 shows the system diagram forthe lung molar balance model A dashed


FIG 4 Molar balance models of respiratory and digestive systems coupled to each other and to (oxygenrequirement for) metabolic heat demand to maintain core temperature

line labeled 1 represents the entrance sur-face to the respiratory system The dashedline labeled 2 represents the exit surfacefrom the respiratory system Moles of ni-trogen oxygen water and carbon dioxideenter the respiratory system The moles ofair entering are calculated from the productof the moles of oxygen needed for the cur-rent guess for heat generation requirementstimes the sum of the percent compositionof the components of air divided by the per-cent of oxygen in the air which may changein burrows Thus the current iterativeguess for metabolic heat production speci-fies how many moles of oxygen are neededto meet the metabolic demand from the re-spiratory system The type of diet (carbo-hydrateproteinlipid) specifies the joules ofheat produced from the oxidation of a moleof oxygen (Schmidt-Nielsen 1979) Theoxygen extraction efficiency of the respi-ratory system and the properties of air de-termine how many moles of air are neededper unit time by the respiratory system Theamount of carbon dioxide added to the re-spiratory system air is calculated from therespiratory quotient RQ which is the ratioof moles of carbon dioxide produced permole of oxygen consumed (Schmidt-Niel-sen 1979)

The RQ changes with different substratesoxidized The respiration model uses theRQ for carbohydrates proteins or lipids ora combination of the three to calculate theamount of carbon dioxide that flows out ofthe respiratory surfaces The user-specifiedproportions of carbohydrate protein andlipid in the food consumed thus ultimatelydetermine the RQ Thus the metabolic ox-ygen demand to maintain core temperatureand the current properties of air specify thevolume of airflow and the amount of wateradded to saturate the respiratory system airAt expiration the user specified tempera-ture difference between the air in contactwith nasal surfaces as air exits at surface 2and the free stream external air (1ndash38C) isused to calculate the amount of water re-covered by condensation on the nasal sur-faces The calculated skin temperature ofthe body would not be relevant for esti-mating nasal air temperature at exit becauseof the different convective environment in-side the nares vs the outer skin coveredwith fur or feathers Since we were tryingto estimate maximum recovery rates as anupper bound we used experimental datasummarized from the literature (Welch1980) for the calculations and used a 38C


difference between exit air temperature andlocal external (free stream) air temperature

Temperature regulation model Anotherimportant addition to the model was tem-perature regulation responses Sensitivityanalyses of the model done by increasingair and radiation temperatures revealed thatthe calculated skin temperature which is afunction of the specified core temperaturemust not exceed core temperature If it doesexceed the core temperature metabolic heatproduction must be dissipated by evapora-tion of respiratory water to achieve steadystate The molar balance model for thelungs just described clearly showed a lim-ited capacity for heat dissipation by watervaporization in the lungs which is consis-tent with experimental data (Welch and Tra-cy 1977 Welch 1980) A user specifiedminimum corendashskin temperature differencewas added to the model The value used inour calculations was 058C If an iterativesolution for heat generation given the spec-ified core temperature produced a skin tem-perature less than the minimum corendashskindifference a three-level hierarchy of phys-iological responses was invoked

First flesh thermal conductivity increas-es to the maximum value measured in theliterature That was never sufficient to in-crease the core-skin temperature gradientsince it only serves to increase skin tem-perature

Second the percentage of the skin sur-face assumed covered with tiny water dropsincreases up to 100 percent of the skin sur-face area to cool the skin The amount ofcooling is constrained by air temperaturewind speed relative humidity and theboundary layer thickness at the skin Thelatter is a function of body characteristic di-mension insulation properties and windproperties defined in Nusselt and Reynoldsnumbers (Bird et al 1960) The Nusseltnumber is simply a nondimensional ratio ofthe heat transfer coefficient times a char-acteristic dimension (often defined as thedistance a fluid such as air travels whenpassing over the object of interest) dividedby the thermal conductivity of the fluidThe Reynolds number is also a nondimen-sional ratio It is the product of the fluid

density velocity and the characteristic di-mension divided by the dynamic viscosityof the fluid The Nusselt number is oftenplotted against the Reynolds number Theregression of the data plotted is a relation-ship that allows for the calculation of theheat transfer coefficient (used to calculateconvective heat loss) for any value of Reyn-olds numbers variables such as changingcharacteristic dimension (body size)

Third failing all else the core tempera-ture is allowed to rise in 018C incrementsuntil a stable solution of the equation isfound that allows a 058C temperature dif-ference between core and skin This ap-proach causes a rise in metabolic rate athigh temperatures that is observed experi-mentally (Schmidt-Nielsen 1979) It alsomimics the rise in core temperature that isobserved experimentally (Schmidt-Nielsen1979) No regressions are needed to emu-late the experimental data

The gut Figure 4 also shows the systemdiagram for the molar balance gut modelIt is related to the well-known batch reactorand plug flow model originally developedin chemical engineering and subsequentlyapplied to animal digestive systems (Penryand Jumars 1987) The model used hereallows for any type of ingested food con-sisting of user specified proportions of car-bohydrates lipids proteins and water con-tent The food can enter the gut any timeduring activity time in any amount subjectto the constraint that the volume of foodingested per day may not exceed the wetmass of the animal The energy value ofabsorbed carbohydrates lipids and proteinsis well known (Schmidt-Nielsen 1979)Details of the model are in the Appendix

Temperature dependent feeding Figure 5shows how these animal models respond todifferent temperatures The metabolic rateof an endotherm changes with increasingenvironmental temperature in a distorted U-shaped curve (Bucher et al 1986 Kleiber1975 Morris and Kendeigh 1981Schmidt-Nielsen 1979 Scholander 1940)It is commonly assumed from a physiolog-ical perspective that the capacity to absorbfood is independent of environmental tem-perature because of the relatively constant


FIG 5 A qualitative comparison between intake and expenditure of mass and energy as a function of envi-ronmental temperature for ectotherms and endotherms In ectotherms mass absorbed depends upon temperaturedependent digestion physiology which typically ceases at temperatures below 15ndash208C Discretionary energyuptake (fitness measure) is a function of environmental temperature because of temperature dependent foragingbehavior digestive physiology and temperature dependent metabolic expenditure In endotherms mass absorbedwould be independent of temperature from the perspective of digestive physiology if core temperature remainsconstant However temperature dependent foraging behavior at temperature extremes (dashed line) reduces foodintake at temperature extremes thereby creating an elliptically shaped region of discretionary mass whose valueis temperature dependent The optimum temperature for maximum discretionary mass decreases with increasingbody size (see Fig 13 below)

body temperatures that endotherms usuallymaintain This is in contrast to the temper-ature dependent digestion of ectotherms(Waldschmidt et al 1987)

However the temperature dependent for-aging behavior and appetite levels of en-dotherms are frequently ignored althoughthey have been considered with respect todomestic animals (Kleiber 1975) Recentseed tray experiments under natural forag-ing conditions show that desert rodents areextremely sensitive to substrate tempera-tures that affect willingness to forage(Mitchell et al ms) and similar resultshave been reported for free ranging rac-coons (Berris 1998) Predation risk andcompetition also influence foraging costsBirds and mammals may compete for the

same resource (Brown et al 1997) Pre-dation risk and competition can be ex-pressed in terms of energetic cost (Brownet al 1994)

Thus the difference between temperaturedependent foraging (mass and chemical en-ergy intake) and temperature dependentmetabolic costs (mass and chemical energyexpenditure) yields temperature dependentdiscretionary mass and energy intake Dis-cretionary mass and energy intake is theoval area in Figure 5 bordered by intakeand expenditure rates Climate and type offood available are important constraints onfitness that can now be calculated from ba-sic principles As we shall soon see bodysize and diet are additional important con-straints on fitness in different climates


FIG 6 A comparison of density profiles as a functionof distance from the skin for fur (A) and plumage (B)

Porous insulation

Fur vs feathers Figure 6 shows sche-matically the difference between fur andplumage density as a function of distanceabove the skin The densities of hair ele-ments are greatest near the skin The den-sity of feather elements in contrast is low-est near the skin and greatest at the featherndashair interface The consequence of this dif-ference in density profiles is that air canpenetrate at least the outer parts of fur moreeasily Feathers however seal off the plum-agendashair interface creating a conductionndashra-diation environment that is easier to ana-lyze

This is true irrespective of whether thefur or plumage elements are normal to theskin or at an angle relative to the skinChanging angle relative to the skin modifiesdensity profiles for either type of porous in-sulation but does not change the generalshape of the density profile with depth Inreality parts of the skin of birds do haveplumaceous elements near the skin Individ-ual plumages will vary between taxa andbetween different locations on the bodyThe density will also vary with degree ofelevation of contour feathers degree ofdensity at the same level of the rachisvanejunction and the presence and density ofdown feathers However vertical serial sec-tions of crow feathers embedded in plasticunder vacuum have shown that the greatest

density of elements is at the plumagendashairinterface (Porter unpublished data)

Fortunately in low wind environmentschanges in individual element density withheight do not have a significant impact onporous insulation heat loss unless the fi-brous elements are either very sparse or ex-tremely dense across a wide range of bodysizes (Fig 25 in Porter et al 1994) Atvery low individual element density theporous insulation becomes very open al-lowing substantial convective and radiantheat transfer from the skin In contrast atvery high individual element density theeffective thermal conductivity of the porousinsulation approaches that of keratin ratherthan air This amounts to an increase inthermal conductivity by a factor of abouteight thus increasing heat loss Sensitivityof heat loss due to density changes withdepth in fur in a conduction-radiation heatexchange is very small (Kowalski 1978McClure and Porter 1983) Kowalski useda measured density of fur as a function ofdepth for cow fur which is described by ahyperbolic tangent function (Fig 6)

If fur density has an optical thickness(Porter et al 1994) less than 0001 the furis so sparse that it is assumed to be trans-parent to infrared radiation and conductionheat transfer along the fibers is negligibleUnder these conditions the model assumesthe functional equivalent of bare skin Forexample a user of the model can explorethe consequences of changing insulation orremoving insulation merely by altering theinput data file the depth and density of furor plumage If it is set to zero or very lowdensity the program automatically checksto be sure that a porous model is appropri-ate and changes to a bare skin model ifnecessary

Finite elements and flow through the furModerate and high wind environments canforce penetration of air through fur Thusit was important to develop a basic princi-ples model that would permit calculation ofvelocity and temperature profiles in a po-rous medium with nonlinear coordinates ona round body Integration of the profiles al-lows for calculations of heat energy andmass transfer from basic principles a taskfirst accomplished only recently (Stewart et


FIG 7 A finite element model in cylindrical coordi-nates The grid lines define curvilinear cells for si-multaneous solutions of equations used in calculatingmass and energy transport in the fur

