cannibalism in a size-structured population: energy ... · 135 ecological monographs, 74(1), 2004,...

135

Ecological Monographs, 74(1), 2004, pp. 135–157q 2004 by the Ecological Society of America

CANNIBALISM IN A SIZE-STRUCTURED POPULATION:ENERGY EXTRACTION AND CONTROL

LENNART PERSSON,1,3 DAVID CLAESSEN,1,2,4 ANDRE M. DE ROOS,2 PAR BYSTROM,1,5 STEFAN SJOGREN,1

RICHARD SVANBACK,1 EVA WAHLSTROM,1,6 AND ERIKA WESTMAN1

1Department of Ecology and Environmental Science, Umea University, SE-90187 Umea, Sweden2Institute of Biodiversity and Ecosystem Dynamics, University of Amsterdam, POB 94084, NL-1090 GB Amsterdam,

The Netherlands

Abstract. Recent size-structured cannibalistic models point to the importance of theenergy gain by cannibals and also show that this gain may result in the emergence of giantindividuals. We use a combination of a 10-year field study of a perch (Perca fluviatilis)population and quantitative within-season modeling of individual and population-level dy-namics to investigate which mechanisms are most likely to drive the dynamics of the studiedperch population. We focused on three main aspects to explain observed discrepanciesbetween earlier model predictions and data: (1) introduction of more than one sharedresource between cannibals and victims, (2) whether or not several victim age cohorts arenecessary to allow giant growth, and (3) the intensity of inter-cohort competition betweenyoung-of-the-year (YOY) perch and 1-yr-old perch.

At the start of the study period, the perch population was dominated by ‘‘stunted’’ perchindividuals, and recruitment of perch to an age of 1-yr-old was negligible. Following amajor death in adult perch, strong recruitments of perch to 1-yr-old were thereafter observedfor a number of years. As 1-yr-olds these successful recruiters subsequently starved todeath due to competition with the new YOY. The few surviving adult perch acceleratedsubstantially in growth and became ‘‘giants.’’ At the end of the study period, the perchpopulation moved back to the situation with stunted individuals. There was a high agreementbetween observed diets of cannibalistic perch and those predicted by the model for boththe stunted and the giant phases. Analyses of growth rates showed that cannibalistic perchcould become giants on a diet of YOY perch only, but that a supplement with the secondshared resource (macroinvertebrates) was needed to reach the observed sizes. Modeling ofgrowth and diet in the giant phase showed an exploitative competitive effect of YOY perchon 1-yr-old perch, but a restriction in habitat use of 1-yr-old perch had to be assumed toyield the observed growth rate and diet. The resource dynamics of zooplankton and mac-roinvertebrates were both accurately predicted by the model. Also, YOY perch mortalitywas accurately predicted and, furthermore, suggested that one of the trawling methods usedmay underestimate the number of YOY perch when they increase in size.

We conclude that the presence of a second shared resource and the restricted habitatuse and absence of cannibalistic consumption by 1-yr-old perch individuals are two im-portant mechanisms to explain the discrepancy between model predictions and data. Ourresults also point to the fact that that the dynamics observed may be explained by complexdynamics not involving the presence of a giant and dwarf cycle.

Key words: cannibalism; competition; complex dynamics; energy gain from cannibalism; Eur-asian perch (Perca fluviatilis); physiologically and size-structured population models.

INTRODUCTION

Cannibalism, like any predator–prey interaction, in-volves two essential processes: the killing of prey caus-ing prey population mortality and the extraction of

Manuscript received 4 November 2002; revised 7 February2003; accepted 11 February 2003. Corresponding Editor: O. J.Schmitz.

3 E-mail: [email protected] Present address: Biomathematics Unit, IACR-Rotham-

sted, Harpenden, AL5 2JQ U.K.5 Present address: Department of Aquaculture, Swedish

University of Agricultural Sciences, SE-901 83 Umea, Swe-den.

6 Present address: Swedish Institute for Ecological Sus-tainability, Box 7980, SE-907 19 Umea, Sweden.

energy changing the condition of the predator. Thesetwo fundamental elements of cannibalism also form thebasis for the several kinds of effects that cannibalismmay have on population dynamics and persistence(Diekmann et al. 1986, Hastings and Costantino 1987,van den Bosch et al. 1988, Claessen et al. 2000, 2002,Persson et al. 2000). First, energy extracted by the can-nibal may allow a population to persist under environ-mental conditions when a noncannibalistic populationwould go extinct, a phenomenon generally referred toas the ‘‘life boat mechanism’’ (Gabriel 1985, van denBosch et al. 1988, Henson 1997). Second, increasedfecundity among cannibals, as a result of increasedenergy intake, may lead to a destabilization of the pop-

136 LENNART PERSSON ET AL. Ecological MonographsVol. 74, No. 1

ulation dynamics (Hastings and Costantino 1987).Third, the mortality imposed on victims may dampenpopulation oscillations (Hastings and Costantino 1987,van den Bosch and Gabriel 1997, Claessen et al. 2000).

The intensity of cannibalistic interactions generallydepends on the size relationship between cannibals andvictims (Orr et al. 1990, Fagan and Odell 1996, Riceet al. 1997, Dong and DeAngelis 1998, Claessen et al.2000, 2002, Persson et al. 2000). The cannibalistic pro-cess per se will also affect the interaction strength be-tween cannibals and victims over time as victims con-sumed by the cannibals are translated into growth ofthe cannibals, and the mortality imposed on victims bycannibals may increase the growth of the remainingvictims. As a result, the intensity of cannibalism willvary because it is strongly coupled to the growth ofcannibal individuals and to the growth of victim in-dividuals (Rice et al. 1997, Claessen et al. 2000).

Although not commonly addressed in theoreticalstudies (but see Dong and DeAngelis 1998, Claessenet al. 2000, 2002), cannibals often share a commonresource with their victims, leading to the potential forsize-dependent competition between cannibals and vic-tims. In this context, cannibalism may have a two-foldevolutionary advantage as the cannibal benefits fromboth the feeding on victims and the reduced compe-tition from victims for the shared resource (Polis 1988).Recent theoretical studies of cannibalistic systems witha shared resource suggest that, in a population-dynam-ical context, cannibals may either control victims andhence profit from reduced competition or profit ener-getically from cannibalism—but not both (Claessen etal. 2000, 2002). Claessen et al. (2000) showed thatwhen cannibals control victims they gain most of theirenergy from the shared resource, and the cannibalisticpopulation is characterized by relatively small, stuntedindividuals. Conversely, when cannibals profit ener-getically from cannibalism, most of the adult cannibalpopulation had been outcompeted by a strong recruitingcohort, and the few surviving adults only impose anonsignificant mortality on the recruiting cohort. Thesefew adult individuals accelerate substantially in growthas a result of cannibalism, thereby becoming ‘‘giants’’(Claessen et al. 2000). The mechanism by which vic-tims outcompete cannibals is that newborn individualsare too small to be encountered by cannibals, and thatthese recruiting individuals depress the shared resourceto a level where cannibals starve to death before theyare able to start cannibalizing on the recruiting cohort.A recent paper confirms the importance of the lowersize boundary for cannibalism for the occurrence ofcannibal starvation death (Claessen et al. 2002).

Interestingly, data from fish populations support theprediction that individuals may accelerate in growth onsuccessfully recruiting year classes (McCormack 1965,LeCren 1992, Persson et al. 2000). Persson et al. (2000)studied the dynamics of a Eurasian perch (Perca flu-viatilis) population and that study includes a detailed

analysis of both individual-level (growth, condition)and population-level (numbers of different cohorts,mortality patterns, resource dynamics) processes. Thatstudy also provided evidence for a major die-off ofadult individuals associated with the successful re-cruitment of young individuals and a correspondingmajor decrease in abundance of the shared resource(zooplankton), as predicted by the model of Claessenet al. (2000). A closer examination, however, revealeda number of significant discrepancies between empir-ical data and model results (Table 1). First, the die-offof adults in the model was a result of competition witha strong cohort of young-of-the year (YOY) individualsfor the common resource (zooplankton), whereas dataprovided no evidence that the die-off of adults was aresult of competition between cannibals and victims.Second, adult individuals had to feed on several agecohorts of victims to accelerate in growth in the modelof Claessen et al. (2000), whereas diet data suggestedthat adult individuals accelerated by cannibalizing onYOY perch only. Third, the growth rate was very lowfor the successfully recruiting cohort (therefore theywere called ‘‘dwarfs’’) in the model, which was not thecase in the data. Fourth, one successfully recruitingcohort dominated the period with giants and alsoformed the main resource of the giant individuals inthe model, whereas data showed that a number of strongYOY year classes were recruited for a number of years.Fifth, the appearance of a strong cohort in the modelwas a result of a strong reproductive output, whereasthis was not the case in the data. Finally, data suggestedthe presence of severe competition between YOY perchand 1-yr-old perch not present in the model (Claessenet al. 2000, Persson et al. 2000). The discrepancy be-tween model predictions and data may have arisen be-cause perch in the study lake to a large extent fed onmacroinvertebrates during the stunted phase and thisresource was not included in the model. Also, 1-yr-oldperch restricted their habitat use to the shore region toavoid cannibalism from larger cannibals. This reducedthe cannibalistic impact of 1-yr-old perch on pelagicnewborn perch larvae (Persson et al. 2000, Bystrom etal. 2003).

One purpose of our present study is to examine moreclosely the basis for the discrepancies between modelpredictions and field data. We do this by using empir-ical data on population numbers and fecundities of dif-ferent size classes at the start of the growth season forthe periods with stunted and giant individuals, respec-tively, and then modeling the within-season dynamicsusing the population model of Claessen et al. (2000).Specifically, we focus on (1) the implications of intro-ducing a second resource (macroinvertebrates) not pre-sent in the model of Claessen et al. (2000), (2) whetherperch could accelerate in growth by cannibalizing onYOY perch only in contrast to what Claessen et al.(2000) found, and (3) the extent to which YOY perchaffected 1-yr-old perch negatively through exploitative

February 2004 137ENERGY GAIN IN CANNIBALISTIC POPULATIONS

competition. Our model predictions include the pop-ulation dynamics of the two resources and perch, andthe individual dynamics of growth and diets of perch$1-yr-old. Model predictions regarding both individ-ual-level and population-level processes are subse-quently confronted with empirical patterns. We also askwhether the dynamics of the studied perch populationmay be explained by mechanisms other than a dynamicbased on the induction of giants and dwarfs after aperiod of stunted adult growth as outlined above. Forexample, stunted and giant periods may represent al-ternative attractors rather than involving the inductionof giants and dwarfs (Claessen and De Roos 2003; seealso Botsford 1981, Cushing 1991, 1992).

