Marin 1997

Ecological Modelling 105 (1997) 6582

A simple-biology, stage-structured population model of thespring dynamics of Calanus chilensis at Mejillones del Sur Bay,

Chile

Victor H. Marn *

Depto. Ciencias Ecologicas, Facultad de Ciencias, Uni6ersidad de Chile, Casilla 653, Santiago, Chile

Accepted 29 July 1997

Abstract

The population dynamics of Calanus chilensis (Copepoda: Crustacea) was analyzed using a mixture of field dataand mathematical models. Field data were obtained in the Humboldt Current upwelling area, at Mejillones del SurBay (northern Chilean coast) during the spring of 1990 and 1991. Those data were used to set the parameter valuesand functions of a stage-structured population model (SSPM). The model was built and run with STELLA-II version3.07, an interactive, iconographic modeling software. The results show that C. chilensis has a generation time of 20days, and that its population dynamics in the spring is controlled by upwelling events, which affect both its growthrate (food dependence) and its local population size (advection). 1997 Elsevier Science B.V.

Keywords: Calanus chilensis, upwelling, population model; Chilean coast; Copepods; STELLA II

1. Introduction

1.1. The problem

Population regulation in marine organisms is arecurrent issue in biological oceanography,fisheries ecology and conservation (Laevastu andLarkins, 1981; Sinclair, 1988; Angel, 1994). Sin-clair (1988) has proposed the member:vagranthypothesis, which emphasizes the effect of ocean

circulation in the life cycle of marine animals. Thehypothesis proposes that the populations of spe-cies with complex life cycles are regulated, to alarge degree, by physical oceanographic processes.The fact that holopelagic species are not ubiqui-tous has been used to suggest that their distribu-tion patterns are actively maintained (Angel,1994). The maintenance mechanism implies lifecycles finely tuned to water circulation patterns(Verheye et al., 1991; Angel, 1994). Calanoidcopepods are good examples of animals with lifecycles tuned to the physical characteristics of* E-mail: [email protected].

0304-3800:97:$17.00 1997 Elsevier Science B.V. All rights reserved.

PII S 0304 -3800 (97 )00139 -7

V.H. Marn : Ecological Modelling 105 (1997) 658266

marine ecosystems (Marn, 1986, 1988; Conover,1988). Different species, however, seem to haveevolved different successful solutions for this tun-ing process for a given ecosystem. For antarcticcalanoid copepods, Marn (1988) has shown thatthree abundant species (Calanus propinquus,Calanoides acutus and Rhincalanus gigas) havedifferent life cycles. Two of them (C. acutus andR. gigas) show strong vertical seasonal (ontoge-netic) migration, two (C. acutus and C, propin-quus) have a 1-year life cycle, and the other has a2-year cycle. All three species are endemic of theAntarctic Ocean and do not occur north of thePolar Front (Antarctic Convergence).

In some coastal areas, such as eastern boundarycurrents, upwelling is the dominant advective fac-tor that explains much of the spatial and temporalchanges in the ecosystem (Marn et al., 1993;Strub et al., in press). The Humboldt Current,which runs parallel to the coasts of Chile andPeru, is one of the large eastern boundary currentsystems (Shermann, 1995). Calanus chilensis is oneof the most abundant, endemic, calanoid cope-pods of the upwelling areas of this current and akey herbivore (Gonzalez, 1993; Escribano andRodriguez, 1994; Marn et al., 1994). From thestandpoint of its general distribution, this speciescan be described as neritic and epipelagic. That is,it is abundant year round in the coastal zone(B10 km offshore; Gonzalez, 1993; Escribanoand Rodriguez, 1994).

One of the mechanisms that explains themaintenance of calanoids in upwelling areas is theinteraction between ontogenetic vertical migrationand the vertically separated onshoreoffshore wa-ter flows (Smith, 1984). In this case, adults arecarried offshore and sink to the onshore (deeper)flow that then brings the eggs back to the up-welling area. Other authors (e.g. Verheye et al.,1991) suggest a behavioral mechanism involvingdiurnal vertical migration in relation to flow re-versal.

Analysis of the distribution of C. chilensis in theChilean coast shows that this species does notperform ontogenetic vertical migration (Gonzalez,1993). However, the duration of the life cycle ofC. chilensis is uncertain and only few data areavailable on its biology. In this situation, there are

two general approaches to propose for furtherresearch: (1) keep collecting biological data ontopics related to the life cycle of the species,together with current measurements; or (2) assem-ble the scanty information on both the biologyand physics of the system and construct a prelim-inary model that may, hopefully, shed some lighton what aspects of the research should be empha-sized.

1.2. The approach

The philosophy put forward by Powell et al.(1990) for the Global Ocean Ecosystems Dynam-ics Program (GLOBEC) has been followed: thefirst step (in the GLOBEC Program) should be amodeling effort to determine how well we are ableto put together our present knowledge of physicaloceanography with the known population biologyof marine organisms that have numerous, distinct,planktonic life stages. However, the development,calibration, and validation of a model againstexisting data are complex activities that most ofthe time separate the scientists into modelers andempiricists (Rykiel, 1996). Thus, the successfuluse of the GLOBEC approach requires a bridgebetween these two groups of scientists. In myopinion, easy-to-learn iconographic modelingsoftware such as STELLA II represents an impor-tant component of that bridge (Hannon andRuth, 1994). STELLA II substantially decreasesthe amount of time that the researcher needs tospend in computer programming, thus makingmodeling available for a wider spectrum of peo-ple. Furthermore, even if a biologist is keen to usethe GLOBEC approach, the generation of three-dimensional circulation models with incorporatedbiology requires a powerful UNIX-based com-puter, with a minimum of 256 megabytes (MB) ofRAM (A. Sepulveda, EIMS Project, Dept. Cs.Ecologicas, Universidad de Chile, personal com-munication). These classes of computers may notbe financially obtainable for many scientists work-ing in developing nations. Simple software run-ning on Windows-based personal computers isthen an alternative to start the modeling ap-proach. This paper shows an example of how touse STELLA II to build a simple-biology, popula-