FIG 8 Diagram of the geometries used to model alarge standing bird (cylinders and ellipsoid) comparedto a sitting bird (ellipsoid)

al 1993 Budaraju et al 1994 1997) Wewill briefly review the basic features of thissophisticated model

Figure 7 shows the finite element modelin cylindrical (radial and angular) coordi-nates from an end view These curvilinearboxes are used to compute the mass andheat flows in the radial and angular direc-tions relative to the skin and to the directionof incoming air for variable densities ofkeratin elements projecting from the skin ofan endotherm This concept is also appro-priate for birds under conditions where airpenetrates the feathers Examples includeresting birds with fluffed feathers or flight-less birds like kiwis whose plumagestrongly resembles mammalian fur In prin-ciple this model would also be useful forthe pulsing (changing angular orientationrelative to the skin) feather conditions ofactive bird flight

Appendages Figure 8 shows an append-age model for birds developed for threelarge ratites the rhea Rhea americana thecassowary Casuarius casuarius and theostrich Struthio camelus These appendag-es are largely bare and constitute a signifi-cant percentage of the surface area of thestanding bird Appendage dimensions weremeasured relative to torso dimensions usingphotographs of the birds of known heightand weight from the side and the front Wemeasured only the exposed areas of ap-

pendages The portions of the legs coveredby torso feathers were assumed to be partof the volume of the torso for heat transfercalculations

The same cross-section model shown inFigure 2 but without porous insulation andrespiratory water loss was used to calculateheat loss in the radial dimension from theseappendages Heat loss from the bottom ofthe appendages in contact with the groundwas assumed to be negligible Total calcu-lated heat loss was the sum computed fromthe torso plus the heat losses from the ap-pendages

The regression equations that were fittedto the appendage dimensions areas andvolumes are listed in the Appendix The ap-pendage dimensions were computed fromregressions based on body weight Append-age volumes were then computed addedand the total subtracted from the total vol-ume of the bird based upon its weight Thedifference was the torso volume The torsolength width and height were calculatedfrom the dimension ratios of the feathered


FIG 9 Profiles of body temperature and insulationtemperature The left side which is shaded has a log-arithmic profile in the porous insulation The right sidewhich is exposed to sunlight absorbs solar radiationin the fur and has a parabolic temperature profile in-dicating heat absorption within the layer as well asheat transport within the layer

torso The calculated torso dimensions thenwere used to compute the effective torsoskin area and plumage depths Plumagedepths agreed well with the few data avail-able

RESULTS

Modeling an individual

Internal body temperature profiles Fig-ure 9 demonstrates the temperature profilefrom core to skin to the insulationndashair in-terface The temperature profiles in the po-rous insulation (left side) represent no ab-sorbed solar radiation vs (right side) ab-sorbed solar radiation When sunlight is ab-sorbed by a porous insulation it will act asa distributed heat source in the medium (Rs

2 Rf) The color of the insulation and itstransparency affect the depth over whichthe radiation is absorbed The temperatureprofile from center to skin (0 ndash Rs) is par-abolic in a slab cylinder sphere or ellipsoidwith uniform heat generation per unit vol-ume (Porter et al 1994 Appendix equa-tions 1ndash3) The temperature difference from

core to skin is equal to the heat generationper unit volume multiplied by the radiussquared divided by the product of a geom-etry constant and the thermal conductivityThe value of the geometry constant may be2 4 or 6 depending on whether the ge-ometry is a slabellipsoid a cylinder or asphere (Bird et al 1960 Porter et al1994)

The calculation of distributed respiratorywater loss had to take this parabolic tem-perature profile into account The averagetemperature for a nonlinear profile can becalculated easily using an integration pro-cedure (Bird et al 1960 p 270) The vol-ume average temperature was used as theaverage lung temperature for the purpose ofcalculating saturation vapor pressure Theamount of water lost in respiration wasequal to the water added internally to sat-urate the air in the lungs at average tem-perature less the water recovered at satura-tion at the exit temperature at surface 2 inFigure 4

The insulation The flow of air throughfur or plumage is influenced by the diam-eter and density of the fibrous elements theair encounters as well as the pressure gen-erated in the flow field around the animalWe illustrate the combined effect of thesevariables on flow through fur in a red deer(Cervus elaphus elaphus) in Figure 10a band c modified from Budaraju et al (1997)Red deer fur is well characterized (Steudelet al 1994)

Flow at very low wind Figure 10a showscalculated flow through the fur of red deerat 001 msec using the finite element model(Budaraju et al 1997) The streamlinesshown are trajectories of airflow throughthe fur layer Free convection is the domi-nant airflow pattern Nearly still air in thevicinity of the animal enters at the bottom(ventral surface) flows along the sides ofthe animal and exits at the top (dorsal sur-face) The velocity is greatest near the skinalong the sides of the animal and least nearthe ventral and dorsal surfaces

Flow at 05 and 3 msec Figure 10b andc show calculated flow through the fur ofred deer in a 05 and 3 msec wind usingthe finite element model (Budaraju et al1997) Now the wind is assumed to be


FIG 10 Streamlines showing simulated air flow through red deer (elk) fur at 001 ms external wind speed(a) Streamlines showing simulated air flow through red deer fur at 05 and 30 ms wind speed (b) and (c)

FIG 11 A comparison of measured vs calculatedmetabolic heat production for animals ranging in sizefrom mice to elephants The diamonds represent theempirical data collected at a body temperature of 368Cand an air temperature of 288C An ellipsoid model isassumed for an animal lying down At this low (met-abolic chamber) wind speed and humidity the presenceor absence of fur makes little difference in the meta-bolic cost

blowing horizontally from left to right Thelong axis of the body is assumed to be nor-mal to the direction of wind flow Thestreamlines diverge on the windward sideenter the fur and then move toward the dor-sal and ventral parts of the animal Air re-circulates near the top and bottom becauseof pressure differences that are a conse-quence of the geometry and the propertiesof air A recirculating eddy then enters thefur moving toward the leeward side of theanimal and finally exits the fur

We might expect similar types of airmovement if birds fluffed their feathers at

rest in a moderately strong wind where aircould enter the plumage from the windwardside However birds typically only flufftheir feathers in very low wind environ-ments Figure 10a suggests that extendingthe insulation further laterally and normalto the flow might slow free convectionaround the body

Scaling across mammal body sizes

Mouse to elephant metabolic rate Skintemperature is a consequence of the solu-tion of heat flux equation (the correct guessof heat generation to maintain core temper-ature) from the core to the skin It is si-multaneously the basis for heat exchangefrom the skin through the porous insulationto the environment The total heat genera-tion must satisfy the coupled body and in-sulation equations whose boundary condi-tions are core temperature and environmen-tal conditions

Figure 11 shows these heat generationcalculations assuming an ellipsoid geome-try for animals ranging in size from miceto elephants The line with filled circles as-sumes a bare skin Alternatively if we putdeer mouse (Peromyscus maniculatus) furon all body sizes instead we get the linewith open circles on it The free-floating di-amonds represent the empirical data

An appendage model was also developedfor mammals using the same principles asjust described for birds However the torsohead and neck were assumed to be cylin-drical in shape with an elliptical cross sec-tion The ratio of the elliptical cross-section


FIG 12 Calculated metabolic rates vs body massand environmental temperature for animals ranging insize from mice to elephants The 288C line representsthe Benedictrsquos experimental environment used to col-lect the empirical data The low and high temperaturecalculations indicate that metabolic scaling with bodysize is dependent on environmental temperature The408C curve approaches the 08C curve at small bodymasses because heat stress is forcing the metabolic rateto high levels No empirical regressions are used inthese calculations other than appendage morphology asa function of body mass

based on photographic measurements of el-ephants and cattle was 127 for the ratio ofheight to width of the torso The appendagemodel was not used for animals smallerthan 100 kg

It is particularly interesting to note thatfor the standing mammal model using nofur vs fur of red deer (a form of elk) thereis no observable difference in metabolicrate from 100 kg to 3833 kg This is rea-sonable since the low wind speed used herewould probably not disrupt the substantialboundary layer of these large mammalsFur would be of little help at this low windspeed in an environment where the air andradiant temperatures are assumed to be thesame

It is important to note that the experi-mental data in the literature used to test thismodel were all collected in a metabolicchamber at an air and radiant temperatureof 288C and a core temperature of 368CBenedict measured the core temperature ofall of his animals in his classic publication(Benedict 1938) A sensitivity analysis ofthe conductionndashradiation fur model showsthat core air and radiant temperatures arethe most sensitive of all variables affectingheat loss from an animal with porous in-sulation (McClure and Porter 1983)

Figure 12 illustrates the impact of chang-ing air temperature on the mouse to ele-phant curve The frame of reference is theexperimental data shown as free-floating di-amonds A simulation for 288C is thedashed line with open circles Metabolicrates at a lower temperature of 2258C andan upper temperature of 408C are also cal-culated The increase in metabolism atsmall body size for 408C air temperature ispart of a consequence of the thermoregu-latory model used in these calculations Itis an emergent property of the model

It is also important to realize that the pos-tures of Benedictrsquos animals were largely un-known In fact posture is rarely monitoredin metabolic rate measurements Metaboliccosts can vary considerably due to simplechanges in posture (Porter et al 1994) El-lipsoid geometry is the best intermediateapproximation for estimating metaboliccosts in mammals (Porter et al 1994)

The term lsquolsquothermal conductancersquorsquo is an

amalgam of all the variables associated withspecific morphological physiological andclimate variables Those state variableshave been explicitly defined in an appendix(Porter et al 1994) where the detailedequations for the model reside The meta-bolic heat lost by an animal is a conse-quence of (1) body morphology and insu-lation properties (2) core temperature andthermal conductivity of body tissues and(3) environmental conditions such as airtemperature sky radiant temperatureground radiant temperature and windspeed Solar radiation and relative humid-ity were not explicitly included in the ear-lier endotherm model (Porter et al 1994)but they are added in the present model

Figure 12 demonstrates the limitations ofthe regression assumptions in the standardmouse to elephant metabolism regressionline when applied to natural environmentsThe slope and intercept of the mouse to el-ephant curve changes with airradiant tem-perature and body size

Mouse to elephant discretionary energyuptake Figure 13a and b show explicitlythe calculated discretionary energy uptakefor mammals of different sizes represented


FIG 13 A topographic view of the log of discretionary energy uptake (Jday) as a function of log of bodymass and environmental temperature Air and radiant temperatures are assumed equal There is a lsquolsquoridgersquorsquo ofmaximum discretionary energy (fitness measure) that is irregular in elevation as it curves upward and to the leftin Figure 13b from its starting point at about 288C where the body size is 001 kg As body size increases theoptimal environmental temperature that maximizes discretionary energy for body size decreases The discre-tionary energy maximum traces a jagged ridge with peaks and valleys going to lower and lower temperaturesThis result occurs because of differences in the temperature at the lowest metabolic rate for animals of differentsizes and the maximum limit on gut mass flow per day at each body size The temperature associated withmaximum distance between those two curves changes with body size