In a broader context, our approach represents a quan-titative modeling framework with the purpose of de-veloping ecology towards a more quantitative science.This framework includes a more critical test of modelpredictions and assumptions, and a route for a closerinteraction between theoretical and empirical studies(cf. Murdoch et al. 1992, Murdoch and Nisbet 1996).The utility of the modeling approach we use—physi-ologically structured population models—for this pur-pose is due to (1) a high independence between modelassumptions and empirical data against which modelpredictions are confronted, and (2) the modeling ap-proach readily allows quantitative predictions at boththe population and the individual level (De Roos andPersson 2001).

MATERIALS AND METHODS

Field data

The field data come from a long-term study of a perchpopulation (Perca fluviatilis) in a small (9.3-ha) low-productivity lake, Abborrtjarn 3, situated in middleSweden (648299 N, 198269 E) (Persson et al. 1996,1999, 2000). The lake lacks surface inlets or outlets.Perch was the only fish species in the lake during 1991–1996. In late autumn 1996 and spring 1997, roach (Ru-lius rutilus) and artificial vegetation were added to thelake as part of a whole-lake experiment. Data up to2001 suggest that the addition of neither the roach pop-ulation nor artificial structure has affected the perchdynamics to any extent—likely because the roach pop-ulation still is small and only limited recruitment hasbeen observed (L. Persson, unpublished data). Wetherefore include data up to 2001 to generate a longertime series for the perch population. Excluding datafor the period 1997–2001 would, however, not haveaffected any of our conclusions. Methods to estimatepopulation numbers, growth rates, and diets of differentcohorts of perch are given in detail in Persson et al.(2000), and therefore here we only give a condensedsummary, and similarly for methods to sample resourc-es (zooplankton and macroinvertebrates).

Estimates of the 1991 population numbers of perch$2 yr old were based on gill-net catches (survey ben-

thic gill nets, mesh sizes 9.5, 14.5, 18, 24, 29.5, 33,38, and 46 mm, each section 7 m long) yielding arelative estimate (catch per unit effort) of populationnumbers and population size distribution. In all otheryears, population numbers and population size struc-tures are based on absolute estimates using multiplemark–recapture methods (see Persson et al. 2000). Alldata on perch population censuses represent the springsituation in each year.

In spring every year, 1-yr-old perch were electrofi-shed from a boat along the shore where they were con-centrated. The entire shoreline was covered, dippingthe anode of the electrofisher every 2 m. In 1995–1999when high numbers of 1-yr-old perch were captured,population estimates were, as for older perch, based onmark–recapture methods. In years when 1-yr-old perchabundance was too low to allow population estimatesbased on mark–recapture (1992, 1993, 1994, 2000,2001), estimates of 1-yr-old perch abundance based onelectrofishing were transformed to absolute densitiesusing a regression of the number of 1-yr-old perch cap-tured during the spring electrofishing on estimatesbased on mark–recapture for the years 1995–1999. Theabundance of 1-yr-old perch also yielded an estimateof the survival of young-of-the-year (YOY) perch fromthe date in the preceding year when they had movedto the shore habitat, to an age of 1-yr-old.

Estimates of the number of perch larvae are presentfor the period 1994–2001. Larval perch were sampledwith a Bongo trawl once a week for five weeks fol-lowing hatching in early June when they were distrib-uted in the pelagic habitat. The Bongo-trawl capturesyielded an absolute estimate of perch larvae abundancein terms of number of individuals per unit volume (By-strom et al. 1998). Catches were corrected for gearavoidance using the equation given by Noble (1970)for Miller samplers. After YOY perch had shifted tothe littoral zone in early/middle July, it was no longerpossible to obtain quantitative estimates due to prob-lems in trawling the near-shore area where the YOYperch resided and to the increased capacity of YOYperch to avoid the trawl at this date. During their littoralperiod YOY perch were caught by electrofishing togenerate data on individual growth. Estimates of thenumber of YOY perch present at the end of the growthseason (September) were obtained by using the fre-quency size distribution of YOY perch each autumntogether with laboratory data on size-dependent wintermortality in perch (P. Bystrom, unpublished data).YOY perch density at the end of the growth seasonwas obtained by dividing next spring’s estimates of 1-yr old perch by the size-dependent winter survivalprobability.

Age and growth of individual fish were determinedby calculating the size of the fish backwards in timeusing opercular bones (Bagenal and Tesch 1978). ForYOY perch and 1-yr-old perch, growth was measureddirectly as these age cohorts could easily be separated


based on size. Perch start to spawn before the lake isaccessible to sampling in spring, hence we could notobtain reliable estimates of fecundity based on sampledfemales. For the period 1992–1996 we instead calcu-lated population fecundity based on length-specific fe-cundity data from Nyberg (1976) who studied perchpopulations with similar growth patterns and size struc-tures. From 1997 and onwards, we directly counted thenumber of roe strands in the lake and the average num-ber of eggs per strand (Persson et al. 2000).

On every sampling date, stomachs of up to 10 perchfrom each 20-mm size class above 100 mm wereflushed for dietary analyses. During 1995–1998, stom-ach samples from 10–20 1-yr-old perch were takenfrom electrofished fish at least once a month. In 1995,additional samples were taken every week in June tostudy the potential presence of cannibalism by 1-yr-oldperch on YOY perch. All diet data presented are basedon dry mass, which, for comparisons with modelingoutputs, was transformed to wet mass using a standardconversion factor. Diet data from each sampling datewere grouped based on perch size classes (1-yr-old,151–200 mm, and .200 mm perch cohorts are pre-sented in this paper).

In every year, zooplankton was sampled 7–8 timesduring the growing season at three pelagic stations.Zooplankton were collected with a 100 mm-mesh net(diameter 25 cm) drawn vertically at an approximatespeed of 0.5 m/s. One tow was made at each pelagicstation from the thermocline (estimated with a therm-istor) to the surface. In August 1992, five macroinver-tebrate samples were taken with an Ekman dredge (area630 cm2) at one littoral station at a water depth of 0.5m. In 1993–1996 the macroinvertebrate sampling wasextended to three littoral stations and in 1997 to 5 sta-tions. For the years 1993–2001, six samples were takenin August at each station with a core sampler. Mac-roinvertebrates were separated into two groups. Onegroup consisted of organisms living on macrophytes,branches, or other substrates (Hirudinea, Ephemerop-tera, Trichoptera, Odonata, Coleoptera, Megaloptera)that are relatively sensitive to fish predation. The othergroup (mainly chironomids) consisted of organismsliving in the sediment that are less sensitive to fishpredation (see Persson et al. [1996] and referencestherein).

Modeling

Our population dynamical model of cannibalisticperch belongs to the class of physiologically structuredmodels (Metz and Diekmann 1986, Metz et al. 1988,De Roos et al. 1990, De Roos 1997), which are spe-cifically suited to handle the dynamics of populationsinvolved in size-dependent interactions. These modelsare based on a state concept at each of two levels oforganization: an i state that represents the state of theindividual in terms of a collection of characteristicphysiological traits (size, age, sex, energy reserves,

etc.) and a p state, which is the frequency distributionover the space of possible i states. The model-formu-lation process consists of the derivation of a mathe-matical description of how individual performance(growth, survival, reproduction) depends on the phys-iological characteristics of the individual and the con-dition of the environment (i-state description). Han-dling the population level (p-state) dynamics is sub-sequently just a matter of bookkeeping of all individ-uals in different states without making any furthermodel assumption at this level. The core of these mod-els is thus the individual state and its dynamics, whichin our case is a description of the dynamics of thephysiological state of perch individuals as a functionof their current values and the condition of the envi-ronment. The environment consists of two resources(zooplankton and macroinvertebrates) and the perchpopulation itself representing all potential cannibalsand victims. The dynamics of the state variables arespecified in Table 1, the equations specifying the in-dividual-level model are in Table 2, and the parametervalues derived for perch are given in Table 3. A com-plete derivation of model assumptions including pa-rameterization can be found in Claessen et al. (2000).Our model differs from the model of Claessen et al.(2000) in that (1) we include two basic resources and(2) we do not consider reproduction as our analysis isfocused on within-season dynamics. Thus our initialstate values are based on spring values observed in thestudy system (see Results: Table 4). Furthermore, incomparison with Claessen et al. (2000) we changed theformulation of the cannibalistic attack-rate functionslightly to better match empirical observations thathave become available more recently (see Materialsand Methods: Cannibalism window, and Fig. 2).

The physiological state of the individual is charac-terized by two i states, irreversible mass x and revers-ible mass y (Table 1, see also Persson et al. 1998).Reversible mass can be starved away when mainte-nance costs exceed energy intake, whereas irreversiblemass cannot. Rules for how energy for growth is al-located between irreversible and reversible mass areexplained in detail in Persson et al. (1998). The rulesare designed such that, given a positive energy balance,the ratio y/x approaches a maximum value asymptot-ically, which is qJ for juveniles, and qA for adults. Weassume that qA . qJ which reflects the fact that adultindividuals in addition to fat reserves also allocate en-ergy to gonads. In our calculations, individuals belowthe maturation size (i.e., x , xf) were assumed to startwith the maximum reversible mass for that size givenby y 5 qJx, whereas individuals above the maturationsize were assumed to start with the maximum reversiblemass for adults, given by y 5 qAx (Table 2). As longas juvenile individuals have a positive energy balance,they will continue to have the same ratio of reversibleto irreversible mass (qJ), but if they reach the size where


TABLE 1. Definitions of state variables and specification of their dynamics.