V.H. Marn : Ecological Modelling 105 (1997) 6582 67

Fig. 1. Geographic location of oceanographic stations at Mejillones del Sur Bay (MB). Station B was located inside the Bay, stationP was located near the point where upwelling occurs.

tion dynamics model (Nival and Carlotti, 1993).Simple biology means that development time isconsidered constant, egg production is forced byphytoplankton (chlorophyll-a) concentrationonly, and mortality is a constant fraction of thepopulation. The specific example is a stage-struc-tured population growth model (GLOBEC, 1993)of C. chilensis. Using a mixture of field dataanalysis and mathematical modeling, the interac-tions between coastal upwelling and the life cycleof C. chilensis (Copepoda: Calanoida) are dis-cussed.

2. Methods

2.1. Field data

2.1.1. Zooplankton samplesVertically integrated (bottom, 40 m, to surface)

zooplankton samples were collected, with a 200mm mesh open net, at two stations in the Mejil-lones del Sur Bay area (2305%S, 7020%W) duringSeptemberOctober 1990 and 1991 (Fig. 1). Anaverage of 10 samples was collected at each sta-tion each year. Individuals of C. chilensis werecounted and identified to adults, copepodite stageand nauplius 6. Eggs or earlier naupliar stageswere not counted because the mesh size was toocoarse for their reliable quantification.

2.1.2. En6ironmental dataData on wind stress, temperature and phyto-

plankton (chlorophyll-a) were collected as part ofa research program on Mejillones Bay, Chile.Most of that information, at least for the 1990period, has been published elsewhere (Marn etal., 1993). There a full account of the methodsused in measuring those variables is given. For thesake of completeness, only a brief description ofthem is given below.

Alongshore wind stress (ty) was calculated fromlocal wind records according to the formula:

tyraCd(VyVy) (1)where: raair density (1.22 kg m3), Cdempirical drag coefficient (0.0013) and Vyalongshore wind velocity. The value ty was usedto estimate the Ekman Transport (ME), which is aparametric way to analyze the upwelling process,according to the formula (Bowden, 1983):

MEty

f(2)

where fCoriolis parameter.Sea surface temperature was measured at sta-

tion B, in Mejillones Bay, by means of reversingthermometers. Finally, water samples from atleast four levels within the euphotic zone, werecollected with Niskin bottles at Station B. Chloro-phyll-a was determined from each sample using aspectrophotometric technique (Strickland andParsons, 1972).


Fig. 2. Diagram of the stage-structured population model (SSPM) built using STELLA II software. State variables appears assquares, one for each developmental stage. Basic equations governing the model can be found in Appendix A.

2.2. A stage-structured population model (SSPM)for C. chilensis

The stage-structured population model (SSPM)built for C. chilensis is shown in Fig. 2. The statevariables are the abundance of nauplius 6, cope-podite stages (from I to V) and adult females.These variables are functions of food-dependentegg production, mortality, molting to the succes-sive stage and wind-dominated advection. Themodel has eight parameters and two forcing func-tions (Table 1). The choices of parameter valuesare explained below. The model was designed torun for 60 days, in order to compare the resultingabundance of copepods with the information

gathered in the field.Time change (using Stella II notation), for each

variable, is calculated on a daily basis as:

Ci(t)Ci(tDt)

(moltC(i1)moltC(i1)mortCi

AdvecCi)Dt (3)where: Ci(t) is the abundance of the stage i attime t, and Dt1 day. The first two terms in theright hand parenthesis represent molt from theprevious stage to the next, mortCimortality ofCi and AdvecCiadvective losses. For the case ofnauplius 6, the first molting term is replaced by:

PopGrowthEggProd:EggStDur (4)


Table 1Parameters (p) and forcing functions (ff) for the stage-structured population model of Calanus chilensis (see text for details)

UnitsCategory ExplanationParameter and forcing func-tions

p Pooled stage duration time from egg to N6 DaysEggStDurDaysStage duration time from nauplii 6 trough copepodite IVN6CIVStDur p

Stage duration time for copepodite V DaysCVStDur pp Mortality rate for nauplii 6mortRateN6 Days1

Mortality rate from copepodite I through IV Days1pMortRateCICIVMortality rate for copepodite V and females Days1MortRateCVFem p

NoneVertical migration parameter for copepodites I through IIIMIGc1 pp Vertical migration parameter for copepodites IV, V and femalesMIGc2ff GRAPH(TIME)of chlorophyll-a concentrationFood mg l1

NoneGRAPH(TIME) of relative Ekman transportMe ff

where:

EggProdFemales(0.08 (Chla0.87)) (5)

and Chlachlorophyll-a concentration (mg l1).

