Features

üf mice and mammoths New approaches to understanding the biological implications

of body size

L ife, says physicist Geoffrey West, is simply fantastic. If you're at all dubious about

that assertion, he's got seme data he thinks you'tl find convincing. Most biologists don't need to be convinced that life is remarkable in a multitude oE ways. Bur whereas much of mod­ern biology zeraes in on life's inrrica­eies in ever finer detail, West's en­thusiasm is sparked by broad patterns woven across the evolutionary land­scape~ from microbes to mammoths and everything in between.

The lens through which West and his ecologisr collaborators view life is a set of general mathematical rela­tionships known as thc laws of al­lometry. ABometric scaling laws de­scribe how different parts and characteristics of living organisms vary (or "scale") in proportion to changes in body size. From mouse to dog to horse co elephant, as bodies get bigger, bones beeome propor­tionally shorter and thicker, hearts beat more slowly, cells become more efficient at using energy, and life­times grow longer. Even ecological traits such as population density and horne range size vary in a predictable manner as a funetion of body mass.

The clearest and best-known pat­terns occur in rnammals, including a precise) cross-species scaling relation­ship between mammalian size and rate of energy consumption (or meta­bolie rate) known as Kleiber's Law (see box page H8H). Across eight or­ders of magnitude, horn 2-gram shrews to 200-million-gram whales, allometry seerns to dictate in coarse terms how any given-sized mammal should be built and how it shouId

by Scott N orris

November 1998

operate_ UThat something so simple as a sealing law exists in something as eomplex as life," West says, "is truly remarkable."

Allometric laws are deseriptions of how things aetually are) distilled from vast quantities of eomparative biological data. But the question of why various bi ologi ca 1 rates and measurements seale as they do has puzzled scientists for years. At a ba­sic level, physieal and mechanieal constraints c1early require that ani­mals change in shape as they change in size. A directly proportional, el­ephant-sized enlargement of a mouse would fall to pieees under its own weight. Or burn itself alive-big­bodied creatures must slow their metabolism to avoid produeing more heat than can be dissipared across proportional1y smaller body surfaces.

Understanding these constraints has not, however, ted co any satisfy­ing general explanation of why the scaling laws work the way chey da. "A unifying theory chat would de­seribe allometric sealing laws has been the Holy Grail in comparative biology for decades," says Uni ver­sity of Arl7.0na comparative physi­ologist earol Beuchat.

Such a general theory may now be at hand_ In a publication last year in Science (276: 122-126) and in a re­cent paper in Nature (39S: 163-165), a trio of New Mexico researchers have presented a general mathemati­eal model that appears to explain and link together a wide range of allometric phenomena in both plants and animals. The work) by West, of Los Alamos National Laboratory and the Santa Fe Institute, and eeologisrs James ßrown and Brian Enquist, of the University of New Mexieo, has caused something of a stir) ac least

among allometry enthusiasts. .. As novel ideas go," remarks evolucion­ary biologist John Gittleman, of the University ofVirginia, "this is a very novel one."

At the same time, however, a new and quite different perspective on allometries has emerged, Jan Koz­lowski and January Weiner) of the Institute of Environmenral Biology atJagiellonian Universicy in Krakow, Poland, want tu redefine ehe enrire problem. The patterns thatappear in mouse-to-elephant comparisons, these authors eontend, have nothing to do wirh how the animaI!> are pur together. Last year in American Natu­ralist (149: 352-380), Kozlowski and Weiner introduced a model suggest­ing that scaling patterns across spe­eies are likely to be mere statistical chimera, byproducts of ehe evolu­tionary logie through wh ich selec­ti on shapes body size within speeies.

In a eommentary in the September 1997 issue of Trends in Ecology and Evolution (12: 338-339), Gittleman and Sarah Cates, ofthe University of Tennessee, focused attention on the differing assumptions and compet­ing claims of the two approaches. At first glance it might appear that nei­ther model should have much bear­ing on the other. West er al. foeus on the physies and geomerry of fluid transport in plants and animals, whereas Kozlowski and Weiner ex­amine tradeoffs in the evolution of body size and other life history char­acteristies. Cates and Gitrleman point out that from these very different starting points, however) borh ap­proaches move toward some genera! eonclusions regarding the nature of allometrie relationships in biology, and it is at this level that the re­searchers appear to be in head-on