A) State variables

Variable Symbol Unit

Individual levelIrreversible mass xi gReversible mass yi g

Population levelNumber of cohorts kDensity of cohorts Ni, i ∈ {1, k} no./L

EnvironmentResource density of zooplankton Rz g wet mass/LResource density of predator-sensitive macroinvertebrates Rm g wet mass/m2

Potential cannibals/victims {Ni, xi}, i ∈ {1, k}

B) Dynamics within years†

Dynamic Equation

Cohort mortalitydNi 5dt

2m(xi, yi)Ni i ∈ {1, k}

Cohort per capita growth in xdxi 5dt

f (x , y )E (x , y ) if E . 0i i growth i i growth50 otherwisei ∈ {1, k 2 1}

Cohort per capita growth in ydyi 5dt

[1 2 f (x , y )]E (x , y ) if E . 0i i growth i i growth5E (x , y ) otherwisegrowth i i

i ∈ {1, k 2 1}

YOY length growth (stunted phase) ,(a) 50.18 3 a 1 6.2 if a , 46.45 0.2913.0 3 (a 2 45.0) otherwise

YOY length growth (giant phase) ,(a) 520.0051a 1 0.180a 1 7.5 if a , 59.95 20.0036a 2 0.097a 1 29.2 otherwise

Resource dynamicsdRz 5dt

k A (x )Nz j jr (K 2 R ) 2 R eOz z z z z, j 1 1 H(x )h(x )j51 j j

dRm 5dt

k A (x )N Vm j jr (K 2 R ) 2 R eOm m m m m, j 1 1 H(x )h(x ) Sj51 j j

† The functions for mortality (m), energy balance (Egrowth), energy allocation ( f ), attack rates (Az, Am, Ac), handling time(H ), and total encounter rate (h) are given in Table 2. Values for encounter efficiencies on different resources (ez, i, em, i, ec, i)were varied between 0 and 1 for different year classes (with index i; k is the index of the YOY [young-of-the-year] cohort)independently. Observe that cohort per capita growth refers to perch $1 yr old.

they mature, the ratio increases, approaching qA. Anindividual is assumed to allocate a larger proportion ofits energy intake to reversible mass if its condition (theratio y/x) is lower (Table 2). If energy intake is smallerthan metabolic costs, reversible mass will be convertedto energy to cover metabolic costs. Individuals can sus-tain a certain mass decrease in reversible mass withoutan increase in starvation mortality down to a reversible-mass-to-irreversible-mass ratio given by y 5 qSx (Table3). If reversible mass decreases below this ratio, theindividual will start to die of starvation at a rate thatincreases to infinity as reversible mass decreases tozero.

All functions describing foraging intake and energyexpenditure depend on size. Attack rates on zooplank-ton (Az), macroinvertebrates (Am) and conspecifics (Ac)are assumed to depend on irreversible mass only, eitherthrough a quantity m(x) 5 (1 1 qj)x, which we referto as ‘‘standardized mass’’ or through the individual

length, which itself is an allometric function of stan-dardized mass (see Claessen et al. 2000). The notionof standardized mass, which reflects the mass of a non-starving individual discounting its gonads, has beenintroduced to allow for parameter estimation from data(see Persson et al. 1998). The attack rate on zooplank-ton is modeled as a dome-shaped curve and the attackrate on macroinvertebrates as a power function (Table2). The cannibalistic attack function plays an importantrole in the analysis and we will return to a descriptionof this function below. The feeding rate (I ) is a functionof prey mass encounter and the capacity to digest preywhere the prey mass encounter is the product of theconsumer’s attack rate, prey density, and prey individ-ual mass. The digestion capacity (grams of prey perunit of time) is assumed to increase with standardizedbody mass (Table 2). For one-year-old and older perch,metabolic costs are assumed to depend on total bodymass (reversible plus irreversible) following a power


TABLE 2. Equations that specify the individual-level model.

Physiological characteristics

Standardized mass m (x) 5 (1 1 qJ)xBody length ,(x) 5 l2l m(x)1

Attack rates

Zooplankton attack ratea

m(x) m(x)A (x) 5 A exp 1 2z 5 6[ ]W Wopt opt

Macroinvertebrate attack rate Am(x) 5 b2b m(x)1

Cannibalistic attack rate

vc 2sv « v v

b if , c ,1 2f « fv v2

« dA (c, v) 5 vc

2 csv d v vb if , c ,1 2f f dv v

2d f

0 otherwise

Total food intakeh(x)

I(x) 51 1 H(x)h(x)

Total digestion time H (x) 5 j2j m(x)1

Encounter rates

Total encounter rate h(xi) 5 e h (x ) 1 e h (x ) 1 e h (x )z, i z i m, i m i c, i c i

Zooplankton encounter rate hz(x) 5 Az(x)Rz

Macroinvertebrate encounter rate hm(x) 5 Am(x)Rm

Cannibalistic encounter rate h (x ) 5 A [,(x ), ,(x )](x 1 y )NOc i c i j j j jj

Energy

Energy balance Egrowth(x, y) 5 Eaquir.(x) 2 Emaint.(x, y)Aquired energy Eaquir.(x) 5 keI (x)Maintenance requirements Emaint.(x, y) 5 r2r (x 1 y)1

Fraction of energy allocated to growth in x

1 yif x , xf(1 1 q )q xJ J

f (x, y) 5 1 y otherwise

(1 1 q )q x A A

Mortality

Total mortality m(x, y) 5 m0 1 ms(x, y) 1 mc(x)

Starvation mortalitys(q x /y 2 1) if y , q xS S

m (x, y) 5s 50 otherwise

Cannibalistic mortalityA [,(x ), ,(x )]Nc i j i

m (x ) 5 eOc j c, i 1 1 H(x )h(x )i i i

Notes: The subscripts i (individual) and J ( juvenile) refer to cohort indices and variables cand v to the length of a cannibal and victim, respectively, which are a function of irreversiblemass. b 5 overall intensity of cannibalism, f 5 optimal size ratio; e 5 encounter efficiency,ke 5 conversion efficiency. See Table 3 for parameter symbol definitions.

function. The energy intake of the individual is thefeeding rate multiplied by a conversion factor.

For YOY perch, we used empirical data on growth;hence the part of the model describing metabolic rateand growth (but not feeding rate) is irrelevant for YOYperch. The reason for not letting the growth of YOYperch depend on their food intake was related to thediscrepancy between data and model predictions re-garding YOY perch growth. Field data suggested that

perch could accelerate in growth by feeding on YOYperch only (Persson et al. 2000). Model predictionssuggested that perch also need access to conspecificsolder than YOY perch to gain sufficient energy foraccelerating in growth (Claessen et al. 2000, 2002). Byletting YOY grow in the model according to the patternas observed in the field (Fig. 1), we could evaluatemore accurately whether perch could actually accel-erate through cannibalism on YOY perch only, as sug-


TABLE 3. Model parameters for perch feeding on zooplankton, macroinvertebrates, and conspecifics.

Subject Symbol Value Unit Interpretation Source†

Lake VS

3 3 108

3 3 104Lm2

total volumebenthic bottom area

74

Season 90 d length of growth season 1Ontogeny xb

xf

qJ

qA

0.0014.60.741.37

gg······

irreversible mass at birthirreversible mass at maturationjuvenile max. conditionadult max. condition

1111

Length–mass relationYOY , 29.2 mm

YOY $ 29.2 mm

Older perch

Planktivory

l91l92l1

l2

l1

l2

aAWopt.

41.20.263

48.00.380

48.30.3170.62

9 3 103

4.7

l2mm/g···

l2mm/g···

l2mm/g······L/dg

allometric scalarallometric exponentallometric scalarallometric exponentallometric scalarallometric exponentallometric exponentmax. attack rateoptimum consumer size

222222336

Benthivory b1

b2

0.20.4

2 21 b2m ·d ·g ‡···

allometric scalarallometric exponent

44

Piscivory sbd«f

0.6400

0.050.450.16

···L·d21·mm2s

·········

allometric exponentcannibalistic voracitylower size limit§upper size limit§optimum size ratio

4, 54, 5

555

Digestion j1

j2

5.020.8

(11j )2d/g···

allometric scalarallometric exponent

11

Metabolism r1

r2

ke

0.0330.770.61

r(12 )2g /d······

allometric scalarallometric exponentconversion efficiency

111

Mortality m0

qS

s

0.0050.20.2

······d21

background mortality ratestarvation mortality thresholdstarvation rate coefficient

411

Zooplankton semi-chemostat dynamicsrz

Kz

0.050.001

d21

g/Lrenewal ratemaximum population density

16

Macroinvertebrates semi-chemosat dynamicsrm

Km

0.052.5

d21

g/m2renewal ratemaximum population density

17

Note: YOY 5 young-of-the-year.† References: 1, Claessen et al. (2000); 2, P. Bystrom, unpublished data; 3, Bystrom and Garcia-Berthou (1999); 4, L.

Persson, unpublished data; 5, Lundvall et al. (1999); 6, Wahlstrom (2000); 7, Persson et al. (2000).‡ See Table 2: Macroinvertebrate attack rate.§ Ratio of victim length to cannibal length, v/c.

gested by Persson et al. (2000) or whether the presenceof the additional basal resource macroinvertebrates (ab-sent in the model of Claessen et al. 2000) was essential.The nonlinear length–age relations fitted to the datashown in Fig. 1 are presented in Table 1. These YOYlength–age relations were transformed to mass–age re-lations using the length–mass relations presented inTable 3.

Both resources (zooplankton and macroinverte-brates) are modeled as unstructured populations withsemi-chemostat resource dynamics (i.e., amount of re-source input per unit of time is independent of resourcedensity present in the system; Persson et al. 1998, DeRoos et al. 2002). The macroinvertebrate resource rep-resents the predator-sensitive macroinvertebrates (seeabove field data), whose densities have been shown tobe the macroinvertebrates that are more accessible to

perch and that also are affected by perch predation(Persson et al. 1996, 2000). Based on lake morphologyand depth distribution of macroinvertebrates, macro-invertebrates are assumed to be present in 20% of thelake volume (at the littoral bottom) (Persson et al.1999). The mean depth of the littoral habitat is assumedequal to 2.0 m. The zooplankton resource is assumedto consist of a homogeneously mixed population pre-sent in the whole lake volume.