2.2.1. Generation time and stages duration timefor C. chilensis

There are no data in the literature regarding thegeneration time, Tgen, of C. chilensis. Several ap-proximations were required to arrive at the valueused in the model. First, Tgen was estimated fromfield-determined temporal changes of the stagestructure (see Section 3). Second, a literaturesearch was done to look for Tgen data for otherspecies of the genus Calanus, especially thoseclosely related to C. chilensis, such as C. australis(Marn et al., 1994). Under laboratory conditions,Peterson and Painting (1990) estimated Tgen for C.australis to be 21 days at 15.5C, a temperatureclose to those measured at Mejillones Bay (Fig.3A). Bradford et al. (1988), also estimating Tgenfor this species, arrived at a similar number (23.8days). Finally, the method discussed by Huntleyand Lopez (1992) was used. There they proposedglobal equations relating temperature to a set ofpopulation parameters for copepods. For Tgenthey suggest the following equation:

Tgen128.8 exp(0.120T) (6)

where T temperature in C. If we evaluate Eq.(6) for 15C, it gives a Tgen21 days. This comesclose to the laboratory estimation of Peterson and

Painting (1990) for C. australis and the lower Tgenestimated for C. chilensis using field data. Thus,for the SSPM model a generation time of 21 dayswas used.

In order to build a stage-structured populationmodel, Tgen has to be divided into stage-by-stageduration times, from eggs to adults. As explainedearlier, data were not available for egg abundancenor for nauplii 15. Thus, to compare the modelwith the field data, the stage duration times fromeggs to nauplius 6 were pooled in one parameter:EggStDur (Table 1). Stage duration times fromnauplius 6 to copepodite V were estimated fromdata on C. australis (Peterson and Painting, 1990).SSPM stage duration times are shown in Table 4.Those stage durations are in close agreement withthe temporal changes in stage structure observedin our field data (see Section 3). The number ofindividuals molted per unit of time were thencalculated as a fraction of the stage duration (seemolt terms in Appendix A).

Stage-specific mortality rates for Calanus cope-pods are not readily available in the literature(Carlotti and Radach, 1996). Following Nival andCarlotti (1993), mortality was considered as aconstant fraction of the population. However,three different terms were used, based on informa-tion from Carlotti and Radach (1996): one appli-cable to nauplii 6, a second mortality term forcopepodite IIV and a third applicable to cope-podite V and females. Normal-run, maximum andminimum values for the stage-specific mortalityrates are given in Table 2.


Fig. 3. Environmental variables measured at Mejillones del Sur Bay during SeptemberOctober 1990 and 1991. (A) Ekmantransport, (B) spectral analysis of the Ekman transport, (C) sea surface temperature, (D) integrated chlorophyll-a.

2.2.2. Population growth and chlorophyll-aGrowth of the C. chilensis population in the

SSPM model is accomplished by food-dependentegg production (Eqs. (4) and (5)). The numericalvalues and the form of Eq. (5) were obtained fromthe work of Peterson and Bellantoni (1987) on C.chilensis at Concepcion Bay (Southern ChileanCoast). The maximum egg rate found by theseauthors was of the order of 25 eggs female1

day1; this value is similar to that reported by

Attwood and Peterson (1989) for C. australis inthe Benguela upwelling system. Thus, Eq. (5) wasused only to a food concentration up to 30 mgChla m3; above this value, EggProd was as-sumed to be food independent and equal to amaximum rate of 26 eggs female1 day1. Themodel was also run with a constant maximum eggproduction in order to analyze the idea of food-independent population growth (Escribano andRodriguez, 1995).

Temporal changes in chlorophyll-a concentra-tion (Chla in Eq. (5); Food in Appendix A), aforcing function in the model, were incorporatedusing the GRAPH(TIME) function of STELLAII. The daily values of the function were thosemeasured in the field.

2.2.3. Ekman transport and the ad6ection termsThe advection terms (AdvecCi, Eq. (7)) were

considered as being negative all the time; theseterms remove organisms. This condition was

Table 2Stage-specific mortality rates used in the SSPM (see text fordetails)

Definition Stage

CVFemN6 CICIV

0.05Maximum 0.10 0.100.040.06Normal run 0.08

Minimum 0.02 0.020.05


Table 3Ekman transport periods. Numbers in m3 s1 km1

YearPeriod

1990 1991

I 3839382 (100%) 3509304 (87%)II 7869495 (63%) 5869223 (38%)

5349311 (58%) 5009533 (106%)III

The ME time series was divided, according to the changesobserved in Fig. 3A, in: days 130 (period I); days 3140(period II); day 4161 (period II). Data correspond tomean9S.D. (coefficient of variation).

3. Results

3.1. Field data

3.1.1. En6ironmental 6ariablesDuring the period studied, both in 1990 and

1991, ME was positive, indicating favorable up-welling conditions (Fig. 3A). The average trans-port was similar for both years (t-test1.0,d.f.60, P\0.30). The fast Fourier transform(FFT) of the 1990 and 1991 ME values, however,revealed differences between years (Fig. 3B). Thespectral analysis for 1990 shows a dominant fre-quency centered on 0.25 day1. On the otherhand, during 1991 the analysis showed a decreas-ing trend with frequency (P0.01), with peaks at0.02, 0.08, 0.13, 0.27 and 0.43 day1. For theSSPM, the 1990 ME time series was used as thewind forcing function in the normal run (seeAppendix A).