887

The mathematics of allometry

Allornetric formulas are power laws of the general form Y = aMbo They sta re (he va lue of one bio logical va ri able (Y) in te rms of

another-usuall y body mass (M)-raised to some power (b). The dependent va ri able, Y, may be almost any th ing-the radius of the trachea, fo r example, or age at fi rst reproducrion. For most phenomena the constanc (a) varies according to the group of orga nisms (e.g., birds or mamma ls) being considered. Si milar laws describe basic geemetrical re larionships. Thc surface areas of spheres and cubes, for exampl e, scale in proportion co volume ra ised ro the 213 power: SA = VO.67•

In a llomet ry, measurements are typica lly expressed as logarithms, pcrmitting a broad range of sizes (0 be plotted on a single graph (see page 891). On sueh logarithmie plots the eonstant (a) bceomes the y­inte reept, a nd the exponent (b) is rhe slope. Thus the terms "seali ng exponent" and "slope" are often used inrerehangeably in d iseussions of allometry. Graph iea l depiet ions of allomet ri e relationships are frequently refc rred to as mouse-elephant eurves.

In the mouse-elepha nt eurve dcpicting merabolie rate as a function of body mass, energetic constraints ensure thar the slope of the line must be less tha n 1.0. Intriguingly, these eurves a lso typ ieally show slopes greater than the 213 (0.67) that would be pred icted fro m a const raint ha vi ng tO do solely with surface-to-volume rati os. In fact, an allomet ri e sea ling exponent-or slope-of 3/ 4 (0.75) may be a eommon feature of size-energy sealing in a nUl11be r of different groups of organisms. In mammals, the "rule" of 3/ 4-power sealing of metabolie rate is known as Kle ibcr's Law.

disagreement. The question comes down to this: Are the broad, CroS5-species allomecries, about which so much has been written for so long, reflections of physical constraints common to most or aIlliving things­or are they me re incidental, statisti­eal eorrelation.s?

Search for a general theory

In theil' Science paper, West and his eollaborators wok aim at what for many has been the allometrie mys­tery of mysteries: so-ealled quarter­power sealing. This is the tendency for many biological variables to i11-crease more or less in proportion to body mass raised to the 1/4 or 3/4

power. Für example, meta bolic rare-the amounc of energy an or­ganism consumes in order to stay alivc-seales as mass to the 3/4;

lifespan seales as mass to the 1/4 . In terms of the more fa miliar powers of

888

ten, an animal that is ten to the fourth (10,000) times larger than another uses only ten co the third (1000) times more energy and lives ten to the one (10) tirnes as long.

Sinee 1932, when Max Kleiber first described the>/4-power scaling relationshipof metabolie rate to body mass in mammals, other researchers have confirmed chis pattern and ex­tended je co ocher taxa-birds, rep­ti!es, invertebrates~ and even unicel­luJar organisms. But what about plants? That's the question that Enquist was asking in the fall of 1994, as he began to plan his disser­tation research. He soon found that relative!y few allometric relation­ships had been described for plants and trees, apart from spatial models of population density. Bur the data were out there, in hundl'eds of pub­lications scattered throughout the agrieultural and botanical literature.

In plant studies, mass was seldom

treated as a causa I variable, or even measured. But ie was known ehat plant rnass could be predicted using a scaling relationship with seem di­ameter. Enquist simply turned this relationship around. Rearranged, ie said that basal stern diameter in tIees scales as mass to the ~Ix power. This result was intriguing because in mam­mals the diameters of the aorta and trachea also seale as Inass to the 3/1;. Reasoning that plant total metabolie rate must elosely eorrespond to the rate of xylem transport (essentially nutrient supply), Enquist went on to sec if thefe might be a plant version of Kleiber's Law. "I kept coming up with slopes that were pretty elose to 0.75," he says. The patterns seemed to suggest that, in terms of total energy expenditure, plants and ani­mals are alike.

Enquist's pre!iminary work led to a eollaboration with Brown, his ma­jor advisor. Seeing the same kind of allometric patterns in plants as in other groups suggested a fundamen­tal question: Are there universal char­acteristics shared by most or all liv­ing organisms that might account for the observed regularities in size­energy sealing relatiol.1ships? Brown and Enquist suspected that the an­swer might lie in the constraints im­posed on physieal growth and en­ergy eonsumption by branching supply networks. For multiee!lular life to have evolved, organisms had to solve the problem of keeping all of their ceIls supplied with nutrients and cleared of wastes. Bl'anehing networks, the hiologists noted, are a common evolutionary solution ro chis problem-from plant vaseular sys­tems, to the tracheal diffusion net­works of insects, to the puJsa rile res­piratory and eardiovascuJar systems of vertebrates.