Cannibalism window

We assumed that positive cannibalistic attack ratesare constrained between two bounds of the ratio ofvictim (v) to cannibal length (c) equal to v/c 5 d and«, respectively (Tables 2 and 3). d sets the smallestvictim size as a fraction of cannibal length below whichthe cannibal does not encounter victims due to diffi-


FIG. 1. Increase in size of young-of-the year perch in1994–1997 (triangles) and in 1999–2001 (circles). Each datapoint is based on one sampling occasion representing themean of $30 individuals.

FIG. 2. Fits of the cannibalistic tent function specified in Table 3 and described in the text (see Materials and methods:Cannibalism window) on relative attack rates for two sizes of perch using data from Lundvall et al. (1999). The relativeattack rate was set to 1 for the highest observed capture rate for each cannibal size, and the other relative attack rates werescaled in relation to these two highest capture rates.

culties in detecting them; « sets the maximum victimsize as a fraction of cannibal length above which escapeability of victims and gap constraints in the cannibalprohibit capture. Within the range of cannibal and vic-tim sizes where cannibalistic attack rates are positive(the cannibalism window), the attack rate on differentlysized victims for a specific cannibal length is assumedto increase with victim size from zero at v 5 dc, to anoptimum at v 5 øc, to thereafter decrease and becomezero again when victim length reaches v 5 «c (Table

1, Fig. 2). Our model formulation differs from that ofClaessen et al. (2000, 2002) in that we, based on newexperimental data, assume that the increase and thedecrease in attack rate are described by nonlinear ratherthan linear functions of victim size (Lundvall et al.1999) (Table 3, Fig. 2). On the ridge v 5 øc representingthe optimum victim length for differently sized can-nibals, the attack rate is assumed to increase with vic-tim length (and thus also cannibal length) according tothe equation b(v/w)s where b represents the overallintensity of cannibalism, w the optimal size ratio ands a size scaling (Claessen et al. 2000, 2002).

RESULTS

Field data

The perch population in the study lake has undergonesubstantial changes in numbers and size structure (Pers-son et al. 2000) (Fig. 3). In the years 1991–1993, theperch population was dominated by intermediatelysized individuals having slow growth and reaching amaximum size of ;180 mm (Fig. 4). Very few 1-yr-old perch were observed (individuals sized 46–61 mmin Fig. 3) despite strong reproductive outputs in allyears. In the summers of 1993 and 1994 the populationof perch $2 yr old decreased to low values. The de-crease in 1994 (but not in 1993) coincided with thesuccessful survival of a young-of-the-year (YOY) co-hort reflected in a high peak in abundance of 1-yr-oldperch in the spring of 1995 (Fig. 3). However, despitethe co-occurrence of a decline in perch $2 yr old andthe presence of larger numbers of YOY perch, the de-crease in 1994 could not be related to competition fora shared resource (zooplankton) with YOY perch (Pers-son et al. 2000). High survival of YOY perch cohorts


FIG. 3. Observed size distributions of the perch population during 1991–2000. Data from 1991 were catch per unit effort(CPUE) whereas data from 1992–2000 are estimated absolute densities (number/ha).

FIG. 4. Length–age relation for differentyear classes of perch during 1984–2001. Dataare means 6 1 SD.

was subsequently observed for another four years lead-ing to high numbers of 1-yr-old perch during the years1995–1999. In the years 1995–1997, the survival of 1-yr-old perch was very low (,5%), which was suggestedto be due to inter-cohort competition with YOY perch(evidence: depression in condition of 1-yr-old perchand decreases in zooplankton resource levels associ-ated with high numbers of YOY perch; Persson et al.2000). Diet data showed no evidence for cannibalism

by larger perch on 1-yr-old perch. In 1998, the survivalof the 1-yr-old cohort of perch to 2 yr old was high(.90%) leading to a strong cohort of 2-yr-old perchbeing present in 1999 (Fig. 3). Despite a high repro-ductive output in 1999, very few YOY survived to anage of one year and in 2000 the perch population hadreturned to a state similar to that in 1991–1993.

The few adult perch surviving in 1994 showedstrongly accelerated growth in all years with high sur-


FIG. 5. Biomass proportion of zooplankton, macroinverte-brates, and young-of-the-year (YOY) perch in the diet of perchsized 161–200 mm in early August during the period 1992–2000; the ‘‘3’’ indicates that no fish were sampled in 1995.

FIG. 6. The relationship between the reproductive outputand the recruitment of 1-yr-old perch in the following year,during 1991–2000. Data on number of eggs before 1996 arebased on regressions of fecundity on body length whereasdata for 1996–2000 are based on direct counts; the data onnumber of eggs was multiplied by 106 before being graphed(so that, e.g., 1 5 106 eggs). Note the logarithmic scale onboth axes.

vival of YOY perch. This high growth was related toa high proportion of YOY perch in the diet in July–August (Fig. 5) (Persson et al. 2000). In contrast, thediet of perch $2 years old during 1992–1993 and1999–2000 was dominated by macroinvertebrates andthe biomass contribution of YOY perch to the diet ofperch $2 yr old was low (Fig. 5) (Persson et al. 2000).The diet of 1-yr-old perch in years when they wereabundant enough to allow adequate sampling consistedmainly of zooplankton and macroinvertebrates (Pers-son et al. 2000). Cannibalism by 1-yr-old perch onYOY perch was present but was restricted to a shortperiod in June (Bystrom et al. 2003).

YOY perch were not sampled in 1991–1993. Thegrowth rate of YOY perch with high survival to 1 yrold (1994–1998) was higher than that of YOY perchin years with low survival to 1 yr old (1999–2001)(Fig. 1). This difference in growth was already presentduring the early larval stages. The steep increase in thesize of YOY perch in early August in 1999–2001 isprobably due to the fact that these individuals repre-sented a very small, remaining number of fast-growingYOY perch sampled along the shore. Although the low-er growth rate of YOY perch in 1999–2001 may haveled to a lower winter survival, trap catches show thatthe number of YOY perch present in September wasalready much higher in 1994–1998 than in 1999–2001(trap1fyke net catches September, 1994–1998: meancatch 334 individuals; 1999–2001: mean catch 19 in-dividuals; t6 5 11.2, P , 0.0001). Thus early canni-balism by the abundant but slow-growing perch $2 yrold remains the likely explanation for the low numbersof 1-yr-old perch in 1992–1994 and 2000–2001. Can-nibalism as a density-dependent factor is also supportedby the strong negative relationship between reproduc-tive output and number of surviving recruits (Fig. 6).

Model results

The model was run for two phases with differentperch population numbers, population structures, pop-

ulation fecundity, YOY perch mortality, and resourcedynamics (i.e., 1992, 1993, 1999, 2000 vs. 1994–1997)(Fig. 3). As outlined in the Introduction, we use themodel to quantitatively scrutinize qualitative discrep-ancies in mechanisms suggested by the previous modelformulation (Claessen et al. 200) vs. those indicatedby our data—in particular, to assess the importance ofadding a second shared resource, macroinvertebrates,and 1-yr-old perch habitat use for the interactions be-tween YOY perch and 1-yr-old perch. The pathway ofthis analysis is given in Fig. 7. Data from 1998 werenot included because that year differed from the otheryears with high numbers of surviving YOY perch byalso having a high survival of 1-yr-old perch. Onephase (1992, 1993, 1999, 2000) is characterized bymany cohorts not growing beyond a size of ;180 mmand this phase will in the following be called the‘‘stunted’’ phase (Fig. 4). The other phase (1994–1997)is characterized by a few adult individuals reachinglengths of up to and beyond 300 mm, and will in thefollowing be called the ‘‘giant’’ phase. For each phasethe estimated number (average between years) of YOYperch (number of eggs), 1-yr-old perch, and perch $2yr at the onset of spring (end of May) were used asinitial values (Table 4). For perch $2 yr, the averagesize distributions in 1992–1993 and 2000 (stuntedphase) and 1995–1997 (giant phase) were used. Startvalues for resource densities were set to their maximum(Table 4). The simulations were run for 90 d, repre-senting the growth season (June–August) in the studylake. YOY perch were assumed to hatch on day 11(June 11), which is an average observed in the studylake (Bystrom et al. 2003). They were assumed to im-mediately move out into the pelagic habitat (Bystromet al. 2003). The day at which YOY perch move back


FIG. 7. Flow chart showing the logical steps in the quantitative contrast of modeling predictions with empirical data. Thefocus of the present study is within the dashed boundaries forming the basis for a modified multigenerational model providinga better description of the dynamics of the cannibalistic perch system (Persson 2003). Input variables were run for both thestunted and giant phases. Abbreviations: YOY 5 young-of-the-year; K 5 carrying capacity.

TABLE 4. Initial values of the number of perch and of the resource levels used to generatemodel predictions for the dynamics in the two phases.

Variable Stunted phase† Giant phase‡

Perch $2 yr (numbers)One-year-old perch (numbers)YOY perch (number of eggs)Zooplankton (g wet mass/L)Macroinvertebrates (g wet mass/m2)

11 000300

4 3 106

0.0012.5

10006000

1.1 3 106

0.0012.5

Notes: Data for the different perch cohorts are based on mean values observed (stunted phase:1992, 1993, 1999–2000; giant phase: 1994–1998). For perch $2 yr old, initial size distributions(not presented) were based on mean values for the two phases. Initial size of 1-yr-old perchwas the same for both phases. Values for zooplankton and macroinvertebrates assume maximumdensity of the resource.

† The phase characterized by many cohorts not growing beyond a size of ;180 mm.‡ The phase characterized by a few adult individuals reaching lengths of $300 mm.

to the littoral area has been shown to depend on size-dependent predation risk (Bystrom et al. 2003). Runsvarying the timing of the habitat shift within the rangeobserved in the field showed that the time chosen atwhich the shift occurred did not affect the patternsobserved. We therefore chose to use a fixed day (day31) for YOY perch to shift habitat to the littoral in allruns. One-year-old perch were assumed to be restrictedto the littoral habitat up to day 20 due to predation risk

from larger cannibals. After this date, 1-yr-old perchspread over the whole lake volume.