Sea surface temperature (SST) was very similar,both in value (P0.08, d.f.9) and temporaldynamics, for 1990 and 1991 (Fig. 3C). Duringthe first 30 days, it remained relatively stable(30-day average15.8C in 1990 and 16.2C in1991), corresponding to the period of lower valuesand higher variability in ME (Table 1). At thebeginning of October (day 32 onwards), ME wasmore steady, presenting lower day-to-day variabil-ity (Table 3). Lower temperatures, correspondingto the most intense upwelling event, characterizedthat period in both years (Fig. 3C). After thatperiod, the Ekman transport decreased in inten-sity and increased in variability. Thus, SSTshowed that a single main upwelling event (i.e.decrease in temperature at day 40) could be iden-tified against a constant background of conditionsfavorable for upwelling (Fig. 3A).

Chlorophyll-a fluctuated during both the springperiods of 1990 and 1991, following the dynamicsof the main upwelling event (Fig. 3D). During thefirst 50 days in 1990 the average euphotic zoneintegrated chlorophyll was 80 mg m2; while in1991 this value was 47 mg m2. After the up-welling event, chlorophyll-a increased to 436 mgm2 in 1990, due to a red tide bloom (Marn etal., 1993), and to 120 mg m2 in 1991.

based on wind analysis of the Mejillones areapreviously conducted by Marn et al. (1993).There the authors show that favorable upwellingconditions occur throughout the spring period(SeptemberOctober). Thus, the model, as writ-ten, should not be used for other times of the yearwhen that assumption might not necessarily ap-ply.

The Ekman transport, a forcing function in theadvection terms (see Eq. (7) below and AppendixA) was built using the STELLA II GRAPH(-TIME) function and field-determined ME data(see Section 3; Table 3). ME series, for each year,were divided by their maximum value to yield adynamic term with a range between 0 and 1. Anadditional parameter in the advection term is themigration component (MIGc1 and MIGc2,Table 1). All stages from copepodite I to femaleswere allowed to migrate vertically. In this simplemodel, however, daily migration is set as aparameter that interacts with the Ekman trans-port in the following way:

AdvecCiCiME(1MIGc i) (7)MIGc1 and MIGc2 had values ranging from 0(no migration or full wind effect) to 1 (wind effectis absent). MIGc1 applied to CI through CIII,and MIGc2 to CIV through females. This sepa-ration of vertical migration capacities has beendocumented for calanoid copepods in upwellingareas (Verheye et al., 1991).


Fig. 4. Temporal changes of stage specific abundance for Calanus chilensis at Mejillones del Sur Bay during 1990. Numbers in they-axis are in organisms per m3.Fig. 5. Temporal changes of stage-specific abundance for Calanus chilensis at Mejillones del Sur Bay during 1991. Numbers in they-axis are in organisms per m3.


3.1.2. Temporal fluctuations of abundance andpopulation stage structure of C. chilensis

Despite similarities between years, the springabundance of C. chilensis in 1990 (average748organisms m3, Fig. 4) was one order of mag-nitude higher than that in 1991 (average81copepod m3, Fig. 5). Abundance at both sta-tions (A and B) was not significantly different(P\0.9). Thus, data from both stations werepooled for further analysis. During 1990, nau-plius 6 were most abundant during the first 30days (average145 organisms m3), then de-creased to 10 organisms m3, and finally in-creased to 50 organisms m3 during the lastsampling date (Fig. 4A). The following year,their abundance remained at around 1 organismm3, for the first 40 days, and increased to 108organisms m3 during the last 20 days (Fig.5A). In both years, however, the abundance ofnauplii was lowest during the period when Ek-man transport was at its highest.

Temporal changes in abundance of cope-podites IIV were well correlated, both in 1990and again 1991 (PB0.05; Figs. 4 and 5). Theoldest copepodite stage (CV) showed a some-what different pattern. In 1990, their maximumabundance was delayed 4 days from the otherstages, with the maximum for adults delayed by2 days from that of CVs (Fig. 4C). During1991, however, the abundance of copepoditeswas very much depressed throughout the entireperiod of study (Fig. 5). The average summedabundance of stage IIV was close to 1.0 or-ganisms m3 during most of the period, with asharp increase toward the end. On the otherhand, CVs never reached 10 organisms m3

even at their peak abundance.Temporal changes in the abundance of fe-

males followed almost an inverse trend thanthat of the nauplii (Fig. 4D and Fig. 5D). Dur-ing 1990, adults remained below 50 organismsm3 for the first 30 days and increased tonearly 150 organisms m3 for the rest of theperiod (Fig. 4D). On the contrary, during 1991a single burst of adults was observed during the12th day ($200 organisms m3); the rest ofthe time their abundance remained below 10 or-ganisms m3 (Fig. 5D).

Differences between 1990 and 1991, regardingC. chilensis, are even more striking if one looksat the relative composition of all developmentalstages and their changes during the period stud-ied (Fig. 6). At the beginning of spring in 1990(Fig. 6A), C. chilensis population was mostlycopepodite I and II ($22 and 50%, respec-tively). As spring progressed, there was a contin-uous shift toward older developmental stages,ending in October with a population composedmostly of adults (between 70 and 80%). Con-versely, during 1991 the population was quitedifferent, where it shifted from almost 100%adults, during the first 30 days, to 80% youngdevelopmental stages (nauplius 6$50%, cope-podite I$14%, Copepodite II$16%), withadults nearly absent (0.6%; Fig. 6B), for the re-maining 30 days of the study period.