A transport model

As the researchers pondered the eon­straints these distribution systems might impose, they devclopcd a set of three basic principles to which, at least in theory, all biologieal supply

BioScience Vol. 48 No. 11

networks must adhere. First, the sys­tem must fill the volume of the or­ganism, to feed all of its cells. Sec­ond, the terminal branches of these networks should be roughly the same size in different species, regardless of body size. "Capillary size doesn't vary much in mammals," says Brown. "The same is true of petioles or ter­minal xylem in plants." The third principle states that supply networks have been honed by natural selection to approach optimal efficiency-flu­ids are transported throughout the body such that the least amount of energy is wasted. All three assump­tions are, Brown says, deliberate oversimplifications. "Some of the scauer in these scaling relationships probably reflects the extent to which organisms can get away with violat­ing the assumptions," he says. "But as deviation becomes too big, selec­tion for conformity to the principles embodied in the model should in­crease in strength."

The next step was to translate these general principles into the mathematical language of a formal model. Through associates at the Santa Fe In"stitute they were intro­duced to West, a theoretical physi­eist and mathematician, who was captivated by the problem. West was soon able to show that not just any branching pattern would meet all three assumptionsj in fact, the ideal­ized distribution system had to fol­low a fractal-like design. "That means there's a geometrie progres­sion as you go down through the network," West explains. "Any piece of it is in some sense a representation of the whole." Speeifically, a fraetal­like pauern me ans that the length and radius of vessels change in a consistent ratio at every branching point across aseries of levels-fram artery, to arteriole, to capillary, for example. One of the original fea­tures of the West et a1. work is that the researehers derived such a pat­tern analytically. "We don't assume the branching is fractal-like," says West. "It folIo ws mathematically from the assumptions."

November 1998

More number crunching led to an­other important realization: T 0 main­tain the smoothest flow throughout the system, in aceordance with the principle of energy minimization, the summed crass-sectional areas of the "daughter" branches at each level should be equal to that of the "par­ent." Such an area-preserving pat­tern is found in trees and at the top­end (artery-arteriole) branchings of cardiovascular systems.

With this additional requirement in place, the physieal structure of the network could be precisely described mathematically in terms of the num­her of branching levels and two "scal­ing factors" that determine how ves­sel radius and length change at each level. These variables in turn could be substituted into equations describ­ing the total fluid volume and rate of flow in the system. Beeause fluids in these networks transport oxygen and nutrients for metabolism, flow rate varies in direct proportion to meta­bolie rate. And for systems with fractal­like, area-preserving branching, fluid volume varies in direct proportion CO

body mass. Thus, returning to the simple allometric formula for the scaling of metabolie rate and substi­tuting values produced by the circu­latory model, West could calculate the value of the scaling exponent. It was 0.75; the model successfully pre­dicted the 3/4-power scaling law.

Complications

At this pointthe model still described a fairly simple, idealized network of rigid tubes, which made it a pretty good representation of the vessel structure of trees. Before it could be applied to vertebrates, however, a major problem had to be resolved. In mammals, the heart pumps blood in rapid waves through the aorta, but the blood must slow down in the capillaries so that exchange processes ean oeeue. But the model depieted fluids moving at a eonstant rate throughout the network.

The solution finally came through a combination ofbiological and math-

ematical insight. Area-preserving branching, West explains, achieves what designers of electrical grids call impedance matching. Where the pulse wave is strang, it minimizes the energy lost or reflected back up the network at each branch point. And in mamma­lian blood vessels, for the first several branchings after leaving the heart, area-preserving is indeed the rule. But the viscosity of blood eventually dampens the pulse, which is barely detectable by the time blood reaehes the capillaries. As the pulse wave di­minishes, branching that increases in total area becomes more energetically efficient. "And area-inereasing," West says, "has the wonderful effect that it slows the blood down." Through a series ofcomplex manipulations, West determined exaetly how and where the branching pattern should change to achieve optimal efficiency in net­works with pulsatile circulation. The general model could now be applied to mammals; all that remained was to explore its implications.