For the simulations in the stunted phase, the numberof perch $2 yr and population reproductive output werehigh, whereas the number of 1-yr-old perch was low(Table 4). For the simulations in the giant phase, theopposite was the case, i.e., the number of perch $2 yrand population reproductive output were low and thenumber of 1-yr-old perch was high. Perch $2 yr during


FIG. 8. Predicted changes in perch mass as a function of initial size for the stunted and giant phases. The curves representpredictions when perch were assumed to feed on macroinvertebrates only (thin dotted line), zooplankton only (thick solidline), young-of-the-year (YOY) perch only (thick dashed line), macroinvertebrates and zooplankton (thin dashed line), andmacroinvertebrates, zooplankton, and YOY perch (thin solid line). The dotted–dashed line (1:1) is the total mass of anindividual that just maintains its mass over the growth season (y 5 qj x), and the dotted thick line is the total mass of anindividual at the starvation level (y 5 qs x). Inserted vectors are observed mass changes (means for each age cohort) basedon Fig. 4 and mass–length relationships from Persson et al. (2000).

the stunted phase were assumed to split their time be-tween the littoral and the open-water habitat in a ratioof 0.3:0.7, which is the estimated ratio based on trapcatches (Persson et al. 2000). During the giant phase,all perch $2 yr were assumed to be in the littoral habitatas trap data show that these perch restricted their habitatuse to the littoral habitat. To test for the effects ofhabitat use by YOY and perch $2 yr on YOY perchmortality, runs were also done altering these assump-tions.

As a default situation, we assumed that 1-yr-old andolder perch searched for all three prey types (macro-invertebrates, zooplankton, and YOY perch) simulta-neously, whereas YOY perch only searched for zoo-plankton. We define the ‘‘encounter efficiency’’ on aprey as being 1 if perch search for that prey type si-multaneously as they search for other prey types. Ifperch do not search for a prey type at all, the encounterefficiency for that prey type is 0. In different scenarios,we varied the encounter efficiencies on different preytypes for YOY, 1-yr-old, and older perch to investigatethe effects on resource dynamics and perch growth.

Growth and diets of perch $2 yr old

Two major focuses of our study are (1) the effectson perch performance of introducing a second (mac-roinvertebrate) resource, and (2) whether perch couldaccelerate in growth by cannibalizing on YOY perchonly. To illustrate growth effects, predicted mass in-

creases are derived for an initial perch size range of100–200 mm (8–60 g) for five different scenarios: (1)perch feeding on all three prey items, (2) perch feedingon zooplankton and macroinvertebrates, (3) perch feed-ing on zooplankton, (4) perch feeding on macroinver-tebrates, and (5) perch feeding on YOY perch.

The predicted mass increase during the stunted phasewhen perch fed on all three prey items was similar tothat when perch fed on zooplankton and macroinver-tebrates only, showing that energy extraction from can-nibalism was small (Fig. 8: left). Actually, the energyextraction from cannibalism was so small that perchfeeding on YOY perch only reached reversible massesbelow the starvation boundary (y 5 qSx) independentof their size. Perch feeding on macroinvertebrates onlyalways had a negative growth but were above the star-vation boundary up to a size of 9 g (Fig. 8: left). Perchfeeding on zooplankton only had a predicted positivegrowth up to a size of 27 g. The predicted maximumsize of perch when they fed on both zooplankton andmacroinvertebrates amounted to 31 g. Comparing pre-dicted growth rates with observed growth rates showedthat observed perch mass increase was substantiallylower than that predicted for perch feeding on zoo-plankton or both zooplankton and macroinvertebratesfor small perch sizes. The difference between observedand predicted mass increase decreased with increasingperch size. Observed maximum sizes were, in 18 outof 21 cases, below or equal to and in only 1 case sub-


FIG. 9. Diets of two size cohorts (start size shown in panels) of perch during the stunted and giant phases. Lines representpredicted proportions of zooplankton, macroinvertebrates, and young-of-the-year (YOY) perch in the diet. The symbolsrepresent observed diets for the two size cohorts of perch during the stunted (1992, 1993, 1999, 2000) and giant (1994–1997) phases; each symbol represents the mean of $10 individuals. Encounter efficiencies were assumed to be 1 for all preytypes.

stantially larger than, the predicted maximum mass in-crease based on perch feeding on all three prey items.

Fig. 9 shows the diet predictions for two differentsize classes of perch $2 yr old. During the stuntedphase macroinvertebrate prey were predicted to formthe bulk of food for both size classes of perch and theirimportance was predicted to increase with perch size.Zooplankton was hardly predicted to be eaten at all bythe largest size cohort, and this size cohort was notpredicted (or observed) to have a positive growth rate.Cannibalism contributed to the diet of both size classesfor a period during the middle of the growth season,but overall the predicted contribution of YOY perch tothe diet of perch was small. The agreement betweenpredicted and observed diets was generally high for thestunted phase (Fig. 9: left). For one year (2000), theobserved diet of perch in summer consisted of a higherproportion of zooplankton than predicted for both sizecohorts. This discrepancy between predictions and ob-servations can be related to the fact that the zooplank-ton biomass in that year consisted of a higher propor-tion of larger (1 mm) Daphnia compared to other yearsand that our parameter estimates for the attack rate onzooplankton is based on a 0.5-mm cladoceran.

During the giant phase the predicted mass increaseof perch feeding on zooplankton only was positive forsize classes smaller than 14 g and ended up below thestarvation boundary for most size classes (Fig. 8:right). In contrast, the predicted maximum size of perchfeeding on macroinvertebrates amounted to 49 g. Thepredicted mass increase of perch feeding on all preyitems was positive for all sizes studied and perchreached giant sizes. Restricting perch consumption tofeeding on YOY perch only still allowed giant growth(Fig. 8: right). Observed growth trajectories were clos-est to the curve for predicted growth of perch feedingon YOY perch only, but 17 of the 21 growth trajectorieswere above this curve. In any case, our modeling sug-gests that perch may accelerate in growth and becomegiants even if their cannibalism is restricted to perchyounger than 1-yr-old.

The predicted diets of the two size cohorts of perchduring the giant phase consisted almost totally of mac-roinvertebrates up to the day when YOY switched tothe littoral habitat (Fig. 9: right). The largest size cohortdid not feed on zooplankton at all. After YOY perchhad shifted to the littoral habitat, both size cohorts ofperch fed mainly on YOY perch and zooplankton was


FIG. 10. Dynamics of zooplankton and macroinvertebrates during the stunted (solid lines) and giant (dashed lines) phaseswhen young-of-the-year (YOY) perch are assumed not to feed on macroinvertebrates. Thick lines represent the situationwhen encounter efficiencies of perch $1 yr old are 1 for zooplankton, macroinvertebrates, and YOY perch; thin lines representthe situation when the encounter efficiency of perch $1 yr old on macroinvertebrates has been reduced to 0.5. Superimposedon model predictions are the observed zooplankton and macroinvertebrate biomasses in different years for the stunted (1992,1993, 1999, 2000) and giant (1994–1997) phases.

totally excluded from their diets. For the giant phase,the predicted diets of both size cohorts before YOYperch moved to the shore were very close to the ob-served diets. There was also a high agreement betweenpredicted and observed diets after the habitat shift ofYOY perch with the exception of two data points (164mm cohort: one observation in early August of 100%macroinvertebrates in the diet, 189 mm cohort: oneobservation in early August of equal amounts of YOYperch and macroinvertebrates in the diet) (Fig. 9: right).

Resource dynamics

For both phases, the predicted zooplankton biomassfirst decreased following the hatching of YOY perch.During the first part of the growth season, zooplanktonbiomass was actually lower during the stunted phasethan during the giant phase (Fig. 10: left). In responseto the high cannibalistic mortality of YOY perch in thestunted phase, zooplankton soon recovered to reachhigh levels during the second half of the growth season(Fig. 10: left). In contrast, in the giant phase the pre-dicted zooplankton biomass was reduced to very lowlevels and never recovered, due to the lower YOY mor-tality during this phase. The fact that the predictedzooplankton resource levels were lower early on in thestunted phase than in the giant phase provides an ex-planation for the empirically observed lower growthrate of small YOY perch during this phase (Fig. 1, Fig.10: left). A comparison of model predictions with ob-served patterns in zooplankton dynamics shows a highagreement between predictions and observations forthe giant phase with respect to overall biomass and thedrastic decrease in biomass over the growth season(Fig. 10: left). Similarly, the lack of this drastic de-

crease in zooplankton biomass during the stunted phasein model predictions was in correspondence with ob-servations. Interestingly, observed zooplankton bio-masses during the stunted phase were also quite vari-able, suggesting that factors other than perch predationwere controlling zooplankton dynamics.

In the stunted phase the predicted dynamics of themacroinvertebrate resource was characterized by astrong decrease in the biomass of macroinvertebratesto ,20% of its maximum density caused by consump-tion of perch $2 yr old (Fig. 10: right). In contrast,during the giant phase the macroinvertebrate biomasswas predicted to be reduced to a much smaller extentas a result of the lower numbers of perch $2 yr old.Observed biomasses of predator sensitive macroinver-tebrates in August in the giant phase were in a rangesimilar to that predicted (Fig. 10: right). For the stuntedphase, observed biomasses were lower than during thegiant phase and also somewhat lower (average 0.25 g/m2) than the predicted biomass (0.5 g/m2) during thisphase.

A reduction in macroinvertebrate encounter efficien-cy for perch $1 yr old to 0.5 only resulted in minorchanges in predicted zooplankton dynamics for bothphases, whereas the predicted macroinvertebrate bio-mass at the end of the growth season was higher witha reduced macroinvertebrate encounter efficiency (Fig.10: right). This difference in response of resources toa changed encounter efficiency of large perch reflectsthe fact that macroinvertebrates are affected by con-sumption of larger perch, whereas the biomass of zoo-plankton is largely under the control of YOY perch.