Another way of visualizing these differences isby calculating the mean stage index, S(Marn, 1987). This index was used to study themesoscale spatial population structure ofcalanoid copepods. However, it can also be usedto study the temporal dynamics of a stagedstructure population. The index is a simpleweighted average of the mean developmentalstage of the population. S was calculatedfrom the following equation:

SS6i0 NiSiS6i0 Ni

(8)

where Sistage index, S0 (nauplius 6)0.1, S1(copepodite I)1, S6 (adults)6, and Ni isthe corresponding abundance for each stage.

During 1990, S increased from 1.9 to 5.4(S1.870.06 days; r20.83), as shown inFig. 7. Two sharp declines of S during 1990,which corresponds to recruitment of nauplii 6,were also observed. If we consider the lapse be-tween low values as an estimate of the popula-tion generation time, the data suggest ageneration time of either 20 or 36 days. Thedata from 1991 showed the reversed trend: thatis, a population dominated by old stages at thebeginning of the period that switched to youngstages at the very end.


Fig. 6. Temporal changes in relative abundance (%) of developmental stages of Calanus chilensis during 1990 (A) and 1991 (B). Thescale for the color pattern appears at the bottom of the figure.

3.2. Stage-structured population model (SSPM)output

3.2.1. Normal runInitial conditions and parameter values for the

normal SSPM run are shown in Table 4. Theinitial conditions corresponded to the maximumabundance observed during the first 10 days of1990. The resulting time series for each develop-mental stage are shown in Fig. 8. Fluctuations ofabundance were qualitatively similar, and withinthe same range, of those observed in 1990 (Fig. 4).The model showed the secondary increase in nau-plii 6 through copepodite III and also the lag in

peak abundance of copepodite IV and V. Thelargest difference between the normal run ofSSPM and the 1990 data corresponded to adultfemales. SSPM produced a peak abundance offemales within the first 10 days of the run (Fig. 8).Such increases correspond to the recruitment ofCVs, a situation that was not observed in thefield. This lack of evidence for female recruitmentin the field data may be explained by either amuch larger mortality, or by a larger advectioneffect. Those possibilities were studied through asensitivity analysis of the models parameters (seebelow). The third alternative is the possibility offield sampling errors.


Fig. 7. Temporal changes in the mean stage index S (see text for details) for Calanus chilensis during 1990 and 1991.Fig. 8. Outcome of the normal run of the SSPM. Numbers in the y-axis are in organisms per m3. See Figs. 4 and 5 for comparisonwith real data from Mejillones Bay.


A further visualization of the model behavior isobtained by a plot of the mean stage index Sthrough time (Fig. 9). Again, the main differencebetween the model and the 1990 data correspondedto the effect of female recruitment at the beginningof the run. The model, however, showed the sharpdecrease in S observed in 1990 after the up-welling event (see Figs. 7 and 9).

3.2.2. Sensiti6ity analysisThe effects of wind and vertical migration were

evaluated using the sensitivity analysis options ofSTELLA II. Time changes of the total copepodabundance were analyzed using: (1) normal values(Table 4) and wind data from 1990 (st90) and 1991(st91); (2) migration terms set to zero, with winddata from 1990 (W90m0) and 1991 (W91m0); and(3) migration terms set to 1 with wind data from1990 (W90m1) and 1991 (W91m1). The results ofthe analysis are shown in Fig. 10. These provideevidence that there are no qualitative differences,and that the curves are similar, although shifted in

the Y-axis, when either winds from 1990 and 1991are used (st90 and st91, Fig. 10). When verticalmigration is set to zero, i.e. full wind effect(W90m0 and W91m0, Fig. 10), the population goesto near zero in less than 20 days in 1990, and 40days in 1991. On the other hand, when migrationis set to one, i.e. wind advection does not affectorganisms (W90m1 and W91m1, Fig. 10), thepopulation grows explosively, especially after themain upwelling event. No combination of windeffect and migration, reproduced the changes incopepod abundance observed in 1991 (Fig. 5). Thesensitivity analysis of mortality rates showed nodifferences among SSPM runs if one uses the rangeof values from Table 2. Finally, in the case of apopulation not regulated by food and with amaximum and constant egg production of 26 eggsper female, the results are different from all previ-ous simulations and field observations (Fig. 11).

4. Discussion

The main objective of this work was to show anexample of how to use STELLA II to study thepopulation dynamics of a planktonic marine or-ganism. The specific example chosen was the studyof the life cycle of a calanoid copepod, C. chilensis,and its interaction with the coastal upwelling in thenorthern Chilean coast. Given this objective, thediscussion will deal with two issues: (1) What newinformation have we gained on the specific exam-ple chosen (i.e. upwelling dynamics and life cyclesof planktonic organisms)?; and (2) What is thepotential use of iconographic modeling software inglobal programs that require a balanced mixture offield data analysis and mathematical modeling?

4.1. C. chilensis and the coastal upwelling in theChilean coast

The results of the SSPM model, together withthe analysis of field data, support the idea that C.chilensis perform daily vertical migration. Thismigration, together with a food-dependent growthrate, explains the spring temporal variation ob-served at Mejillones del Sur Bay, Chile. Theseresults are similar to those obtained by Carlotti

Table 4Initial conditions and parameter values for the normal run ofthe SSPM

State variables (initial conditions)

Variable Value Units

N6 70 Organisms m3

Organisms m3350CIOrganisms m3700CII

1000CIII Organisms m3

460CIV Organisms m3

CV 60 Organisms m3

30FEM Organisms m3

Parameters

Parameter Value Units

EggStDur Days10N6CIVStDur 2 DaysCVStDur Days3mortRateN6 Days10.08

0.06 Days1mortRateCICIV0.04mortRateCVFem Days1

0.05MIGc1 NoneMIGc2 None0.60


Fig. 9. Temporal changes in the mean stage index S of the normal run of the SSPM.

and Radach (1996) for their modeling of theseasonal dynamics of C. finmarchicus.