Figure 13a and b were calculated assuming a diet of seeds for all body sizes The proportions of carbohydratefats and protein in the dry matter are similar to those of alfalfa hay and grass hay forage (see Appendix) Whenthe diet is assumed to be alfalfa hay (reference number 100056 USndashCanadian nutrient composition tables1994) with the same digestive efficiency of 57 as for seeds Figure 13c shows a similar optimal body sizelandscape but the lsquolsquoridgersquorsquo is shifted to larger body size for the same temperature The magnitude of the lsquolsquopeaksrsquorsquois much reduced The landscape is also much flatter The body size where the animal is in negative mass balanceis much larger for the same temperature

Figure 13d shows the landscape for an assumed diet of grass hay (reference number 102250 USndashCanadiannutrient composition tables 1994) for mice to elephants The digestive efficiency is 61 to reflect the overalldigestive ability of ruminants This makes for slightly higher peaks but the same general landscape The changein digestive efficiency more than compensates for the change in quality of diet Thus when examining all threecontour plots the higher the quality of diet the smaller the optimal body size at any given temperature


Figure 13e compares four different sizes of mammals all assumed to be consuming seeds as their diet The10 g mammal has a net throughput capacity that matches metabolic cost slightly below 08C Temperatures lowerthan this we calculated will cause the animal to be in negative mass balance without an insulating nest or changein posture (Porter et al 1994) A 30 g mammal has the same intersection at approximately 2188C A onekilogram mammal has a body size large enough to assure adequate gut mass flow until approximately 2408Cassuming deer mouse fur and appendages that are extended If a 4000 kg mammal were able to process seedsof the same nutritional properties as the smaller mammals it would have sufficient gut throughput to allow itto have no mass flow constraints even with only deer mouse fur at this very low wind speed of 01 ms

qualitatively in Figure 5 Selection for max-imum discretionary energy uptake repre-sents selection for growth and reproductionpotential key elements of fitness The threedimensional and the contour map of bodysize and temperature effects on discretion-ary energy uptake assume no food limita-tion The animals are simply allowed to filltheir gut digest and absorb the food Attemperatures where sweating must be ini-tiated to cool the animal it is assumed thatanimals no longer forage These figures arean upper estimate of discretionary mass in-take as a function of body size Air tem-perature is assumed to be the same as theradiant temperature of the sky and groundThus this set of calculations representsmetabolic chamber environments The ef-fects of changing wind sunlight and hu-midity are not included in these figures

A very interesting feature of the three di-mensional and contour surfaces is the sug-gestion of discontinuous optimal body sizesin nature where temperature varies in timeand space There is a lsquolsquoridgersquorsquo of maximumdiscretionary energy (fitness) that is irreg-ular in elevation as it curves upward and tothe left in Figure 13b from its starting pointat about 288C where the body size is 001kg body size As body size increases theoptimal environmental temperature thatmaximizes discretionary energy for bodysize decreases The discretionary energymaximum traces a jagged ridge with peaksand valleys going to lower and lower tem-peratures This result occurs because of dif-ferences in the temperature at the lowestmetabolic rate for animals of different sizesand the maximum limit on gut mass flowper day at each body size The temperature


associated with maximum distance betweenthose two curves changes with body sizeThus the greater payoff in discretionary en-ergy (fitness) at some temperaturebody sizecombinations relative to others of lowervalue at nearby temperatures suggests thereshould be a selection for the size that hasthe highest value in the neighborhood of asmall temperature range This would createone or more lsquolsquogapsrsquorsquo in the distribution ofanimal sizes in nature The largest gapshown here is between 25 and 08C and abody size of approximately 100 kg

Diet effects on optimal body size Figure13a and b were calculated assuming a dietof seeds for all body sizes The proportionsof carbohydrate fats and protein in the drymatter are similar to those of alfalfa hay andgrass hay forage (see Appendix) Howeverthe water content is very different Whenthe diet is assumed to be alfalfa hay (ref-erence number 100056 USndashCanadian nu-trient composition tables 1994) with thesame digestive efficiency of 57 as forseeds Figure 13c shows a similar optimalbody size landscape but the lsquolsquoridgersquorsquo isshifted to larger body size for the same tem-perature The magnitude of the lsquolsquopeaksrsquorsquo ismuch reduced The landscape is also muchflatter The body size where the animal isin negative mass balance is much larger forthe same temperature

Figure 13d shows the landscape for anassumed diet of grass hay (reference num-ber 102250 USndashCanadian nutrient com-position tables 1994) for all animals rang-ing in size from mice to elephants The di-gestive efficiency is 61 to reflect theoverall digestive ability of ruminants Thismakes for slightly higher peaks but thesame general landscape The change in di-gestive efficiency more than compensatesfor the change in quality of diet Thuswhen examining all three contour plots thehigher the quality of diet the smaller theoptimal body size at any given temperature

Figure 13e compares four different sizesof mammals all assumed to be consumingseeds as their diet The ten gram mammalhas a net throughput capacity that matchesmetabolic cost slightly below 08C Temper-atures lower than this we calculated willcause the animal to be in negative mass bal-

ance without an insulating nest or changein posture (Porter et al 1994) A 30 gmammal has the same intersection at ap-proximately 2188C A1 kg mammal has abody size large enough to assure adequategut mass flow until approximately 2408Cassuming deer mouse fur and appendagesthat are extended If a 4000 kg mammalwere able to process seeds of the same nu-tritional properties as the smaller mammalsit would have sufficient gut throughput toallow it to have no mass flow constraintseven with only deer mouse fur at this verylow wind speed of 01 msec A quick ex-amination of the maximum distance be-tween the two curves of the four sizes ofanimals shows different temperature optimawhere maximum discretionary energy isavailable assuming unlimited seeds As wesaw from Figure 13c and d a change in dietfrom seeds to green forage shifts the opti-mum body size at any given temperature tohigher values These results ignore co-prophagy and other subtle but significantmodifications of digestive systems None-theless it provides some useful guidelinesfor identifying future modifications of thegut model and provides some understand-ing of multiple constraints on optimal bodysize of animals

Bergmannrsquos Rule These results are rem-iniscent of Bergmannrsquos rule an empiricalobservation that as climates get colder an-imal sizes tend to get larger Body size in-creases with decreasing temperature pro-vide the greatest advantage at small size(Steudel et al 1994) At larger body sizeschanges in fur insulation confer a greateradvantage Steudel et al 1994) Experimen-tal data from different types of fur on a flatplate (Scholander et al 1950) suggestedthis but animals of larger size also havethicker boundary layers A thicker bound-ary layer reduces convective heat loss andsimultaneously enhances radiation temper-ature effects (Porter and Gates 1969)Larger animals are taller which means ex-posure to greater wind speeds higher abovethe ground Higher wind speed reducesboundary layer thickness and may engendergreater wind penetration of the fur A firstprinciples fur model can separate boundarylayer effects due to size and wind from fur


FIG 14 The calculated effect of posture on meta-bolic rate in birds (solid vs dashed line) The birdsrange in size from hummingbirds to ostriches Opentriangles attached to lines represent the calculated val-ues for large standing birds The calculated values forsitting birds are represented by the closed triangles onthe solid lines The empirical data (summarized inSchmidt-Nielsen 1979) are free floating filled circlesEnvironmental temperatures used to obtain these em-pirical data were approximately 25ndash308C

properties effects and provide better esti-mates of combined effects

Assessment of consequences of Berg-mannrsquos rule have pointed out that larger an-imals have the advantage of longer fastingability under conditions of climate or foodavailability stress (Morrison 1960) How-ever smaller animals have the advantage oflowering body temperature and seekingmuch more favorable microclimates espe-cially underground habits in severe coldCareful transient modeling analyses ofthese two strategies in the animalsrsquo micro-climates would yield a testable hypothesisof the relative benefits of these different so-lutions to the same problem of dealing withcold

Of course survival in extreme tempera-ture events is also important in affectingcommunity structure However extremetemperature survival may be overrated interms of its effects on community structureat least for mammals Temperature depen-dent behavior and selection of microhabi-tats by both small and large animals cangreatly reduce cold or heat stress For ex-ample moving under or into trees and mod-ifying the solar and infrared radiation andwind protection they provide can changeequivalent local microenvironment temper-atures by 208C or more Underground bur-rows or tunneling beneath the snow canprovide habitats that typically do not dropbelow 08C in winter when an animal is pre-sent due to local heat from metabolismPhotoperiod-induced temperature depen-dent physiology such as hibernation or es-tivation is another way that mammals canpersist in habitats during periods of extremeheat or cold stress and thereby maintaincommunity structure Birds typically opt tomigrate from extremely cold habitats inwinter that they occupy in the summer Byexercising temperature dependent behavior-al selection of microclimates through mi-gration the scale of their selection move-ments is simply larger due to the short timeand lower costs of long distance bird trans-port

Scaling across bird body size

Hummingbird to ostrich metabolic ratemdashAppendage effect Figure 14 shows the im-

pact of appendages on heat loss in largebirds by comparing data on bird metabo-lism with calculations of bird metabolismusing two different models The filled cir-cles represent bird metabolism vs body sizein the absence of sunlight (Schmidt-Niel-sen 1979) The sitting bird model calcula-tions use an ellipsoid approximation for abird with legs and head tucked into thefeathers The standing bird model repre-sents the torso as an ellipsoid and the ap-pendages as cylinders with diameters aver-aged over the appendage length The solidline marked with solid triangles is the sit-ting bird model We assumed an air tem-perature and radiant temperature of 308CThe dashed line with open triangles repre-sents the standing bird model calculationsonly for the ratite birds rheas cassowariesand ostriches All smaller birds are assumedto be sitting We assume that the birds aremaintaining a core temperature of 398C atthe center of the torso and at the centers ofthe appendages

Hummingbird to ostrich metabolicratesmdashAir temperature effect Figure 15demonstrates the effect of air temperatureon metabolic rates as a function of bird


FIG 15 The calculated effect of temperature differ-ences on metabolic rate for birds ranging in size fromhummingbirds to ostriches The 408C curve approach-es the 08C curve at small body masses because heatstress is forcing the metabolic rate to high levels Noempirical regressions are used in these calculationsother than appendage morphology as a function ofbody mass

rarr

FIG 16 Calculated optimal mammal body size that maximizes discretionary energy uptake as a function ofglobal temperatures in January and in July No food limitation or variation in food type is assumed Theseresults suggest that climate variations in time and space place important constraints on the functional types ofanimals that can coexist as communities

body size As in Figure 14 we assumed thatair and radiant temperatures are the sameand there is no significant sunlight The cal-culations at 08 258 and 408C assume thatlarge birds (mass 10 kg or greater) arestanding up At 408C small birds are pre-dicted to have high metabolic rates becausethey would be in heat stress