Field data show that YOY perch to a certain extentinclude macroinvertebrates in their diet after they have


FIG. 11. Dynamics of zooplankton and macroinvertebrates during the stunted (solid lines) and giant (dashed lines) phaseswhen young-of-the-year (YOY) perch feed on zooplankton only (thick lines), with an encounter efficiency on macroinver-tebrates of 0.2 (medium thick lines) and with an encounter efficiency on macroinvertebrates of 0.5 (thin lines). Dependingon macroinvertebrate encounter efficiency, YOY perch can start to feed on macroinvertebrates on day 31 after having movedto the littoral habitat. Superimposed on model predictions are the observed macroinvertebrate biomasses in different yearsfor the stunted (1992, 1993, 1999, 2000) and giant (1994–1997) phases.

FIG. 12. Changes in the density of young-of-the-year(YOY) perch over the growth season during the stunted (solidlines) and giant (dashed lines) phases. Thick lines show pre-dicted abundance of YOY perch for default values of habitatuse of cannibals and victims. Thin lines show predicted abun-dance of YOY perch when both cannibals and victims spendtheir whole time in the pelagic habitat (observe that the totalmortality of YOY perch for both habitat scenarios during thestunted phase is almost identical). Symbols are observedchanges based on Bongo trawlings (V 5 stunted phase, m 5giant phase) and mark–recapture (n 5 giant phase).

shifted to the shore habitat (Bystrom et al. 1998, Pers-son et al. 2000). Although predator-sensitive macro-invertebrates only contributed a small fraction of theYOY perch diet (Persson et al. 2000), we investigatedhow increasing the encounter efficiency of YOY perchon macroinvertebrates affected zooplankton dynamics.The effects of changing the YOY perch encounter ef-ficiency on macroinvertebrates (from day 31) for thedynamics of zooplankton was only minor, and the smalleffect was a result of the handling (digestion) time on

the alternative prey macroinvertebrates (Fig. 11: left).During the stunted phase, the effect of increasing themacroinvertebrate encounter efficiency of YOY perchon macroinvertebrates was negligible and restricted toa time window at the middle of the growth season (Fig.11: right). This small effect of YOY perch encounterefficiency on macroinvertebrates was due to the highmortality induced on YOY perch by cannibalism. Incontrast, for the giant phase the impact of increasingthe macroinvertebrate encounter efficiency of YOYperch on macroinvertebrates was substantial, leadingto macroinvertebrate biomasses at the end of the seasonsimilar to those during the stunted phase (Fig. 11:right).

YOY perch mortality

The predicted mortality rate of YOY perch duringthe stunted phase was high, and few YOY individualswere predicted to be present at day 60 (Fig. 12). Achange in assumptions about habitat uses of big andYOY perch to a situation where both YOY and $2-yr-old perch spend their whole time in the pelagic led toa small initial increase in YOY perch mortality, but atthe middle of the season the number of surviving YOYperch was hardly distinguishable between these sce-narios. Comparing the predicted mortality of YOYperch with the observed based on Bongo-trawl catchescorrected for gear avoidance (Noble 1970) showed agood correspondence. The predicted mortality rate ofYOY perch during the giant phase was considerablylower than that during the stunted phase especially upto day 31 (Fig. 12). The observed mortality of YOYduring the giant phase was substantially higher thanthe predicted mortality (Fig. 12). The difference be-tween predicted and observed mortality rate was re-stricted to the first 10 d after hatching. Empirical es-


FIG. 13. Growth of 1-yr-old perch when young-of-the-year (YOY) perch are assumed to not feed at all (dashed line),feed on zooplankton only (search efficiency 5 1.0; thin solidline), or feed on zooplankton and macroinvertebrates (searchefficiencies 5 1.0 and 0.5, respectively; dotted line). Thefigure also shows growth results when 1-yr-old perch can onlyfeed on zooplankton to a limited extent (search efficiencieson zooplankton, macroinvertebrates, and YOY perch: 0.05,1.0 and 1.0, respectively) (dashed-dotted line), and when 1-yr-old perch can only feed on zooplankton to a limited extentand do not cannibalize (search efficiencies on zooplankton,macroinvertebrates, and YOY perch: 0.05, 1.0, and 0.0, re-spectively) (thick solid line). Solid circles are the observedsizes of 1-yr-old perch (at day 60 a bimodal size distributionwas present, and circles show the average of the upper andlower peaks).

timates of the number of YOY perch alive at the endof the growth season during the giant phase agreedclosely with the predicted numbers. An assumption thatall cannibalistic perch occupied the pelagic habitat dur-ing the whole growth season resulted in a higher mor-tality early on, but a higher number of YOY perchsurviving at the end of the growth season (Fig. 12).Assumptions about habitat use during the giant phasethus affected YOY perch mortality, but the main dif-ference in mortality of YOY perch between phases canbe attributed to the difference in the number of can-nibals $2 yr old present (Table 4, Fig. 12).

Growth and diet of one-year-old perchduring the giant phase

The comparison between model predictions and em-pirical data (Claessen et al. 2000 vs. Persson et al.2000) pointed to a discrepancy in the extent to whichcompetition from YOY perch affected the performanceof 1-yr-old perch during the giant phase. To examinethis issue, we simulated growth rates and diets of 1-yr-old perch during the giant phase. Predicted growthrates of 1-yr-old perch were estimated assuming thatYOY perch did not feed at all, fed on zooplankton only,or fed on both zooplankton and macroinvertebrates (en-counter efficiency 0.5). Assuming no consumption byYOY perch (i.e., no exploitative-competitive effect),the predicted size of 1-yr-old perch increased steadilyover the whole growth season (Fig. 13). The predicted

growth of 1-yr-old perch when YOY perch were as-sumed to feed on zooplankton only was not affectedby YOY perch up to day 30 (i.e., before YOY perchstarted to depress zooplankton) (Fig. 10: left, Fig. 13).Thereafter, the growth rate of 1-yr-old perch was lowerthan when YOY perch were assumed to have no effecton zooplankton, but growth was still positive duringthe rest of the growth season. Allowing YOY perch toalso feed on macroinvertebrates (from day 31) causedonly a small further growth reduction in 1-yr-old perch.A comparison of predicted and observed growth showsthat the observed growth rate was considerably lowerthan the predicted (Fig. 13). In the data, a size bimo-dality developed in August, hence data points for themeans of both modes are shown. The discrepancy ingrowth between model predictions and data developedearly on in the season and may be related to a muchhigher proportion of zooplankton in the predicted dietof 1-yr-old perch compared to observed diets (Fig. 14:left). The predicted larger size of 1-yr-old perch alsoled to high levels of cannibalism of YOY perch by 1-yr-old perch over the entire period. This prediction con-trasts with observations as well (Fig. 14 left). Empiricaldata also suggested a decline in the condition of 1-yr-old perch over time and a massive mortality of 1-yr-old perch at the end of the season (no 1-yr-old capturedin late August) (Persson et al. 2000). Such a situationwas not observed in the model, as 1-yr-old perchshowed positive growth during the whole season.

One hypothesis to explain the discrepancy betweenmodel predictions and data with respect to growth tra-jectories and diets may be that predation risk from big-ger perch restricted the habitat use of 1-yr-old perchto the very shore area where they had only limitedaccess to the zooplankton resource and YOY perch.This hypothesis is supported by the fact that 1-yr-oldperch were only captured at shore trap stations (Perssonet al. 2000). To investigate this hypothesis, we studiedthe situation when 1-yr-old perch only encountered thezooplankton resource with a reduced efficiency. A re-duction of the encounter efficiency on zooplankton to0.05 resulted in a predicted growth rate and diet closerto that observed (Fig. 13, Fig. 14: middle). The pre-dicted intensity of cannibalism was still higher (andmacroinvertebrate consumption lower) than that ob-served, which is the main explanation for the somewhathigher predicted growth rate compared to the observed.Preventing 1-yr-old perch from cannibalizing on YOYperch resulted in a close correspondence between pre-dictions and observations both with respect to growthand diet (Fig. 13, Fig. 14: right).

DISCUSSION

Empirical patterns

Our study provides qualitatively new empirical in-sights into the dynamics of the system studied. Earlierwork (Persson et al. 2000) provided indirect but in-


FIG. 14. Diet of 1-yr-old perch during the giant phase. (A) The default situation; (B) the situation with restricted encounterefficiency on zooplankton; and (C) the situation with restricted encounter efficiency on zooplankton and no cannibalism (seeFig. 12). The lines represent predicted proportions of three food resources (prey) in the diet: zooplankton, macroinvertebrates,and young-of-the-year (YOY) perch. The symbols are observed diets; each symbol represents the mean of $10 individuals.

conclusive evidence that low population fecundity wasnot the cause of the low recruitment of young-of-the-year (YOY) perch during the stunted phase. Based ondirect egg calculations for the period 1996–2001, wecan now conclude that population fecundities are ifanything higher in years with low recruitment of YOYperch to age 1 yr than in years with high recruitmentof YOY perch to age 1 yr. These population fecunditydata also underscore the discrepancy between the mod-el predictions of Claessen et al. (2000) and data re-garding the conditions necessary for the induction ofgiants: data show that the induction of giants coincideswith low population fecundity, whereas the inductionof giants in the model is a result of a high reproductiveoutput. Although Claessen et al. (2002) show that gi-ants may indeed be induced at low population fecun-dities, this only occurs for values of the cannibalisticvoracity (b) far above that found for perch. The ob-served negative relationship between successful re-cruitment and population fecundity over the studieddensity region ultimately resulting in a hump-shapedRicker stock-recruitment curve in itself also points tothe fact that cannibalism is a major mechanism regu-lating perch recruitment (Ricker 1954). Second, theaddition of growth data for YOY perch for the years1999–2001 shows that growth in YOY perch is densitydependent—a density dependence that our modelingsuggests to be a result of competition for food. Finallyand most importantly, the extended time series up to2000 shows that the perch population has moved backto its previous stunted phase with high density of perch$2 yr old, slow individual growth rates of perch in-dividuals, high mortality of YOY perch leading to low

recruitment to age 1 yr, cannibalism contributing onlyto a small extent to perch’s diet and growth, and theabsence of a strong depression in zooplankton biomass.A difference between the years 1991–1993 and 2000was present in that more giant individuals were presentin 2000 than in 1991–1993. The reason for this dif-ference is not known, but may be due to the fact thatthe years 1991–1993 represented a later part of thestunted phase when giant individuals had died off be-cause of lack of suitable prey items.