Escribano and Rodriguez (1995) argued thatbecause C. chilensis seems to have a continuous (i.e.year-round) production in the Humboldt upwellingecosystem, this implies that these animals do notexperience food-shortage periods (p. 380). On thecontrary, the SSPM output for C. chilensis (Figs.4, 8 and 11) shows that food is a controlling factorin the spring development of this species. A poten-tial explanation for this disagreement is the differ-ence in temporal scale between this investigationand Escribano and Rodriguezs study; theirs was amonthly scale, while this study was daily.

A generation time, Tgen, for C. chilensis of 21 daysat 15C was used in the SSPM. This Tgen producedgood agreement between field data and SSPMresults. Thus, given a Tgen of 21 days, it is ratherdifficult to obtain population information withmonthly samples as used by Escribano and Ro-driguez (1995). Here it is an example of the kindof research guidance that field data analysis andsimple models can generate. In this specific case, it

is clear that a daily sampling program, or eventwice-a-day, of the C. chilensis population is neces-sary in order to determine Tgen more precisely.

The SSPM also shows that if the populationdoes not migrate vertically, the abundance falls tonear zero in about 10 days. Conversely, if thepopulation is allowed to migrate, the results com-pare favorably to those obtained in the field.However, given the preliminary way in whichmigration was set up in the model (see Section 2and Appendix A), little can be said about thespecific migration pattern. Peterson et al. (1979),in their study of the Oregon upwelling zone,argued that different zooplankton species aremaintained within the upwelling zone by a specificrelationship between their distributions and thecirculation patterns. The results of this study sug-gest that, at least for C. chilensis, there may notbe such a clear relationship. Indeed, the SSPMonly required that the population may not beaffected by wind advection on a daily basis (Fig.10). Thus, these model results suggest that al-though C. chilensis migrate vertically, changes in


Fig. 10. Temporal changes of the total copepod abundance in the SSPM. The runs correspond to the following conditions: st90,standard run; st91, standard run, using the wind conditions of 1991; W90m1, wind conditions for 1990 with migration terms set to1; W90m0, wind conditions of 1990 with migration term set to 0; W91m1, wind conditions for 1991 with migration terms set to 1;W91m0, wind conditions of 1991 with migration term set to 0.

abundance reflect the time evolution of the up-welling dynamics, both through food and advec-tion effects. That is, vertical migration does notcompensate for the general drifting problem, butit is more than likely an attenuation factor.

4.2. Iconographic modeling software

Through the development of a simple-biology,stage-structured population model (SSPM), it has

been shown that iconographic modeling software,such as STELLA II, can be used as a communica-tion link between two scientific activities: fielddata collection and mathematical modeling. Themodel developed here (see Appendix A) can beeither improved, if one wants to follow a straightmodeling approach, or be used as a hypothesis-generating mechanism that may highlight key un-resolved problems, that then will require furtherfield sampling programs. There are many details


Fig. 11. Outcome of the SSPM considering constant, maximum egg production. Numbers in the y-axis are in organisms per m3.

5. Conclusions

The simulation of changes in stage-specific abun-dance of copepods through a stage-structured pop-ulation model, SSPM, shows that the maintenanceand growth of a local population of C. chilensis atMejillones del Sur Bay, Chile, can be explained asa combination of advective forces and verticalmigration plus food-dependent egg production.

Easy-to-learn iconographic modeling software,such as STELLA II, can be an effective tool inclosing the gap between empiricists and model-ers whose interaction will be vital in the develop-

left aside by using this simple modeling approach,such as three-dimensional oceanic circulationequations, which requires more powerful model-ing platforms than the Windows95-based, Pen-tium-PC used for this paper. However, by usingthis approach, modelers may benefit from theinteraction with non-modelers and their insightsinto the characteristics of the ecosystems that theystudy. This may be especially true in fields such asmarine zooplankton and zooplanktoncirculationinteraction studies, where a large percentage ofthe information that appears every year is stilldescriptive in nature.


ment of marine global programs. These tools arealso available to scientists working in third worldcountries where budgets are unlikely to be avail-able for large computers. However, the use ofthese simple modeling tools should be consideredonly in the preliminary phase of the studies, atleast for three-dimensional advective systems suchas marine ecosystems.

Acknowledgements

This work was partially funded by projectsFONDECYT 268:89 and 1049:92 from CONI-CYT-CHILE and also by project EIMS (Environ-mental Information and Modeling System)awarded to Universidad de Chile by IBM Envi-ronmental Research Fund (IBM InternationalFoundation). The author is thankful to DonaldD. Adams (State University of New York, Platts-burgh) and to two anonymous reviewers for theircritical comments of the manuscript.

References

Angel, M.V., 1994. Spatial distribution of marine organisms.In: Edwards, P.J., May, R.M., Webb, N.R. (Eds.), Large-scale Ecology and Conservation Biology. Blackwell Sci-ence, New York, pp. 59110.

Attwood, C.G., Peterson, C.G., 1989. Reduction in fecundityand lipids of the copepod Calanus australis (Brodskii) bystrong pulsed upwelling. J. Exp. Mar. Biol. Ecol. 129,121131.