Global communities-climatic constraints

Figure 16 shows temporal and spatialvariation in optimal body size based on dis-cretionary massenergy for mammals forthe months of January and July on a globalscale In January (winter) in the NorthernHemisphere the optimal sizes are larger asone moves north Large topographic fea-tures such as the Rocky Mountains arealso predicted to have larger animals withtheir optima In the Southern Hemispherewhere it is summer topographic features donot stand out as strongly

In July (winter) in the Southern Hemi-sphere there is somewhat of a lsquolsquomirror im-agersquorsquo effect on optimal body size However

different topographic and latitudinal fea-tures create somewhat different patterns Ingeneral though the model suggests thatlarger animals have the advantage In theNorthern Hemisphere at the same timesmaller animals should have the advantageLarge topographic features like the Tibetanplateau with its cool weather in summerstill show up fairly clearly as affecting op-timal body size For clarity variation invegetation type and food quality were notincluded in these graphs

The criteria for optimization were maxi-mum discretionary energy uptake for a giv-en temperature at all possible body sizesThis figure was generated from the endo-therm model driven by global weather dataat half-degree intervals in latitude and lon-gitude

The map of optimal body size is differentat different seasons of the year This sug-gests that climate places important con-straints on what functional types can co-exist in a locality Because the environmentis constantly changing it creates a constant-ly changing optimal body size in any lo-cality Changing environments create theopportunity for multiple functional types tocoexist in the same area

What is unknown at present is over whattime intervals does natural selection inte-grate time and environmental conditions tolsquolsquochoosersquorsquo body size Figure 16 representsthe beginnings of the effort to understandclimatic constraints on community structurefrom basic principles The vegetation on thelandscape is certainly a very important var-iable that will modify the current version ofthe model The spatial and temporal distri-bution of available food places importantadditional constraints on optimal body sizeThese constraints include encounter proba-bilities handling time food energy valueand metabolic cost to get to the food Threeof these variables are related to body sizeand the lsquolsquopackagingrsquorsquo and lsquolsquodistributionrsquorsquo of



FIG 17 The rare and endangered Orange-bellied Par-rot of Australia and Tasmania

food on the landscape It is clear that thisconstruct can also be applied to species ofbirds to study migratory patterns and otheraspects of bird ecology

It is important to note as one reviewerdid that lsquolsquoevolution may select less for op-tima under average daily climate cycles andmore for adaptations that increase survivor-ship during winnowing events At any giv-en time a population may consist of indi-viduals with below or above optimal bodysizes should recent history include highmortality linked to extreme climate withavailability or predationrsquorsquo These importantconsiderations have not been added to thesemodels yet

Conservation applicationThe Orange-bellied ParrotNeophema chrysogaster

The Orange-bellied Parrot (Fig 17) hasonly approximately 200 individuals stillalive It breeds in Tasmania After theyoung have fledged the parents fly north forthe winter to the southern coast of Austra-lia The young follow shortly thereafter(Hutchins and Lovell 1982 Loyn et al1986) There is nothing known about theirmetabolic rates and little about their phys-

iology although it is now known that coretemperature is maintained at about 4118C(P Menkhorst personal communication)There are important energetic questions thatmay pertain to the speciesrsquo survival It ap-pears that survival during the winter seasonis more important than their reproductivesuccess in summer (Drechsler et al 1998)Food supplies in nature particularly SeaRocket appeared to have dwindled butthey have shifted somewhat to other plantsNumbers of individuals in the last few yearsseem to have stabilized (P Menkhorst per-sonal communication) The causes of theOrange-bellied Parrotrsquos decline remain anenigma If there were reliable estimates ofmetabolic cost estimates of necessary for-aging time and amount of food required tosustain it in its seasonal habitats could bemade This could lead to quantitative esti-mates of the amount of habitat needed toassure its survival especially in what ap-pear to be its critical northern winteringhabitat

Ontogeny of metabolic costs We areaware of only two papers in the literatureon parrot metabolism (Bucher 1983 Buch-er and Morgan 1989) Bucherrsquos metabolicchamber data can be used to test the birdmodel for metabolic chamber conditionsFigure 18 shows that the model can closelyapproximate experimental data on an Afri-can parrot Agapornis roseicollis thepeach-faced lovebird of similar weight anddimensions as the Orange-bellied ParrotWe can calculate parrot metabolism acrossthe experimental temperature range that thebird experienced This allows us to havemore confidence when extending the modelto field conditions to estimate its energy userequirements in its native habitat We cal-culated metabolic rate up to airradiant tem-peratures of 408C even though experimen-tal measurements only go to 358C

Calculations for low air temperaturesagree best when a spherical posture is as-sumed a lower 4118C core temperature isused as was measured (Bucher 1983 Buch-er and Morgan 1989) and the feathers aresomewhat fluffed (07 cm) At higher airtemperatures an ellipsoid approximationwith slightly higher core temperature(4148C) and normal plumage depth (04


FIG 18 Comparison of bird model calculations vsmeasured metabolic rates for a 48 g African parrotAgapornis roseicollis the peach-faced lovebird Ex-perimental data covered the temperature range from2258C through 358C (Bucher and Morgan 1989) Themodel calculations explore changes in posture (ellip-soid vs sphere) Observed range of variation in coretemperature was 4118ndash4198C (Bucher and Morgan1989) Feather lengths of normal plumage we mea-sured from UW Zoology Museum specimens rangedfrom 10ndash15 cm Depth of plumage was typically 04cm We assumed fluffing of feathers would changefeather depth from 04 to 07 Calculated results agreewith data best if the birds in the cold are placing theirhead under their wing and fluffing their feathers to 07cm depth At higher temperatures calculations agreewith data best when postures approximate an ellipsoidthere is a slightly higher core temperature and thefeathers are not fluffed An ellipsoid model calculationassuming a core temperature of 4198C (measured byBucher and Morgan [1989] at 308 and 358C) was donetoo but the results were nearly identical to the ellip-soid model with a core temperature of 4148C and aplumage depth of 04 cm

FIG 19 Current estimates of metabolic rate throughthe ontogeny of the Orange-bellied Parrot with an ob-served core temperature of 4118C (P Menkhorst per-sonal communication) for airradiant temperaturesranging from 08C to 408C

cm) agree best with the experimental dataIt would seem that plumage depth clearlyhas a greater impact than either posturalchange or core temperature change for abird this size in a low wind speed environ-ment lacking sunlight

Figure 19 shows our current estimates formetabolic rate as a function of the ontogenyof the Orange-bellied Parrot These meta-bolic chamber simulations use current esti-mates of insulation thickness of the downand feathers of the birds The results indi-cate that temperatures lower than 58Cwould be a challenge for hatchling birdsTemperatures below 208C at weights of 20ndash40 g impose significant additional metabol-

ic costs on young birds This might be re-flected in reduced potential for growth atthese lower temperatures Minor modifica-tions in the gut model that include reason-able estimates of the range of foodstuffs in-gested can be used to estimate growth andreproductive potential as the birds growThat is the next step in our research onthese birds

DISCUSSION

Surrogates for size in modeling metabo-lism Body weight is a surrogate for bodyradius Posture is a surrogate for body ge-ometry Empirical metabolism data collect-ed since the time of Benedict in the 1930shave related metabolic heat production tobody mass However mass is only one ofthe variables that drive metabolic heat pro-duction A key variable is the radius of thetrunk of the animal which is in turn a func-tion of the posture Most of the analyses ofmetabolic scaling in the literature that weknow ignore this important aspect Further-more the role of a variety of environmentalvariables and different types of porous in-sulation in modifying metabolic demandhave not been predictable because of thelack of reliable quantitative models

However our new animal models and themicroclimate model that links them to mac-


roclimate data have changed the outlook forunderstanding the quantitative relationshipsof these variables Fortunately there havebeen some careful experiments on endo-therm heat loss in wind tunnels with solarradiation They make it possible to testthese models in much more realistic settingsthan metabolic chambers (Bakken 1991Bakken and Lee 1992 Bakken et al 1991Hayes and Gessaman 1980 1982 Rogow-itz and Gessaman 1990 Walsberg 1988ab c Walsberg and Wolf 1995)

Climatebody size effects on biodiversityBody size affects discretionary mass andenergy intake Growth and reproduction po-tential affects fitness As Figures 11 through15 demonstrate body size has importantimpacts through geometric form and radialdimensions on energy expenditure and in-take The surrogate for these primary vari-ables is body weight (mass) We have point-ed out here how air and radiant temperatureand posture can make important modifica-tions in energy cost in different environ-ments These energy costs are not linearwith body size Heat transfer mechanismsare not all linear with body size and neitherare temperature regulation responses Scal-ing of the gut is not linear with body sizeeither (Calder 1984) The combinations ofthese nonlinear functions result in calcula-tions that suggest discontinuous optimalbody size with temperature This is consis-tent with empirical data (Brown et al1993 Brown and Maurer 1987 Brown andNicoletto 1991 Holling 1992 Maurer etal 1992 Peterson et al 1998) Howeverthere is an important reanalysis questioningthese empirical results (Siemann andBrown 1999) Our results of climatebodysizegut modeling suggest that whether ornot animal sizes are clumped in nature maydepend on the digestive efficiencies offoods consumed and the locations of thosefoods High quality foods suggest greaterclumping low quality foods suggest verylittle in the way of body size clumping (Fig13andashd)

Body size effects on cost of foragingtemperature dependent foragingactivitytime Body size has multiple effects on costof foraging It affects heat and mass balance

(Figs 12 13 15 and 16) Body size affectscost of locomotion which is constrained bythe respiratory and mitochondrial systemsof animals as Taylor and his colleagueshave so eloquently demonstrated (Mathieuet al 1981 Taylor et al 1982 Weibel etal 1991) Their studies interface very nice-ly with recent work on animal scaling (En-quist et al 1998 West et al 1997 1999)

The work presented here explains thatchanges in boundary conditions such as en-vironmental constraints on heat and massexchange alter fluxes and therefore alter in-ternal scaling requirements that must adaptto changing needs Thus we suggest thattemperature dependent behavior may be animportant response to environmentalchange that tends to keep the organism asclose as possible to optimal function as dic-tated by its internal and external anatomythereby maximizing fitness

Body size determines whether a speciescan be fossorial or not which affects diurnalmicroclimates and heat and mass balancesBody size affects likelihood of predationwhich can be cast as a cost of foraging(Brown et al 1994) Body size affects com-petition which alters temperature-dependentactivity time which also affects cost of for-aging

Body size effects on total annual activitytime Body size effects on total annual ac-tivity time are mediated through heat andmass exchange with the environment Theonset of heat or cold stress appears to be animportant constraint in limiting activityThat is temperatures that force skin tem-peratures below 38C or conditions whereevaporative water loss must be elevated toprotect organism integrity are bounds onactivity time that impact animal fitness