The Science paper contains a tour­de-force table comparing observed sealing exponents for the mamma­lian cardiovascular and respiratory systems with values derived from the model. (A separate paper presenting more details and predictions for plant systems has been submiued for pub­lication.) The model correctly pre­dicts a wide array ofknown allomet­rie relationships-quarter-power and otherwise~including scaling expo­nents of -1/n for capillary density and blood oxygen affinitYj -1/4 for heart rate and respiratory frequency; 1/4 for circulation time; 3/8 for aortal and tracheal radiusj 1/4 for cardiac output, oxygen consumption rate, and metabolie rate; and even the puzzling 11/n-power sealing of lung surface area, a relationship known as Weibel's Paradox.

The trio's Nature article presents details of some ofEnquist's disserta­tion work, including his original ob­servation that, based on rates of xylem transport and ehe sealing of stern di­ameter to mass, an analog of Kleiber's Law P/4-power allometric scaling of

889

Fractal-like branching supply nerworks, such as the human cardiovascular system and plant vascular systems, are ubiquitous in nature and may represent a common evolution­ary solution to the problem of distributing nutrients through­out mulricc1lular organisms. A new model of allometric seal­ing uses the physical and math­ematical requirements of such networks to explain a long­standing biologie al mystery. Illustration: Gloria Sharp.

metabolie rate) applies for plants. This work also shows that, at least in plants, the constraints imposed by re­souree distribution networks in individuals ean influence higher levels of biological organization.

Specifically, the research­ers build on predictions of their general model to show why plant population den­sity should sc ale as the _3/4 power of body mass, aprediction supported by empirical data and identieal to known reJationships between size aod population density in animals. The extended model also predicts that total resouree use by plants per unit land area in different habitats should be independent of plant size­the same amount of resouree ean support a few big trees or a large nuruber of smaller plants. Here again, thc pattern eoincides with previous data from anima I populations. Thus, the authors eonclude, "a eommon body of allometrie theory promises to provide a general framework for explaining many features of biologi­eal diversit}'."

Rcaction: hopeful

The work by West, Brown, and Enquist is impressive, but is their model the general theory that has been eluding students of allometry for years? Ex­perts in the field say it's a good start-but how good remains to be proven. "Ir does do a neat job of

890

explaining how things eould be," says William Calder, a biologist at the University of Arizona. 'Tm willing to believe it, at least undl someone tears it apart." Prineeton biologist John Bonner agrees that time will tell how widely applicable the model iso "It's a genuine advance," Bonner says, "but it may turn out to apply only to a particular group of organ­isms." Several critics have pointed out that eirculatory systems often deviate from perfeetly symmetrieal, fraetal-like branehing, a fact that the New Mexico team does not deny. They counter that unless these devia­tions are extreme, the model's pre­dictions are not altered substantially.

Another eautionary note comes from biologists who question how precise and how prevalent quarter­power scaling rclationships really are. Oxford University evolutionary ecologist Paul Harvey thinks that over the years, the search for a gen­eral theory has caused allometry re­searehers to see quarter-power seal­ing in da ta that are actually clouded with statistical variation. "The esti-

mates of exponents are not that ac­eurate," Harvey says. To some ex­tent, it seems to be a matter of per­spective. In every allometric plot some species do veer away from the general trend. But, West and others say, over large size ranges the pat­terns are intriguingly eonsistent. "If you look at a11 the evidenee," West says, "it's pretty hard not to con­c1ude that quarter powers are play­ing some very curious role."

Although Beuchat calls rhe model a "stunning sueeess" for vertebrates, she also adds a caveat-sorne organ­isms that do seem to fo11ow the quar­ter-power patterns appear to lack branching distribution networks. Such taxa may, however, have some nonobvious means of nu trient distri­bution that mimies the essential be­havior of branehing systems. "With a model now in hand that prediets how supply distribution systems should behave, even in single cells, we may diseover features of simpler organisms that were previously over­looked," Beuchat says. But if a seareh for fractal-like distribution networks in simple organisms comes up empty, she adds, the model's claim of gen er­ality may be difficult to uphold.

For their part, West, ßrown, and Enquist believe that the model's prin­ciples will hold where strueturally branehing supply networks are not obvious. How resourees are distrib­uted within ce11s, for example, is not weIl known. "One predietion is that, if we really knew how resomees are supplied to the metabolie machinery in the mitoehondria, we will find at least thc essenee of the struetural and functional properties of our model," Brown says. Indeed, West and another co11aborator, William Woodruff, of Los Alarnos National Laboratory, have already produced da ta suggesting that the 3/4-power mass-energy relationship holds at the intraeellular level. Their latest mouse-elephant eurve spans 26 or­ders of magnitude, from hfe's small­est energy-producing unit-the ey­toehrome oxidase molecule in the mitochondrion-to the blue whale.