Bowden, K.F., 1983. Physical Oceanography of Coastal Wa-ters. Ellis Horwood Series in Marine Science. Wiley, NewYork, 302 pp.

Bradford, J.M., Ohman, M.D., Jillett, J.B., 1988. Larval mor-phology and development of Neocalanus tonsus, Calanoidesmacrocarinatus, and Calanus australis (Copepoda:Calanoida) in the laboratory. N. Z. J. Mar. FreshwaterRes. 22, 301320.

Carlotti, F., Radach, G., 1996. Seasonal dynamics of phyto-plankton and Calanus finmarchicus in the North Sea asrevealed by a coupled one-dimensional model. Limnol.Oceanogr. 41, 522539.

Conover, R.J., 1988. Comparative life histories in the generaCalanus and Neocalanus in high latitudes of the northernhemisphere. Hydrobiologia 167:168, 127142.

Escribano, R., Rodriguez, L., 1994. Life cycle of Calanuschilensis Brodsky in Bay of San Jorge, Antofagasta, Chile.Hydrobiologia 292:293, 289294.

Escribano, R., Rodriguez, L., 1995. Seasonality of size andgrowth of Calanus chilensis in northern Chile. Rev. Chil.Hist. Nat. 68, 373382.

GLOBEC, 1993. Population dynamics and physical variabil-ity. Report of the First Meeting of an InternationalGLOBEC Working Group, St. Johns College, CambridgeUniversity. GLOBEC Report No. 2. 104 pp.

Gonzalez, A., 1993. Distribucion espacial de dos copepodoscalanoideos Calanus chilensis (Brodsky) y Centropagesbrachiatus (Dana) en el norte de Chile. Tesis de Gradopara optar al grado de Licenciado en Biologa Marina,Universidad Austral de Chile, 69 pp.

Hannon, B., Ruth, M., 1994. Dynamic Modelling. Springer-Verlag, New York, 248 pp.

Huntley, M.E., Lopez, M.D.G., 1992. Temperature-dependentproduction of marine copepods: a global synthesis. Am.Nat. 140, 201242.

Laevastu, T., Larkins, H.A., 1981. Marine Fisheries Ecosys-tem. Its Quantitative Evaluation and Management. FishingNews Book, Farnham, 159 pp.

Marn, V., 1986. Distribution and life cycle of three antarcticcopepods (Calanoides acutus, Calanus propinquus andRhincalanus gigas). Ph.D. Dissertation, University of Cali-fornia, San Diego, CA, USA, 144 pp.

Marin, V., 1987. The oceanographic structure of the EasternScotia Sea. IV. Distribution of copepod species in relationto hydrography in 1981. Deep-Sea Res. 34, 105121.

Marn, V., 1988. Independent life cycles: an alternative to theasynchronism hypothesis for antarctic calanoid copepods.Hydrobiologia 167:168, 161168.

Marn, V., Rodriguez, L., Vallejo, L., Fuenteseca, J., Oyarce,E., 1993. Efectos de la surgencia costera sobre la produc-tividad primaria de Baha Mejillones del Sur (Antofagasta,Chile). Rev. Chil. Hist. Nat. 66, 479491.

Marn, V., Espinoza, S., Fleminger, A., 1994. Morphometricstudy of Calanus chilensis males along the Chilean coast.Hydrobiologia 292:293, 7580.

Nival, P., Carlotti, F., 1993. Zooplankton models. In: Popula-tion Dynamics and Physical Variability. Report of theFirst Meeting of an International GLOBEC WorkingGroup, St. Johns College, Cambridge University.GLOBEC Report, No. 2, pp. 6165.

Peterson, W.T., Bellantoni, D.C., 1987. Relationships betweenwater-column stratification, phytoplankton cell size andcopepod fecundity in Long Island Sound and off CentralChile. S. African J. Mar. Sci. 5, 411421.

Peterson, W.T., Painting, S.J., 1990. Developmental rates ofthe copepod Calanus australis and Calanoides carinatus inthe laboratory, with discussion of methods used for calcu-lation of development time. J. Plankton Res. 12, 283293.

Peterson, W.T., Miller, C.B., Hutchinson, A., 1979. Zonationand maintenance of copepod populations in the Oregonupwelling zone. Deep-Sea Res. 26, 467494.

Powell, T., Hofmann, E., Osborn, T., Price, J., Rotschild, B.,Roughgarden, J., 1990. Theory and modeling in GLOBEC:a first step. Report to the GLOBEC Steering Committeefrom the Working Group on Theory and Modeling, 9 pp.


Rykiel, E.J. Jr., 1996. Testing ecological models: the meaningof validation. Ecol. Model. 90, 229244.

Shermann, K., 1995. Large marine ecosystems and fisheries. In:Munasinghe, M., Shearer, W. (Eds.), Defining and Measur-ing Sustainability. The Biogeophysical Foundations. TheUnited Nations University and the World Bank, pp. 207233.

Sinclair, M., 1988. Marine Populations. An Essay on PopulationRegulation and Speciation. Books in Recruitment FisheryOceanography, Washington Sea Grant Program, Seattle,WA, 252 pp.

Smith, S.L., 1984. Biological indications of active upwelling inthe northwestern Indian Ocean in 1964 and 1979, and a

comparison of zooplankton in the southeastern Bering Sea.Deep-Sea Res. 31, 951967.

Strickland, J., Parsons, T.R., 1972. A practical handbook ofseawater analysis. Bull. Fisheries Res. Board Can. 5, 1128.