The boundary layer thickness in the airnext to the animal surface constrains massand heat transfer from an animal Boundarylayer thickness is a function of the frictionbetween the animal surface and the air Theamount of friction depends on the dimen-sion of the animal fluid and animal speedrelative to each other and fluid propertiesof density viscosity and thermal conductiv-ity On the one hand small animals havethin boundary layers and are more respon-


sive to convective environments than to ra-diant heat exchange (Porter and Gates1969) On the other hand large animalshave thicker boundary layers and are moresensitive to the diurnal changes in infraredradiation and solar radiation fluxes in theenvironment For large animals absorptionof radiant energy is a much greater chal-lenge since cooling by convective heattransfer is diminished because of the thickerinsulating boundary layer around the largeranimal

Body size affects competitive successhence temperature-dependent behavior in-cluding habitat utilization which impactson total annual activity time

Vegetationbody size effects on biodiver-sity Vegetation modifies microclimate con-ditions available to animals in predictableways Animal body size determines whereanimals spend their time in the wind pat-terns near the ground Figure 16 is basedon empirical climate data Those empiricaldata reflect how vegetation may modify lo-cal microclimates Vegetation also affectsanimal energetics either by direct shadingof the animals or by providing cool surfacesthat radiate back to animals Thus by di-rectly and indirectly affecting the animalheat fluxes vegetation impacts optimalbody size and constrains functional typesthat might coexist in a community

The distribution and quality of food inspace and time changes in an annual cycleAnimal food encounter probabilities andfood handling time are consequences ofvegetation structure and type The calcula-tions used in Figure 16 do not yet incor-porate various possible distributions of foodof various types in the environment Di-verse food distributions have not yet beenexplored using our models Food encounterprobabilities and handling times which area key part of food intake are only begin-ning to be explored The different foodtypes sizes and spacing also place impor-tant constraints on the range of body sizesof animals which can efficiently utilizethem

Body size cost of locomotion and homerange size are also interconnected Homerange size must be a function of body size

cost of locomotion and the foraging ther-mal and vegetative environment The min-imum time and cost to forage for a partic-ular type distribution and size of foodshould be calculable for a broad range ofbody sizes and environments

Feathers and plumage When we watchthe development of feathers through the on-togeny of a bird it is apparent that thedown structure is very much like the ex-tremely dense fur of some mammals Bothtypes of fibers emerge from single openingsin the skin as multiple fibers and then lsquolsquofanoutrsquorsquo in three dimensions as multiple fibersas they grow In so doing they extend thelayer of still air above the skin (and in theinsulation) substantially The second stageof plumage development with the eruptionof feathers that tend to seal off air flow evenfurther from the skin is unique in its effi-ciency of cross linking elements to holdcomplex units together and seal out airflow The only fur that seems even closelycomparable is that of the snowshoe harethat has fur tips that are flattened like tinyshovels (Porter unpublished data) Thesestructures probably assist in minimizing airand snow penetration into the coat

The restriction of feather tracts to por-tions of a birdrsquos skin provide for flexibilityin opening up skin areas to much more rap-id heat transfer is also unique to birdsSome mammals like polar bears have in-guinal regions that are highly vascularizedand lightly furred Polar bears sometimesapply them to the snow to dissipate heatbut mammals unlike birds have notevolved the ability to open large areas ofnearly bare skin to dissipate or absorb heat

CONCLUSIONS

1 Temporal and spatial variation in phys-ical environments impose important con-straints on functional types of animals thatcan coexist in biological communitiesThese constraints are further refined locallyby food diversity representing different di-gestive qualities

2 Morphology physiology and temper-ature-dependent activity in animals link in-dividual energetics to population dynamicsand community structure by specifying total


annual activity time and massenergy avail-able for growth and reproduction

3 Porous insulation in birds at rest canbe modeled with current state-of-the-art furmodels Resting birds have feather posi-tions that tend to seal off convective trans-port This creates a conductionndashradiationheat transfer environment This is simplerto calculate than an environment wherethree heat transfer mechanisms are all im-portant

4 Posture plays an important role in met-abolic heat loss This is true mainly becauseposture affects the radial dimension of theanimal which is a key variable in the equa-tion governing an animalrsquos total heat gen-eration requirements Posture is typicallyignored in metabolic chamber metabolismstudies The model presented here allowsthe calculation of the upper and lower limitsof metabolic expenditure for a wide varietyof climatic conditions

5 Animal geometry and posture insula-tion properties and environmental condi-tions influence lsquolsquothermal conductancersquorsquoThermal conductance is a term implying apassive transport of heat through a non-heat-generating medium Thus it is inap-propriate for describing fluxes throughflesh where heat generation is occurring Itis also inappropriate in porous media thatlsquolsquoact aliversquorsquo by absorbing solar radiation inthe insulation Thermal conductance is af-fected by properties and boundary condi-tions that can have nonlinear effects on heattransport through the medium in questionIt can be useful as a descriptive concept forheat source-free systems if all of the rele-vant boundary conditions and properties arespecified

6 The novel thermoregulatory model inconjunction with user specifications for di-urnalnocturnalcrepuscular activity allowsfor estimates of activity time that are ingood agreement with published data

7 Climatebody sizegut model calcula-tions for different food types suggest thatoptimal body size (maximizing discretion-ary massenergy) changes with differentfood types and their associated digestive ef-ficiencies and the temperature This sug-gests that vegetation diversity in a localityallows for specific multiple body sizes to

coexist at the same point in time As foodquality declines from high digestive effi-ciencies of fleshseeds to lower digestive ef-ficiencies of grassesleaves optimal bodysize increases lowest survival temperaturerises and the degree of clumping predictedfor species in nature declines Land usechanges that tend toward monocultureswould appear to dictate that fewer specieswould survive as vegetation diversity de-clines Global warming trends would leadto smaller optimal body sizes with nochange in vegetation However vegetationchanges associated with climate warmingwould specify larger or smaller body sizesdepending on whether vegetation digestivequalities decrease or increase respectively

8 Application of the microclimate andendotherm models to rare or endangeredspecies requires relatively few easily mea-sured data to estimate food and water re-quirements potential for activity timegrowth and reproduction for a wide varietyof habits This information will be useful asan aid for identification of potential re-servestransplantation sites and modifica-tionmanagement of existing habitats

ACKNOWLEDGMENTS

This work was supported in part by asabbatical fellowship to the senior authorby the National Center for Ecological Anal-ysis and Synthesis and by sabbatical sup-port from the University of WisconsinMadison We thank Dr Paul Maderson andDr Dominique Homberger symposium or-ganizers for the invitation to the sympo-sium and for their meticulous editing andthoughtful comments on the manuscriptWe thank Dr Joel Brown Dr Jordi Bas-compte and two anonymous reviewers formany thoughtful helpful comments on themanuscript We thank Dr Teresa Bucher forhelpful information on birds and their met-abolic measurements We thank Dr MarkCook and Dr William Karasov for infor-mation on digestion and gut function Wethank Dr Mark Burgman Brendan WintleDebra McDonald and Peter Menkhorst forspecimens and data on the Orange-belliedParrot We thank Dick Dwelle for parrot so-lar reflectance measurements and featherdepth measurements on museum specimens


of the Orange-bellied parrot and the peach-faced lovebird

REFERENCES

Adolph S C and W P Porter 1993 Temperatureactivity and lizard life histories Am Nat 142273ndash295

Adolph S C and W P Porter 1996 Growth season-ality and lizard life histories Age and size at ma-turity Oikos 77267ndash278

Bakken G S 1991 Wind speed dependence of theoverall thermal conductance of fur and feather in-sulation J Therm Biol 16121ndash126

Bakken G S and K E Lee 1992 Effects of windand illumination on behavior and metabolic rateof American goldfinches (Carduelis tristis) Auk109119ndash125

Bakken G S M T Murphy and D J Erskine 1991The effect of wind and air temperature on metab-olism and evaporative water loss rates of dark-eyed juncos Junco hyemalis A standard operativetemperature scale Physiol Zool 641023ndash1050

Bartlett P N and D M Gates 1967 The energy bud-get of a lizard on a tree trunk Ecology 48315ndash322

Beckman W A J W Mitchell and W P Porter1971 Thermal model for prediction of a desertiguanarsquos daily and seasonal behavior TransASME Paper No 71-WAHT- 351ndash7

Benedict F G 1938 Vital energetics A study in com-parative basal metabolism Carnegie Institute ofWashington 503133ndash164

Berris L B 1998 Habitat selection in time and spaceThe foraging ecology of raccoons In Departmentof Biological Sciences University of Illinois Chi-cago

Bird R B W E Stewart and E N Lightfoot 1960Transport phenomena Wiley and Sons Inc NewYork

Burington R S 1957 Handbook of mathematical ta-bles Handbook Publishers Inc Sandusky Ohio

Brown J H P A Marquet and M L Taper 1993Evolution of body size Consequences of an en-ergetic definition of fitness Am Nat 142573ndash584

Brown J H and B A Maurer 1987 Evolution ofspecies assemblages Effects of energetic con-straints and species dynamics on the diversifica-tion of the North American avifauna Am Nat1301ndash17

Brown J H and P F Nicoletto 1991 Spatial scalingof species composition Body masses of NorthAmerican land mammals Am Nat 1381478ndash1512

Brown J S B P Kotler and T J Valone 1994 For-aging under predation A comparison of energeticand predation costs in a Negev and Sonoran desertrodent community Austral J Zool 42435ndash448

Brown J S B P Kotler and W A Mitchell 1997Competition between birds and mammals A com-parison of giving-up densities between crestedlarks and gerbils Evol Ecol 11(6)757ndash771

Bucher T L 1983 Parrot eggs embryos and nes-

tlings Patterns and energetics of growth and de-velopment Physiol Zool 56465ndash483

Bucher T L G A Bartholomew W Z Trivelpieceand N J Volkmann 1986 Metabolism growthand activity in Adelie (Pygoscelis adeliae) andemperor penguin (Aptenodytes forsteri) embryosAuk 103485ndash493

Bucher T L and K R Morgan 1989 The effect ofambient temperature on the relationship betweenventilation and metabolism in a small parrott(Agapornis roseicollis) J Comp Physiol B 159561ndash567

Budaraju S W E Stewart and W P Porter 1994Prediction of forced ventilation in animal fur froma measured pressure distribution Proc Roy SocLondon B 25641ndash46

Budaraju S W E Stewart and W P Porter 1997Mixed convective heat and moisture transfer froma horizontal furry cylinder in transverse flow IntJ Heat and Mass Transfer 402273ndash2281

Calder W A I 1984 Size function and life historyHarvard University Press Cambridge