BioScience Vol. 48 No. 11

An evolutionary alternative

Kozlowski and Wein er view lifc­and evolution-at a different level. Their foeus is on life hiscory rfairs in mammals-things such as growth, mocralit)', and reproduction.ln seek­ing to understand the evolution of variation in these characteristics, bi­ologists have long noted some i111-portant tradeoffs. Species that grow quickly tend to produce larger and more frequent litters of faster-wean­ing offspring, but ehey da so Qver a shorter lifcspan. Siower-growing spe­eies have smaller litters, but they continue reproducing longer and of­ten provide better eare for thei[ YOllng. Much of this variation is size related-smaller species tend to live "faster" lives than large ones. But even for different spccies of iden ti ca 1 sizc, different combinations of life history parameters are possible. Harvey ealls chis variation «the slow­fast eontinuum."

Kozlowski and Weiner view size not as a determining variable from which other things follow but as the outeome of an evolutionarily mo­mentous "dccision" to stop growing larger. Strategies about when to stop allocating resourees to growth and start alloeating them to reprodue­rion are part of the genetie heritage of every speeies. Bur these strategies are not fixed-se1ection peessures con­tinue to operate and, the researehcrs assurne, favor those individuals that time this switeh so as to maximize theie lifetime reproductive output.

Thus, for every speeies there is an optimal body sizc, whieh is reached at the point when energy invested in further growth is no longer repaid by an increase in energy available for rcproduetlon later in life. This opti­mum can be calculated from equa­tions that describe how rates of growth and mortality, or of lift:: ex­pectancy, scalc with size. For ex­am pie, if two species follow identi­eal growth eurves but differ in mortality rate, the one with the tower life expectancy should mature at a smaller size, and start producing

Novemher 1998

" " -;;; y

'" ~ -~ = y

HP

H,.

10- ~

o 10-· <> ~ -Q,) Unlcellular Organlsms :r

10-1

10- "

10- '1 10- '

Homeotherms

10-· ,o- ~ H" ,,)'

Mass (gI

Allometric scaling of metabolie rate for aselection of homeotherms (hirds and mammals), poikilothcrms (fish, reptiles, amphibians, and invertebrates), and uni­cellular organisms. Allometric scaling laws describc how various parts and charac­teristics of living organisms vary (or "scale") in proportion to body size. The solid !irres allilave a slope of 0.75. Modified horn a graph by A. M. Hemmingsen.

young sooner. The other speeies can afford to grow larger, thereby in­creasing thc size and survival prob­ability of its offspring. Sjmilarly, on an evo[uc[onJry scale, variation in adu It body size within speeies stems from differences in alloeation strate­gi es among individuals. Ir is at this intraspecifie level, Kozlowski and Weiner emphasize, that natural se­leetion sorts winning strategies from losing ones. They argue that before allametrie sealing across speeies can be explained~ one must first under­stand the eauses and eonsequences of withill -speeies sizl;! variation.

The researchers aeeept that for eaeh speeics, boJy size and life his­tory parameters co-vary according to aHornetrie relationships similar to Kleiber's Law. But they explicitly ass urne that the scaling exponents­for metaholie rate, for example­differ between speeies. This assump­tion is based on the observation that

species oeeupying different positions along the slow-fast continuum~ with different combinations of life his­tory parameters, may have the SillTIe optimal body size. Physiologieal pro­cesses such as metabolism and growth do scale with body mass, hut the precise form these relationships take-the value of the sealing expo­nents-may differ from one species to another. In Kozlowski and Weiner's argument, the chain of eau­sation hegins with ecological fea­tures, such as resource availability or predation risk, wh ich are likely to vary hetween speeies. For each kind of organism, these faetors determine which allocatiofi strategies will he most successful.

Thc model operates through simu­lation; fiO real data are used. Rather, for a number of imaginary speeies, intraspeeifie sealing factors for growth and mortality are chosen ran­domly from a biologically plausible,

891

bell-shaped distribution, Random­iZ<ltion intro duces the assumed varia­tion in size-energy scaling relation­ships across species. Optimal body SLze for each model organism can ehen he ca1culated based on its ran­domly assigned scaling parameters. Thc simulation thus produces a set of species that have "evolved" tu different body sizes, in keeping wirh initial differences in life history.