Conditions necessary for the developments of giants

The model predictions by Claessen et al. (2000, seealso Claessen et al. 2002) showed that giant growthwas a result of cannibals ‘‘surfing’’ on a slow-growingyear class for several years. Empirical data are in con-flict with this dynamical pattern as (1) diet data suggestthat giant perch only cannibalize YOY perch and notolder perch, and (2) the mean size of 1-yr-old perchdid not differ between study years (Fig. 4) (Persson etal. 2000). Our modeling of within-season dynamicsshows that perch can indeed accelerate and becomegiants without cannibalizing on perch older than YOYperch. Actually, our modeling suggests that perch maypotentially accelerate in growth and become giantseven if they do not include any other prey items thanYOY perch. It should, however, be noted that (1) theobserved growth rates in most cases were above thosepredicted from a diet of YOY perch only, and (2) thepredicted growth rates are based on the assumption thatperch can search for both YOY perch and macroin-vertebrates simultaneously (i.e., encounter efficienciesof 1.0 for both prey). Taking both these aspects into


consideration suggests that a supplementation withmacroinvertebrates is necessary to reach the observedsizes.

Our modeling of the stunted phase suggests that zoo-plankton is an important resource for perch up to a sizeof 30 g and that a combination of zooplankton andmacroinvertebrates is necessary to reach observed siz-es. It should be pointed out that the zooplankton sizewe used to simulate consumption and growth was a0.5-mm cladoceran, which is the average size of zoo-plankton in the study lake (Wahlstrom et al. 2000),whereas Claessen et al. (2000) used a 1.0-mm cladoc-eran size, which will allow perch to reach a larger sizefeeding on zooplankton only. Still, macroinvertebratesmay be important in reducing the coupling betweenlarge perch growth performance from the zooplanktondynamics as affected by YOY perch (see Discussion:Does the perch population dynamics involve dwarf andgiant cycles?).

Resource dynamics

Our predictions (and observations) regarding the im-pact of perch on zooplankton dynamics show that thedynamics of this resource was affected by YOY perch(during the giant phase) but not by older perch. Thesmall effect of larger perch (i.e., perch .150 mm) onzooplankton biomass can be related to their low attackefficiency on small zooplankton (Bystrom and GarciaBerthou 1999, Wahlstrom et al. 2000). Larger perch dohave an impact on the zooplankton community sizestructure reflected in the small average size of the zoo-plankton community (dominance of Bosmina and Cer-iodaphnia) (Wahlstrom et al. 2000). However, the onlyperch cohort having an impact on the population abun-dance of the species dominating the zooplankton com-munity is YOY perch. When these perch are absentduring most of the growth season due to high canni-balism, the zooplankton resource remains close to itscarrying capacity (see Claessen et al. [2000] for similarconclusions). Also our predictions regarding macro-invertebrate biomasses were largely in correspondencewith observations. Our modeling suggests that the dif-ference in macroinvertebrate biomass between phases(higher in the giant phase) is mainly explained by thedifference in adult perch density between phases.

As described in Materials and Methods, above ourtreatment of macroinvertebrates was restricted to pred-ator-sensitive macroinvertebrates. Diet analyses ofperch show that they do consume other macroinver-tebrates, particularly chironomid larvae (Persson et al.1996), however, functional-response experiments showa very low (and prey-density-independent) attack rateon sediment-dwelling chironomids (B. Christensen andL. Persson, unpublished data). Furthermore, field dataprovide no evidence for a density-dependent relation-ship between perch density and macroinvertebrate bio-mass not sensitive to predators (Persson et al. 1999,2000). Given these circumstances, it is likely that the

inclusion of macroinvertebrates other than predator-sensitive ones would have only added marginally toperch energy intake.

Mortality and habitat use of YOY perch

We predicted that YOY perch mortality for the giantphase should be lower than the estimated ones basedon Bongo trawlings. It is well known that escape offish larvae constitutes a major error in estimates of fishlarvae abundance (Noble 1970, Wanzenbock et al.1997). The correction we used is based on studies onthe Miller sampler (Noble 1970, Rudstam et al. 2001)since estimates of size-dependent escapes are not avail-able for Bongo trawls. The Miller sampler is a high-speed sampler (approximately double the speed of aBongo trawl), suggesting that problems with size-de-pendent escape should be larger for Bongo trawls thanfor Miller samplers. We have several lines of evidencethat the model predictions yielded more correct esti-mates of YOY perch abundance than the corrected Bon-go-trawl estimates. First, observed growths and dietsof perch and the biomass of zooplankton were correctlypredicted, and this combination of correct predictionsis not possible assuming that the Bongo trawlings gavecorrect estimates. Further more it is not possible togenerate the observed growth and diet of giant perchif the estimates of YOY perch abundance based oncorrected Bongo trawlings at day 31 were used, evenif it is assumed that the perch totally eradicated thewhole YOY perch cohort (which was not the case) (L.Persson, simulation results not shown). Second, inde-pendent estimates of the impact of different densitiesof YOY perch on zooplankton biomasses from enclo-sure experiments show that the densities of YOY perchpredicted by the model yielded an impact on zooplank-ton as predicted and observed (Bystrom et al. 1998,Bystrom and Garcia-Berthou 1999). Third, the inde-pendent estimates of YOY perch abundance at the endof the season were in agreement with model predic-tions. A size-dependent escape is also in agreementwith the fact that the discrepancy between empiricallyestimated numbers and predicted numbers of YOYperch was larger for the giant phase when YOY perchgrew faster. Our interpretation is therefore that our pre-dicted mortality rates more closely match actual mor-tality rates than the mortality rates estimated from Bon-go trawlings.

Our empirical data on habitat use of YOY perch andtheir cannibals show that the habitat use of cannibalsand victims differed between the two phases. In yearswith high densities of cannibals, cannibals use the off-shore benthic habitat to a larger extent than in yearswith low densities of cannibals (Persson et al. 2000).The time when YOY perch switch to the shore habitat(studied during the giant phase) also depended on thedensity of shore cannibals (Bystrom et al. 2003). Thispattern led Persson et al. (2000) to suggest that habitatselection of cannibals and victims may have substantial


population dynamical consequences. In our modelingof YOY perch mortality we found that altering the as-sumptions about habitat use of cannibalistic and YOYperch within phases only had small effects on YOYperch mortality. Instead, the main difference in mor-tality rates of YOY perch between the two phases isexplained by a difference in the number of cannibals.Persson et al. (2000) showed that the changes in can-nibal numbers were associated with major changes incannibal habitat use, hence the interaction betweennumbers and habitat use may nevertheless still be im-portant to explain shifts in YOY perch survival be-tween phases.

Interactions between YOY perch and 1-yr-old perch

The model predictions by Claessen et al. (2000) andthe empirical results by Persson et al. (2000) differedin that the latter suggested a strong negative compet-itive impact of YOY perch on 1-yr-old perch to bepresent. Our within-season modeling supports the ideathat YOY perch affect the growth of 1-yr-old perchnegatively through competition. If encounter efficiencyon zooplankton was not reduced, the severity of thiscompetition was small and 1-yr-old perch were pre-dicted to grow to a substantially larger size than ob-served early on in the growth season due to heavyzooplankton feeding. The larger size of 1-yr-old perch,in turn, led to the fact that YOY perch remained in thecannibalism window of 1-yr-old perch for the wholegrowth period (i.e., a substantial positive effect of YOYperch on 1-yr-old perch). Restricting 1-yr-old perchencounter efficiency with zooplankton and YOY perchreflecting a restricted habitat use resulted in a predictedgrowth and diet similar to those observed. The ob-served restricted habitat use of 1-yr-old perch can berelated to predation risk from larger giant perch as 1-yr-old perch at the start of their growth season aresusceptible to giant perch cannibalism (size ratio 50-mm perch/200-mm perch 5 0.25, maximum ratio 50.4) (Claessen et al. 2000).

Our results concerning 1-yr-old perch thus suggestthat adaptive habitat use of 1-yr-old perch may havesubstantial effects on the long-term dynamics of thiscannibalistic system. This conclusion results from thefact that the restricted habitat use of 1-yr-old perch mayalter the interaction between YOY perch and 1-yr-oldperch from being a mainly cannibal–victim interaction(positive effect on 1-yr-old perch) to a mainly inter-cohort competitive interaction (negative effect on 1-yr-old perch). It can be hypothesized that the die-off of1-yr-old perch for a number of subsequent years duringthe giant phase is an essential element to keep the sys-tem in the giant phase characterized by repeated suc-cessful recruitment of YOY perch (see Fig. 3). In theabsence of this die-off, the system would move backto the stunted phase once the first successfully recruit-ing perch cohort reached a size where they could ef-

ficiently deplete the YOY cohort (see sequence 1998–2000 in Fig. 3).

The importance of 1-yr-old perch habitat use for de-termining the interaction type points to the idea thatadaptive habitat use may be of substantial importancefor population dynamics. Experiments that have sug-gested significant effects of flexible behavior (includ-ing activity level) on population and community dy-namics have generally been carried out at short-term(within-generation) and small spatial (enclosure, pond)scales (Turner and Mittelbach 1990, Werner and Anholt1993, Persson and Eklov 1996, Anholt and Werner1998, Peacor and Werner 2001, Schmitz and Suttle2001), and hence cannot address the long-term popu-lation dynamical consequences of behavior. Whetherflexible adaptive behavior of perch is necessary to in-clude or whether a fixed behavior of 1-yr-old perch issufficient to explain the dynamics observed for theperch population also remains an issue for further anal-yses (see De Roos et al. [2002] for an analysis of aconsumer-resource case with habitat and size-depen-dent habitat use).