Christian K C R Tracy and W P Porter 1983 Sea-sonal shifts in body temperature and use of mi-crohabitats by Galapagos (Ecuador) land iguanas(Conolophus pallidus) Ecology 64463ndash468

Conley K E and W P Porter 1986 Heat loss fromdeer mice (Peromyscus) Evaluation of seasonallimits to thermoregulation J Exp Biol 126249ndash269

Drechsler M M A Burgman and P W Menkhorst1998 Uncertainty in population dynamics and itsconsequences for the management of the orange-bellied parrot Neophema chrysogaster BiolCons 84269ndash281

Enquist B J J H Brown and G B West 1998Allometric scaling of plant energetics and popu-lation density Nature 395163ndash165

Frost T M S R Carpenter A R Ives and T KKratz 1994 In C G Jones and J H Lawton(eds) Linking species and ecosystems pp 224ndash239 Chapman and Hall New York

Grant B W and W P Porter 1992 Modeling globalmacroclimatic constraints on ectotherm energybudgets Am Zool 32154ndash178

Guyton A C 1991 Textbook of medical physiology8th ed WB Saunders Philadelphia

Hainsworth F R 1981 Animal physiology Addison-Wesley Publishing Co Reading MA

Hayes S R and J A Gessaman 1980 The combinedeffects of air temperature wind and radiation onthe resting metabolism of avian raptors J ThermBiol 5119ndash126

Hayes S R and J A Gessaman 1982 Prediction ofraptor resting metabolism Comparison of mea-sured values with statistical and biophysical esti-mates J Therm Biol 745ndash50

Holling C S 1992 Cross-scale morphology geome-try and dynamics of ecosystems Ecol Monog62447ndash502

Hutchins B R and R H Lovell 1982 Australianparrots Aviculture and their habits Orange-bel-lied parrot Neophema chrysogaster (Latham)Austral Avicult January11ndash16


Hutchinson G E 1959 Homage to Santa Rosalia orwhy are they are so many kinds of animals AmerNat 93145ndash159

Kelrick M R and J A MacMahon 1985 Nutritionaland physical attributes of seeds of some commonsagebrush-steppe plants Some implications forecological theory and management J RangeManage 38(1)65ndash69

Kenagy G J R D Stevenson and D Masman 1989Energy requirements for lactation and postnatalgrowth in captive golden mantled ground squir-rels Physiol Zool 62470ndash487

Kingsolver J G 1979 Thermal and hydric aspects ofenvironmental heterogeneity in the pitcher plantmosquito (Wyeomyia smithii) Ecol Monog 49357ndash376

Kleiber M 1975 The fire of life An introduction toanimal energetics 2nd ed Krieger PublishingCo Huntington New York

Kowalski G J and J W Mitchell 1976 Heat transferfrom spheres in the naturally turbulent outdoorenvironment J Heat Transfer 98(4)649ndash653

Kowalski G J 1978 An analytical and experimentalinvestigation of the heat loss through animal furIn Department of Mechanical Engineering Uni-versity of Wisconsin Madison Wisconsin

Lawton J H and V K Brown 1993 In E D Shultzand H A Mooney (eds) Biodiversity and eco-system function pp 255ndash270 Springer-VerlagBerlin

Lide D R and H P R Frederikse (eds) 1996 CRChandbook of chemistry and physics A ready-ref-erence book of chemical and physical data CRCPress Orlando

Levey D J and W A Karasov 1992 Digestive mod-ulation in a seasonal frugivore the American rob-in (Turdus migratorius) Am J Physiol 262(4Part 1)G711ndashG718

Loyn R H B A Lane C Chandler and G W Carr1986 Ecology of orange-bellied parrots Neophe-ma chrysogaster at their main remnant winteringsite The Emu 86195ndash206

MacArthur R E H Recher and M Cody 1966 Onthe relation between habitat selection and speciesdiversity Am Nat 100319ndash332

Mathieu O R Krauer H Hoppeler P Gehr S LLindstedt R M Alexander C R Taylor and ER Weibel 1981 Design of the mammalian respi-ratory system 7 Scaling mitochondrial volume inskeletal muscle to body mass Resp Physiol 44113ndash128

Maurer B A J H Brown and R D Rusler 1992The micro and macro in body size evolution Evo-lution 46939ndash953

McClure P A and W P Porter 1983 Developmentof insulation in neonatal cotton rats (Sigmodonhispidus) Physiol Zool 5618ndash32

McCullough E M and W P Porter 1971 Computingclear day solar spectra for the terrestrial ecologicalenvironment Ecology 521008ndash1015

McNaughton S J 1977 Diversity and stability of eco-logical communities A comment on the role ofempiricism in ecology Am Nat 111515ndash525

McNaughton S J 1985 Ecology of a grazing eco-

system The Serengeti (Tanzania Kenya) EcolMonogr 55(3)259ndash294

Mitchell J W and G E Myers 1968 And analyticalmodel of the counter-current heat exchange phe-nomena Biophys J 8(8)897ndash911

Mitchell J W 1976 Heat transfer from spheres andother animal forms Biophys J 16561ndash569

Mitchell J W W A Beckman R T Bailey and WP Porter (eds) 1975 Microclimatic modeling ofthe desert pp 275ndash286 Scripta Book Co Wash-ington DC

Morris J G and S C Kendeigh 1981 Energetics ofthe prairie deer mouse Peromyscus maniculatusbairdii Am Mid Nat 105368ndash376

Morrison P R 1960 Some interrelations betweenweight and hibernation functions Bull MusComp Zool Harvard U 12475ndash91

Norris K S 1967 Color adaptation in desert reptilesand its thermal relationships In Symposium on liz-ard ecology pp 162ndash229 University of MissouriPress Columbia Missouri

Penry D L and P A Jumars 1987 Modeling animalguts as chemical reactors Am Nat 12969ndash96

Peterson C C K A Nagy and J Diamond 1990Sustained metabolic scope PNAS v 87(6)2324ndash2328

Peterson G R Allen Craig and C S Holling 1998Ecological resilience biodiversity and scale Eco-systems Jan Feb 16ndash18

Porter W P and D M Gates 1969 Thermodynamicequilibria of animals with environment EcolMonog 39227ndash244

Porter W P and F C James 1979 Behavioral impli-cations of mechanistic ecology II The Africanrainbow lizard Agama agama Copeia 1979(4)594ndash619

Porter W P J W Mitchell W A Beckman and CB DeWitt 1973 Behavioral implications ofmechanistic ecology Thermal and behavioralmodeling of desert ectotherms and their micro-environment Oecologia 131ndash54

Porter W P J C Munger W E Stewart S Budarajuand J Jaeger 1994 Endotherm energetics Froma scalable individual-based model to ecologicalapplications Austral J Zool 42125ndash162

Press W H B P Flannery S A Teukolsky and WT Vetterling 1986 Numerical recipes The art ofscientific computing Cambridge University PressCambridge

Rogowitz G L and J A Gessaman 1990 Influenceof air temperature wind and irradiance on metab-olism of white-tailed jackrabbits J Therm Biol15125ndash132

Roughgarden J 1974 Niche width Biogeographicpatterns among Anolis lizard populations AmerNat 108422ndash442

Schmidt-Nielsen K 1979 Animal physiology Adap-tation and environment 2nd ed Cambridge Uni-versity Press Cambridge

Scholander P F 1940 Experimental investigations onthe respiratory function in diving mammals andbirds Hvalradets Skrifter 221ndash131

Scholander P F R Hock V Walters S Johnson andL Bruibs 1950 Heat regulation in some arctic


and tropical mammals and birds Biol BullWoods Hole 99237ndash258

Siemann E and J H Brown 1999 Gaps in mam-malian body size distributions reexamined Ecol-ogy 88(8)2788ndash2792

Steudel K W P Porter and D Sher 1994 The bio-physics of Bergmannrsquos rule A comparison of theeffects of pelage and body size variation on met-abolic rate Can J Zool 7270ndash77

Stewart W E S Budaraju W P Porter and J Jaeger1993 Prediction of forced ventilation in animalfur under ideal pressure distribution FunctionalEcology 7487ndash492

Taylor C R N C Heglund and G M O Maloiy1982 Energetics and mechanics of terrestrial lo-comotion 1 Metabolic energy consumption as afunction of speed and body size in birds and mam-mals J Exp Biol 971ndash22

Tilman D and J A Downing 1994 Biodiversity andstability in grasslands Nature 367(6461)363ndash365

Waldschmidt S R S Jones and W P Porter 1987Reptilia In Pandian (ed) Animal energetics Bi-valvia through Reptilia Vol 2 pp 553ndash619 Ac-ademic Press San Diego

Walsberg G E 1988a The significance of fur struc-ture for solar heat gain in the rock squirrel Sper-mophilus variegatus J Exp Biol 138243ndash258

Walsberg G E 1988b Heat flow through avian plum-ages The relative importance of conduction con-vection and radiation J Therm Biol 1389ndash92

Walsberg G E 1988c Consequences of skin colorand fur properties for solar heat gain and UV ir-radiance in two mammals J Comp Physiol BBiochem System Environ Physiol 158213ndash222

Walsberg G E and B O Wolf 1995 Solar heat gainin a desert rodent Unexpected increases withwind speed and implications for estimating theheat balance of free-living animals J Comp Phy-siol B Biochem System Environ Physiol 165306ndash314

Wathen P J W Mitchell and W P Porter 1971 The-oretical and experimental studies of energy ex-change from jack rabbit ears and cylindricallyshaped appendages Biophys J 11(12)1030ndash1047

Wathen P M J W Mitchell and W P Porter 1974Heat transfer from animal appendage shapes-cyl-inders arcs and cones Trans of the ASME No-vember 40536ndash540

Weibel E R C R Taylor and H Hoppeler 1991The concept of symmorphosis A testable hypoth-esis of structurendashfunction relationship Proc NatAcad Sci USA 8810357ndash10361

Weiner J 1987 Limits to energy budget and tactics inenergy investments during reproduction in theDjungarian hamster (Phodopus sungorus sungo-rus) Pallas 1770 In Reproductive energetics inmammals Symp Zool Soc London 57167ndash187

Welch W R and C R Tracy 1977 Respiratory waterloss A predictive model J Theor Biol 65253ndash265

Welch W R 1980 Evaporative water loss from en-

dotherms in thermally and hygrically complex en-vironments An empirical approach for interspe-cific comparisons J Comp Physiol (B) 139135ndash143

West G J H Brown and B J Enquist 1997 Ageneral model for the origin of allometric scalinglaws in biology Science 276122ndash126

West G J H Brown and B J Enquist 1999 Thefourth dimension of life fractal geometry and al-lometric scaling of organisms Ecology (In press)