When rnouse-elephant curves are plotted Iinking these computer-gen­erated taxa, two interesting things happen. The model indeed produces strong cross-species scaling patterns that c10sely resemble known empiri­cal allometries. But the scating expo­nents that emerge from these simu­lated, interspecific plots may differ from those characterizing size-related changes within each model species. A mouse-e1ephant curve with a slope of O. 75, foe example, may appear even when the average intraspecific scaling exponent for all of the speeies in the al!ometry is same lower value.

A statistical artifact?

Ir is this difference between the \o;rithin-species and cross-species scal­ing exponents that, Kozlowski and Weiner believe, poscs a problem for big-picture theories of allometry. In (heir model, causatity operates onry at the level of body size optimization wichin species. Nothing is said ab out design constraints or shared charac­teristics among organisms. Yet strang cross-species patterns are produced anyway-seemingly by accident. "The main point of our model is that the same physiological process­meta bohc rate for example-may have a different slopc on the intcr­specific and intraspecific level," Kozlowski says. He and Weiner a1'­gUt that if size alone is a causa I variable that determines rates of rnetabolism and growth, via same mechanism such as that proposed by \Vest et al., then scaling patterns should be identical within and across spccies. In the absence of such a partern, an)' fllnctional explanation

892

foe size-energy sealing should be sought at the level at which selection operates-within spceies. Life his­tory allometries across species are just incidental statistical patterns genera ted by body size optimization.

The Kozlowski-Weiner model does not explain why different bio­logical variables should exhibit quar­ter-power scaling at any level. Given constraints on the plausible range of va lues for life history parameters, the simulations do produce slopes for size-energy allometries that cen­ter more or less around 0.75. But there is no reason to expeet any par­ticular value-which leads back to the argument about what the eom­parative biological data really show. "In my opinion, it is belief and not empirical fact [that] the exponent is exactly 0.75," says Kozlowski. On the other hand, the model does ac­count foe same of the known varia­tion in empirica! patterns, inclllding animals oE ehe same size with difter­ing liEe histories. And it correctly reproduces the right-skewed distri­bution of mammalian body size, in which size varia.tion is greater for animals of above-average size than for animals of below-average size.

Harvey says that the work has broad implications for allomeny studies in general. "Ir says that the interspeeifie exponenrs per se have no intuitive explanation," he notes. "They are revealing deep principles, which West et a1. will have to come to terms with." Gitdeman agrees that the Kozlowski-Weiner model brings an important new perspeccive to scal­iug relationships. "TheY'1'e not say­ing that the laws of allometry are wrong," he observes. "Just that by trying ro explain the whole mouse­elephant curve, you might came up with the wrong explanation. You have to look at what individual mice and elephants are doing."

But, Calder counters, such a change in perspective is also, at least to some extent~ changing the su bject. "The reason aHometry works is that if you get a big enough size range, size swamps everything else," Calder

says. "When you start talking about intraspecifie variation, that size range is very much shortcr. It's na longer the same kind of analycical cool." Brown agrees that difterences be­tween the within- and cross-species scaling relationships are to be ex­pected, and he seems puzzled by the significance Kozlowski and others read into this variation. The New Mexico trio also point out that by ming randomization, the Kozlowski­Weiner model rests on an assumed­but never explained-set of scaling values for growth and mortality.

A common thread

Ultimately, Gittleman says, both models may serve to steer aHornetry research toward a more rigorous approach to data collection and hy­pothesis testing. "The West et al. paper in particular says there should be causal links among all these a][o­metric variables," he observes. Wich data from carefully chosen model systems, Gittleman continues, "we can see whether some of these net­work properties reaUy da extend up to very high level organismal charac­teristics." He notes that the two ap­proaches are alike in one important respect: botb assume that at same level, energy use is optimized.

Whether or not the tWO ap­proaches can be reconcilcd around this unifying theme remains to be seen, but the New Mexico research­ers are eager to explare further im~ plications of their transport model at the levels of species life history and ecology. "I think it's an extremely interesting challenge to show that the two models are reconcilable," West sa ys. If common constraints on energy 'distribution and allocation do indeed reverberate thruughout mueh of life, and across different levels oE biologie al organization, the range of possible evolutionary out­comes may be even narrower than biologists have long believed. 0

Scott Norris is a freelance science writer based m AJbuquerque, New Mexico.

BioScience Vol. 48 No. 11