Strub, P., Mesas, J., Montecino, V., Rutllant, J. Coastal oceancirculation off western South America. In: Robinson, A.,Brink, K. (Eds.), The Sea. First Workshop on Coastal OceanAdvanced Science and Technology Studies (COASTS). IOC,Liege, Belgium, in press.

Verheye, H.M., Hutchings, L., Peterson, W.T., 1991. Lifehistory and population maintenance strategies of Calanoidescarinatus (Copepoda:Calanoida) in the Southern Benguelaecosystem. S. African J. Mar. Sci. 11, 179191.

Appendix A

Equations and terms of the stage-structured population model (SSPM) for C. chilensis. The model wasbuilt and run using the modeling software STELLA II (version 3.0.7 for windows). Comments appearin square brackets.

{Initialization}[Values for the standard run are given in Table 4; GRAPH(TIME) data were taken from Fig. 3]INIT N6INIT CIINIT CIIINIT CIIIINIT CIVINIT CVINIT Fem

FoodGRAPH(TIME)[(day, value)]

(0.00, 2.00), (3.16, 2.00), (6.32, 2.00), (9.47, 3.50), (12.6, 3.50), (15.8, 7.00), (18.9, 7.00), (22.1, 6.50),(25.3, 6.50), (28.4, 9.00), (31.6, 6.00), (34.7, 7.00), (37.9, 3.00), (41.1, 1.50), (44.2, 2.00), (47.4, 2.00),(50.5, 1.00), (53.7, 1.30), (56.8, 44.5), (60.0, 9.00)

MeGRAPH(TIME)[day, value]

(0.00, 0.222), (1.00, 0.203), (2.00, 0.291), (3.00, 0.138), (4.00, 0.11), (5.00, 0.894), (6.00, 0.715), (7.00,0.014), (8.00, 0.003), (9.00, 0.005), (10.0, 0.32), (11.0, 0.377), (12.0, 0.006), (13.0, 0.384), (14.0,0.002), (15.0, 0.07), (16.0, 0.465), (17.0, 0.39), (18.0, 0.121), (19.0, 0.32), (20.0, 0.193), (21.0, 0.171),(22.0, 0.019), (23.0, 0.022), (24.0, 0.212), (25.0, 0.299), (26.0, 0.204), (27.0, 0.763), (28.0, 0.276), (29.0,0.001), (30.0, 0.036), (31.0, 0.425), (32.0, 0.308), (33.0, 0.231), (34.0, 0.229), (35.0, 0.536), (36.0,1.00), (37.0, 0.743), (38.0, 0.146), (39.0, 0.279), (40.0, 0.885), (41.0, 0.15), (42.0, 0.001), (43.0, 0.768),(44.0, 0.401), (45.0, 0.273), (46.0, 0.276), (47.0, 0.349), (48.0, 0.322), (49.0, 0.229), (50.0, 0.241), (51.0,0.603), (52.0, 0.479), (53.0, 0.107), (54.0, 0.078), (55.0, 0.443), (56.0, 0.425), (57.0, 0.212), (58.0,0.201), (59.0, 0.388), (60.0, 0.549)

{Runtime equations}


N6(t)N6(tdt)(PopGrowthmortN6moltN6AdvecN6)*dtCI(t)CI(tdt)(moltN6mortCImoltCIAdvecCI)*dtCII(t)CII(tdt)(moltCImortCIImoltCIIAdvecCII)*dtCIII(t)CIII(tdt)(moltCIImortCIIImoltCIIIAdvecCIII)*dtCIV(t)CIV(tdt)(moltCIIImortCIVmoltCIVAdvecCIV)*dtCV(t)CV(tdt)(moltCIVmortCVmoltCI5AdvecCV)*dtFem(t)Fem(tdt)(moltCI5mortFemAdvecFem)*dtTotalCICIICIIICIVCVFemN6S ((N6*0.1)(CI*1.0)(CII*2)(CIII*3)(CIV*4)(CV*5)(Fem*6)):Total

{PRODUCTION and MOLTING TERMS}

PopGrowth (EggProd:EggStDur)EggProdIF (Food530) then (0.08(Food*0.87))*Fem ELSE 26moltN6N6:N6CIVStDurmoltCICI:N6CIVStDurmoltCIICII:N6CIVStDurmoltCIIICIII:N6CIVStDurmoltCIVCIV:N6CIVStDurmoltCVCV:CVStDur

{MORTALITY TERMS}

mortN6N6*mortRateN6mortCICI*mortRateCICIVmortCIICII*mortRateCICIVmortCIIICIII*mortRateCICIVmortCIVCIV*mortRateCICIVmortCVCV*mortRateCVFemmortFemFem*mortRateCVFem

{ADVECTION TERMS}

AdvecN6N6*MeAdvecCICI*Me*(1MIGc1)AdvecCIICII*Me*(1MIGc1)AdvecCIIICIII*Me*(1MIGc1)AdvecCIVCIV*Me*(1MIGc2)AdvecCVCV*Me*(1MIGc2)AdvecFemFem*Me*(1MIGc2){PARAMETERS}[See Table 4 for standard run parameter values and units]

EggStDurN6CIVStDurCVStDurmortRateN6mortRateCICIVmortRateCVFemMIGc1MIGc2

Date post:	21-Nov-2015
Category:	Documents
Upload:	heron-surbakti
View:	233 times
Download:	0 times

Marin 1997

Documents