ABBREVIATIONS

Symbols

T 5 temperature (C K)m 5 mass (kg)Q 5 heat flux (W)R r 5 radius (m)RH 5 relative humidity ()V 5 wind speed (ms)Subscriptsabs 5 absorbedair 5 free stream aircond 5 conductionevap 5 evaporationf 5 furgrd 5 groundIR 5 infraredmet 5 metabolismopt 5 optimalresp 5 respirations 5 skin

APPENDIX

Allometry model

Equations used for calculating allometry of largebirds were derived from their weight and photographsAll units are SI (m kg W) Equations used for allom-etry of large birds are for the size range Rhea (25 kg)to Ostrich (100 kg)

Body feathered length (top of head to base of tail)(m) 5 0225 mass (kg)0312

Bare portion of leg only feathered leg part treatedas part of the body

Leg length (m) 5 L(leg)

5 000613[mass(kg) 2 25] 1 061

Leg diameter (m) 5 D(leg)

5 0000453[mass(kg) 2 25]

1 0057

Area of one leg 5 A(leg) 5 pD(leg)L(leg)

2Volume of one leg 5 p(D(leg)2) L(leg)

Headneck (assuming no feathers for the rattites)


Head plus neck length (m)

5 000253[mass(kg) 2 25] 1 057

Head and neck diameter (m)

5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead

5 pD(neck)L(headampneck)

Volume of Head amp neck

25 p(D(neck)2) L(headampneck)

3Total volume(m )

35 mass(kg)1000(kgm )

Torso volume

5 Total volume 2 Leg volume

2 Headampneck volume

Estimating average feather depth of rattite birdsfrom photographs and weights

Estimating featherndashair surface area for calculatingconvection from feather surface from photographs andweights

Semi-major axes of an ellipsoid for featherndashair in-terface of rattites

a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2

The area of a prolate ellipsoid is2 2 21Area(m ) 5 2p((b 1 c)2) 1 2p(a((b 1 c)2)e)sin (e)

where2 2 05e 5 [(a 2 ((b 1 c)2) )] a (Burington [1957])

Estimating unfeathered torso dimensions for theequation of ellipsoid heat generation needed to main-tain core temperature

We assume geometric similarity of shape (uniformfeather depth) for the bare torso surface and the feath-erndashair surface

The volume of a prolate ellipsoid contained withinthe featherndashair interface is

Volume feathered torso 5 (43) pabc

Assuming the same ellipsoid shape for torso andfeatherndashair interface

3Volume bare torso 5 V baretorso 5 (43) p(abc)x

where x is the common fractional factor for a b andc that gives the exact torso semi-major axes We knowthe feathered torso volume from the equation aboveand the semi-major axes of the feathered torso a band c We can solve for x the common fractional fac-tor for a b and c

03333x 5 (3Vbaretorso(4p abc))

Thus the bare torso semi-major axes are

Atorso 5 ax Btorso 5 bx Ctorso 5 cx

Average feather depth is the difference between anyof the feathered and unfeathered semi-major axes eg(a feathered torsomdashA bare torso)

The characteristic dimension for the NusseltndashReyn-olds heat transfer coefficient calculation is

03333D 5 Volumefeathered torso

Gut model

The goal here was to determine an upper bound forabsorbed food It does not explicitly consider impor-tant constraints on food intake that are affected by howfood is distributed in the environment which affectsencounter probability and what the handling time iswhich is a function of feeding apparatus morphologyBoth encounter probability and handling time may af-fect how much food is actually ingested This versionof the gut model waits until a 24 hr activity simulationcycle starting at midnight has been completed Then itlooks back at the dayrsquos energy requirements and usesthat to calculate how much of the food would have tobe processed in the gut that day to meet those de-mands

The user specifies the food properties They includepercent of proteins carbohydrates lipid and percentdry mass relative to wet mass There is an upper boundconstraint the animal may never consume more wetweight food per day than its body mass

The gut model deals only with the part of the gutassociated with the actual digestive process Handlingtime and internal storage of food in the stomach(s) isnot considered These will place additional constraintson gut function Because retention time may vary fromapproximately one-third of a day to more than a daydepending on body size it was finally decided to usea dayrsquos energy requirements and the mass flow of foodper day needed to meet those requirements In all thesesimulations the assumption was made that the total en-ergy requirements were 35 times the energy neededto maintain core temperature on the particular day thatwas simulated

A digestive efficiency of 57 was used for most ofthe simulations except for grass hay Reference No102250 (USndashCanadian nutrient composition tables1994) A 57 digestive efficiency has been measuredfor seeds in small rodents and is very close to the valuefor digestive efficiency by cattle (61) The modelrequires empirical data on digestive efficiency foodproperties defined above The gut model assumes thatthe gut can alter flow rates to maintain the same di-gestive efficiency for a particular type of food (Leveyand Karasov 1992)

Animals typically do not overeat or gain weight un-necessarily The model assumes that the amount offood ingested is determined by todayrsquos metabolicneeds and is constrained by maximum volumetric flowrate less than or equal to body mass The user definespercent digestive efficiency percent water in fecespercent urea in urine and a multiplier from 1 to 7above basal metabolic energy requirements to specifyfood intake to meet current needs The user also de-fines percent protein percent fat percent carbohydrateand percent dry matter in ingested food


The dry grams of food needed to meet the metabolicdemand are estimated based on food properties and theconstraints in the paragraph above

The gut model is related to work by Penry and Ju-mars (1987) Their equation (9) p 73 for a batchreactor model is

Xaf

time 5 C (dX 2 r )A E A A0

0

where

X 5 mole fraction of species A (dimensionless)A

X 5 (C 2 C )CA A A A0 0

C 5 food component A concentration (moles)A

C 5 initial concentration of food component A inA0

moles

Many of the components of reactor models are notknown Since the endotherm model can calculate met-abolic heat production to maintain a specified coretemperature it is straightforward to calculate thegrams dry weight and then wet weight of user-definedfood to meet the metabolic demand The followingpseudoequations are an example of these calculationsfor a seed diet

The amount of fat protein and carbohydrateg drymass of food is first computed from user specified per-centages of these components of food

gfatpg 5 pctfat(g fatg dry mass)

gprotpg 5 pctpro(g proteing dry mass)

gcarbpg 5 pctcar(g digestible carbohydrateg dry mass)

gsum 5 gfatpg 1 gprotph 1 gcarbpg

Next undigested massg dry mass of food is calcu-lated and used to compute total carbohydrates

gundig 5 100 2 gsum

TOTCARB 5 gcarbpg 1 gundig

Then joulesg dry food is calculated

fatJpg 5 gfatpg 3 (9400 3 4185)

3 (g fatg dry food 3 caloriesg fat

3 Jcalorie)

protJpg 5 gprotpg 3 (4199 3 4185)

carbJpg 5 TOTCARB 3 (4200 3 4185)

TotJpgram 5 fatJpg 1 protJpg 1 carbJpg

Not implemented here is the variable protein diges-tion efficiency for ruminants vs monogasters (75vs 13) While proteins are important from a proteinand amino acid balance standpoint in terms of abso-lute energy available it is a small factor since alfalfa(reference number 100056) vs grass forage (referencenumber 102250) varies from approximately 86 pro-tein to 181 protein (USndashCanadian nutrient com-pound composition tables 1994) Seed protein is 15

(Kelrick and MacMahon 1985) Calculation of joulesabsorbed per gram of dry food is

Jabspgr 5 fatJpg 1 protJpg 1 DigEff carbJpg3

The moles availableg dry food can now be calculated

Totmolpgram 5 gfatpg 3 850 1 gprotpg 3 137

1 gcarbpg 3 180

We can then calculate the joules of chemical energyneeded to be absorbed by the gut day 5 (Js) 3 (sh)3 24h 3 basal multiplier for metabolic rate (activityabove resting)

FoodJ 5 Qmetab 3600 24 timbas3 3 3

The dry mass needed to be absorbedd to meet themetabolic demand is then

DRYABS 5 FoodJJabspgr

We then calculate the grams of dry food that must beingestedday and then the total moles of each of thefoodstuffs

Drymas 5 DRYABS(10 2 gundigest)

Total moles available for absorption 5 molesdry gram3 dry grams

Totmoles 5 (gfatpg 3 850 1 gprotpg 3 137

1 gcarbpg 3 180) 3 drymas

The J of food needed in gutday to meet nesting me-tabolism plus user specified activity level 5 (JDAY)3 basal multiplier

FoodJ 5 DaysMETAB 3 timbas

The needed g of food absorbedd 5 J neededdayFoodJg


The g food dry ingestedday 5 g absorbDi-gestpEfficiency

Drymas 5 DRYABS(10 2 gundiest)

Wetmas 5 DrymasPctDry

We then test for whether the required food mass perday exceeds body mass If it does absorbed mass isreset to the maximum value allowed by body weightand energy available is adjusted accordingly

Upprlim 5 Gmass

If (Wetmas greaterthan Upprlim) then

Wetmas 5 Upprlim

Drymas 5 Wetmas 3 PctDry

DRYABS 5 Drymas 3 DigestpEfficiency

Jpdaymax 5 DRYABSJabspgr

Jpsavail 5 Jpdaymax(24 3 3600)

Endif

Once we have checked to make sure the upper boundhas not been exceeded the dayrsquos joules of energy ab-sorbed DaysJabs can be calculated


The input data file for the mouse to elephant calculations is listed below Labels above it describe each datum

Animal species 5 Mouse to elephant deer mouse fur grass haymdashRef 102250ALLOMETRIC properties

Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)

Geometricapprox(integer)1 5 cyl

2 5 spher3 5 ellips4 5 lizard

lsquoIbgirdrsquo orlsquoIgmamlrsquo 5 20kguses complex geomrsquos

ventral areaon substrate(decimal )

10000 0010 00 3 lsquoIgmamlrsquo 005

DaysJabs 5 Jabspgr DRYABS

The energy available Avlnrg in joulessec availablecan be calculated

Avlnrg 5 DaysJabs(24 3600)

We calculate the g wet weight through the gutdayCRTOT to monitor part of the water balance of theanimal

gH O 5 (Drymas 2 PCTDRY 3 Drymas)PCTDRY2

CRTOT 5 gH O 1 Drymas2

We also keep track of the hourly dry grams absorbedof protein fat and carbohydrate for use in the growthmodel (Adolph and Porter 1996)

Dryinphr 5 DRYABS24

GPROTH 5 Dryinphr 3 gprotpg

GFATH 5 Dryinphr 3 gfatpg

GCARBH 5 Dryinphr 3 gcarbpg

Size dependent constraints appear when the energy(mass) needs for the day exceed the daily gut volumeflow rate for the body size Available activity timeavailable is calculated That can be used to back cal-culate required handling time of the food needed tomeet the energetic demands and to estimate time effi-ciency of massenergy acquisition for all body sizesfor a given food type and configuration

Data sources This model assumes 040 g watergprotein oxidized Hainsworth (1981)

Proteins

Approximate gram molecular weight of amino acidsis 137 gmole

Based on information from the CRC Handbook ofChemistry and Physics (1996)

Alanine 5 891 gmole (with water 2 18 gmole)

Arginine 5 1742 gmole (with water 2 18 gmole)

Aspargine 5 1321 gmole (with water 2 18 gmole)

Aspartic acid 51331 gmole (with water 2 18 gmole)

Cystine 5 1212 gmole (with water 2 18 gmole)

Glutamic acid 5 1471 gmole (with water 2 18 gmole)

Glutamine 5 1461 gmole (with water 2 18 gmole)Glycine 5 751 gmole (with water 2 18 gmole)

Histidine 5 1552 gmole (with water 2 18 gmole)Isoleucine 5 1312 gmole (with water 2 18 gmole)

Leucine 5 1312 gmole (with water 2 18 gmole)Lysine 5 1462 gmole (with water 2 18 gmole)

Methionine 5 1492 gmole (with water 2 18 gmole)

Phenylalanine 5 1652 gmole (with water 2 18 gmole)Proline 5 1151 gmole (with water 2 18 gmole)

Serine 5 1051 gmole (with water 2 18 gmole)

Threonine 5 1191 gmole (with water 2 18 gmole)

Tryptophan 5 2042 gmole (with water 2 18 gmole)

Tyrosine 5 1812 gmole (with water 2 18 gmole)

Valine 5 1171 gmole (with water 2 18 gmole)

Average 5 137 gmole

Lipids

Data from Guyton (1991) The gut model assumesthat triglycerides are used for energy They are stearicacid (880 gmol) oleic acid (879 gmol) and palmiticacid (754 gmol) Based on these data the model as-sumes as an average 850 gmol The model uses 47caloriesml O2 which is 9400 caloriesg fat (Kleiber1975) There are 107 g water producedg lipid oxi-dized Hainsworth (1981)

Carbohydrates

This model assumes that glucose data values are 180gmol 50 calml O2 4200 caloriesg (Kleiber 1975)and that there are 056 g water producedg carbohy-drate oxidized Hainsworth (1981)

Digestion capability data come from Weiner (1987)Kenagy et al (1989) and Peterson et al (1990) Seedcomponent values come from Kelrick and MacMahon(1985)


FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014

PHYSIOLOGICAL propertiesmdashtemperature and water loss from metabolism amp skin

Coretemp

Min diffTc-Tskin (C)

Texpir-Tair (C)

skin wet(sweat)

Thermal conductivity offlesh (0412ndash28 WmC)

360 05 30 1 09

PHYSIOLOGICAL propertiesmdashgut and excretory system

Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )

X basal metabolism (W)for est food intake (15ndash7)

061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)

carbohydrate(decimal)

dry matter (decimal)(025 green veg

075 seed humid stor09219 dry seed)

0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)

Ground shadeseeking OK

(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)

lsquonrsquo lsquonrsquo lsquonrsquo lsquonrsquo lsquonrsquo lsquonrsquo

NEST properties if nest thickness 5 00 amp thermal cond 5 00 no nest assumed

Nest wallthickness (m)

Nest wallthermal conductivity

(Wm-C)

000 00

A sample input data file for the microclimate model is listed below to illustrate the data required for microclimatecalculations The format is like that for the endotherm model listed above Animal height is average height tothe middle of the body This allows for calculation and output of the air temperature and wind speed at averageanimal height for outdoor calculations

Site Label

Savannah River Site Aiken County South Carolina

Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator

errorAnimal aveheight (cm)

0001 25 030 2650 837 090 2 5

Startmonth

Endmonth

Percent of bareground in shade(0 5 full sun)

1 12 0


Hemi-sphereN 5 1S 5 2

Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15

Time of MAXIMUMS (top row) Minimums (bottom row) Air Wind maxrsquos solar noon (integer hours relativeto sunrise or solar noon) Rel Hum Clouds maxrsquos sunrise

Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010

Maxrsquos (top row) minrsquos (bottom row) REL HUMIDITIES () for ave day each month

830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530

Maxrsquos (top row) minrsquos (bottom row) CLOUD COVER () for ave day each month

0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

Maxrsquos (top row) minrsquos (bottom row) WIND SPEED (ms) for ave day each month

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

Maxrsquos (top row) minrsquos (bottom row) AIR TEMPERATURE (C) for ave day each month

14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408

The executable code and data for input to the program for these calculations are available from the seniorauthor to interested readers Questions about code details should be directed to the senior author

597

AMER ZOOL 40597ndash630 (2000)

Calculating Climate Effects on Birds and MammalsImpacts on Biodiversity Conservation Population Parameters and

Global Community Structure1

WARREN P PORTER2 SRINIVAS BUDARAJU3dagger WARREN E STEWARTdagger AND

NAVIN RAMANKUTTYDaggerDepartment of Zoology University of Wisconsin 250 N Mills St

Madison Wisconsin 53706daggerDepartment of Chemical Engineering University of Wisconsin 1415 Johnson Drive

Madison Wisconsin 53706DaggerInstitute for Environmental Studies 1225 West Dayton Street

Madison Wisconsin 53706

SYNOPSIS This paper describes how climate variation in time and space canconstrain community structure on a global scale We explore body size scaling andthe energetic consequences in terms of absorbed mass and energy and expendedmass and energy We explain how morphology specific physiological propertiesand temperature dependent behaviors are key variables that link individual en-ergetics to population dynamics and community structure

This paper describes an integrated basic principles model for mammal energeticsand extends the model to bird energetics The model additions include molar bal-ance models for the lungs and gut The gut model couples food ingested to respi-ratory gas exchanges and evaporative water loss from the respiratory system Weincorporate a novel thermoregulatory model that yields metabolic calculations asa function of temperature The calculations mimic empirical data without regres-sion We explore the differences in the quality of insulation between hair andfeathers with our porous media model for insulation

For mammals ranging in size from mice to elephants we show that calculatedmetabolic costs are in agreement with experimental data We also demonstratehow we can do the same for birds ranging in size from hummingbirds to ostrichesWe show the impact of changing posture and changing air temperatures on en-ergetic costs for birds and mammals We demonstrate how optimal body size thatmaximizes the potential for growth and reproduction changes with changing cli-matic conditions and with diet quality Climate and diet may play important rolesin constraining community structure (collection of functional types of differentbody sizes) at local and global scales Thus multiple functional types may coexistin a locality in part because of the temporal and spatial variation in climate andseasonal food variation We illustrate how the models can be applied in a conser-vation and biodiversity context to a rare and endangered species of parrot theOrange-bellied Parrot of Australia and Tasmania

INTRODUCTION

A brief history

Ever since the era of Charles Darwin bi-ologists have been intrigued by how and

1 From the Symposium Evolutionary Origin ofFeathers presented at the Annual Meeting of the So-ciety for Integrative and Comparative Biology 6ndash10January 1999 at Denver Colorado

2 E-mail wportermhubzoologywiscedu3 Current address West Vaco Laurel Research Lab-

oratory 11101 Johnrsquos Hopkins Road Laurel MD20723

why animals live where they do and whatis it about their properties that makes themappear where they do and appear in thespecies associations that they form Hutch-inson (1959) defined the concept of theniche MacArthur et al (1966) Roughgar-den (1974) and many others explored as-pects of how size and habitat may influencecommunity structure Norris (1967) andBartlett and Gates (1967) were the first tocalculate explicitly how climate affects an-imal heat and mass balance and the conse-quences for body temperature in outdoor




































Model cross section










Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408





































Model cross section










Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408






























Model cross section










Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408



















Model cross section










Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408









Model cross section










Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408










Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




Inside the body





























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408























Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408



















Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408










Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




Porous insulation



















RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408














RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408





RESULTS
























































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408

















































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408







































rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




























rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408
























rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




















rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408













rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




rarr


























DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408


















DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408

















DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408








DISCUSSION





















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




















CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408











CONCLUSIONS












ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408











ACKNOWLEDGMENTS




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




REFERENCES
































































































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408






























































ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408























ABBREVIATIONS

Symbols


APPENDIX

Allometry model





5 000613[mass(kg) 2 25] 1 061


5 0000453[mass(kg) 2 25]

1 0057






5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




5 000253[mass(kg) 2 25] 1 057


5 00000507[mass(kg) 2 25] 1 00572

Area of neckhead




3Total volume(m )


Torso volume






a 5 long axis(m)2

5 (2000227(mass(kg) 2 100) 1 175)2

b 5 width(m)2 5 (000173(mass(kg) 2 25) 1 10)2

c 5 height(m)2

5 (2000267(mass(kg) 2 100) 1 10)2
















Gut model









Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408





Xaf


0

where


X 5 (C 2 C )CA A A A0 0



moles








gundig 5 100 2 gsum



fatJpg 5 gfatpg 3 (9400 3 4185)


3 Jcalorie)









1 gcarbpg 3 180


















Upprlim 5 Gmass


Wetmas 5 Upprlim





Endif





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408





Maxweight

(kg)

Minweight

(kg)

Fatinsul

thick (m)













Dryinphr 5 DRYABS24






Proteins



















Average 5 137 gmole

Lipids


Carbohydrates




FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408



FUR Properties

Hair dia(mm)

dsl vntl

Hair length(mm)

dsl vntl

Fur depth(mm)

dsl vnt

Hair dens(1cm2)

dsl vntl

Fur solarreflect

nd

Fur solartransmiss

nd

30 30 9 9 66 66 12000 12000 02 014


Coretemp


Texpir-Tair (C)

skin wet(sweat)


360 05 30 1 09


Digest eff(dec )

Fecal water(dec )

Urea inurine (dec )


061 010 020 35

FOOD properties

protein(decimal)

fat(decimal)




0086 0023 042 025

BEHAVIORAL data

Diurnal(YN)

Burrow(YN)

Climb toCool OK

(YN)


(YN)

Crepuscularactivity

(YN)

Fossorialonly)(YN)





(Wm-C)

000 00


Site Label


Roughnessheight (m)

Soiltherm cond

(WmC)Sub refl(dec)

Sub dens(kgm3)

Subspecific

heat(Jm3-K)

SublongIRemiss

(dec)Integrator


0001 25 030 2650 837 090 2 5

Startmonth

Endmonth


1 12 0



Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408




Latitude

(deg) (min)

W Longitude

(deg) (min)

15 3integerLongit

time zone(deg)

Slope(deg)

Azimuth(S 5 0(deg)

Elev(m)

Cm H2Oin aircol

10 330 240 810 390 750 100 00 00 15


Airtemp

Windspeed

Relhum

Cloudcover

1000

1000

0010

0010


830550

820495

840475

850440

865485

865515

885545

920565

920555

910505

890510

845530


0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0


2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505

2505


14305

17526

22056

26989

302140

334188

352212

332205

308168

25499

21158

15408


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