Does the perch population dynamicinvolve dwarf and giant cycles?

Based on perch parameter values, Claessen et al.(2000) showed that the population dynamics of can-nibals competing with their victim for a basic resourcein one phase was characterized by high cannibalisticmortality on very young and small victims. This re-sulted in the fact that the shared resource was notstrongly depressed by recruiting individuals as wouldhave been the case in the absence of cannibalism (Pers-son et al. 1998). This effect represents an indirect pos-itive effect of cannibalism (Polis 1988). Although can-nibalism thus reduced inter-cohort competition throughcannibal control of victims, the main part of the energyintake by cannibals was derived from the shared re-source, and the maximum size of cannibals was small.In this phase of the cannibalistic dynamics, energy ex-traction is hence low and the effect of cannibalism issimilar to that found in cannibalistic models that as-sume that cannibals do not gain energy from but onlyimpose a mortality on victims (Diekmann et al. 1986,Hastings and Costantino 1987, Costantino et al. 1997,Van den Bosch and Gabriel 1997). The empirically ob-served dynamics of perch during the stunted phase inseveral respects resembles this dynamic as our mod-eling and empirical data confirm that cannibals imposea high mortality on YOY perch, and that the contri-bution of YOY perch to the diet and energy balance ofcannibalistic perch is small in this phase. A discrepancyis that our modeling analysis shows that the additionof a second shared resource (macroinvertebrates) is es-sential to allow cannibalistic perch to have a positive,albeit small growth up to the maximum size that isempirically observed during the stunted phase.


While the observed dynamics during the stuntedphase qualtitatively resemble that predicted by Claes-sen et al. (2000), the induction of giants is very dif-ferent between observed data and the model. In themodel by Claessen et al. (2000), recruiting individualsfrom a strong reproductive output depressed the re-source to such a degree that most of the older individ-uals starved to death, leading to a low mortality of thisrecruiting cohort. There is no empirical evidence tosupport this mortality mechanism (Claessen et al. 2000,Persson et al. 2000). One explanation for the discrep-ancy between model predictions and data is that themacroinvertebrate resource, not included in the model,in addition to being critical for the performance ofstunted cannibals also may prevent YOY perch frommore or less eradicating cannibals. Even if YOY perchwere assumed to affect macroinvertebrates, their im-pact on this resource was restricted to the time periodafter their shift to the shore habitat. At that time, YOYperch are highly susceptible to and energetically prof-itable for larger perch.

Data and predictions of the model of Claessen et al.(2000) also differ in three other major aspects. First,the shared resource (zooplankton) is expected to in-crease during the phase with dwarfs and giants in themodel as dwarfs approach maturity. In contrast, datasuggest a discrete difference in zooplankton dynamicsbetween the two phases (Persson et al. 2003). Second,the repeated successful recruitment of YOY perch ob-served over a number of subsequent years (1995–1998)and the concomitant die-off of 1-yr-old perch everyyear in 1995–1997 is clearly in contradiction to modelpredictions. Third, although giants in the model fedextensively on the numerous cohort for several years,the low number of giants precluded a substantial dy-namical impact (energy extraction but no control)(Claessen et al. 2000). In the data there was a 10-folddifference in number of cannibals between phases, butas a result of increased individual growth of the re-maining individuals due to energy extraction from can-nibalism on YOY perch, increased per capita fecunditypartly compensated for the lower number of cannibals.As a result, successful recruitments of YOY perch wereobserved for a number of years (1995–1998). Thesestrong YOY cohorts, in turn, exerted a substantial com-petitive impact on 1-yr-old perch cohorts, so energyextraction from cannibalism giants in the lake had asignificant dynamical impact. Although most cannibalmodels ignore the energy gain of cannibalism (andhence the effects of per capita fecundity on energyintake) (Diekmann et al. 1986, Hastings and Costantino1987, Dennis et al. 1997, Van den Bosch and Gabriel1997), our results strongly suggest that ignoring energyextraction may lead to important elements of the in-teractions between cannibals and victims being ne-glected (Persson et al. 2003).

The fact that both zooplankton dynamics and perchrecruitment differed in a discrete way between phases

raises the question whether the mechanisms behind thetemporal appearance of giants may be better explainedby alternative attractors than by a dynamics involvinga combination of dwarf and giant cycles and cannibal-driven dynamics (see Fig. 3). Recent size-structuredmodeling of cannibalistic dynamics using a continuousmodel with energy gain indeed shows that alternativeequilibria may exist for intermediate values of the low-er size limit (d) of the cannibalistic window (Claessenand De Roos 2003). These two equilibria involve astunted and a giant state, and, in accordance with ob-servations on perch, the resource level of the sharedresource (zooplankton) is lower in the giant state. Thepopulation numbers of cannibals are, however, higherin the giant state than in the stunted state in this model.The extent to which these results carry over to the perchsystem—which is better described by a combination ofdiscrete (reproduction) and continuous (foraging, me-tabolism, mortality, resource dynamics) processes thanby a purely continuous system—is also unclear (Claes-sen 2002). Fisher (1987) showed in a discrete modelwith size-dependent cannibalism and competition thatbistability might be present, with the stunted state hav-ing a higher population density. However, like mostother cannibal models his model lacked energy ex-traction. This contrasts to our study where energy ex-traction is shown to be dynamically important by set-ting up the competitive interaction between YOY and1-yr-old perch through the recurrent production ofYOY perch cohorts by giants. Our within-season mod-eling and empirical data suggest that (1) the secondresource (macroinvertebrates) and (2) the restrictedhabitat use of 1-yr-old perch may be critical for theextended existence of the giant phase over severalyears. Indeed, an extended multigenerational analysissuggests that the inclusion of both these factors is es-sential to generate the dynamics observed. Further-more, our modeling analysis suggests that a dynamicsinvolving both stunted and giant phases does not nec-essarily involve alternative attractors (Persson et al.2003).

Physiologically structured models as a frameworkfor a quantitative ecology including a closer

interaction between theory and data

A classical dilemma running through the history ofecology is the contrast between simple strategic modelsthat offer generality but may be hard to test againstempirical data from field systems especially in quan-titative terms, and complex tactical models that havea high testing power but are less prone to offer gen-erality (Levins 1966, DeAngelis and Waterhouse 1987,Murdoch et al. 1992, Murdoch and Nisbet 1996). Mur-doch et al. (1992) advocated a research strategy thatinvolved a logical linking of highly testable more com-plex models and more simple general models, wherethe essential mechanisms of the former models are pre-served in the latter models, but details are removed


through a strip-off process. Physiologically structuredpopulation models (PSPMs)—which we have used inour study where distributions or cohorts rather thanindividuals are followed–represent models of inter-mediate complexity in the span from purely individual-based models to unstructured models. Despite their in-termediate complexity, distribution models have prov-en able to successfully address general ecological is-sues (De Roos et al. 1990, Persson et al. 1998, Claessenet al. 2000, 2002, De Roos and Persson 2001). Fol-lowing Murdoch et al. (1992), it has also been shownfor some configurations that the fully structured modelsmay be reduced to simpler stage-based models thatpreserve the essential mechanisms; whereas the fullystructured models lend themselves to more quantitativepredictions, the stage-based models allow a more com-plete analysis of stability properties (consumer–re-source interactions: Persson et al. (1998) vs. De Roosand Persson (2003), structured tritrophic food chains:De Roos and Persson (2002) vs. De Roos et al. 2003).However, in the case of cannibalism, the strong sizedependence of the cannibal–victim interactions and thefeed-back effect of energy extraction on individualgrowth (size) and per capita fecundity makes a reduc-tion of model complexity to stage-structured versionsmuch more problematic (De Roos and Persson 2001).Individual-level functional formula may be simplifiedand the discrete reproduction assumption used in ourpaper relaxed, allowing, for example, the tracking ofunstable equilibria (Claessen and De Roos 2003). How-ever, in that case (and insofar as is known today) thereduction in model complexity has to take place withinthe domain of PSPMs.

A major advantage of the PSPM approach as illus-trated by our study is that within-season modeling mayfill an important role in delineating the essential mech-anisms driving the dynamics, where population-levelformulations would have been much less informative(Fig. 7). Through the study we have used a number ofindividual-level (individual growth, diet) and popula-tion-level (mortality, resource levels) analyses with theaim to uncover the basic mechanisms underlying thedynamics of the cannibalistic perch population. Con-ceptually, the advantage of the PSPM approach to testpredictions and to develop a closer relationship be-tween empirical and theoretical research can be relatedto its two-state-levels nature. In PSPMs, model as-sumptions adhere to the individual level, and no furtherassumptions are introduced at the population level—in contrast to contemporary population-level formu-lations (Metz et al. 1988, De Roos 1997, De Roos andPersson 2001). In our model, the individual-level as-sumptions are due to specifying functions for size-de-pendent attack rates, metabolic rates, energy channel-ing, etc. The derivations of these functions, includingparameter estimations, are based on experiments totallyindependent of the cannibalistic system under study,leading to a higher independence between model as-

sumptions and model testing of population-level dy-namics than in, for example, time-series approacheswhere (population-level) data from the system understudy are used to fit model parameters (cf. Turchin etal. 2000). Furthermore, the quantitative predictions ofindividual-level dynamics such as individual growthand diet has a strong independence from individual-level formulations (assumptions) since the populationfeedback on individual performance (i.e., the appear-ance of gigantic growth) cannot be predicted a priorifrom individual-level formulations (assumptions).

The utility of the approach that we have used alsolies in the fact that individual performances (growth,diet) as a result of the population feedback are readilymeasurable empirically in a quantitative way. It is im-portant to realize that the quantitative contrast betweenpredictions and empirical observations regarding theimpact of the second shared resource (macroinverte-brates) and 1-yr-old perch habitat use was essential tobe able to show that a dynamics including coupleddwarf and giant cycles is highly unlikely for the systemwe studied. More importantly, our within-season anal-ysis allowed us to suggest the mechanisms that werenecessary to incorporate in order to yield a more correctdescription of the long-term dynamics of the canni-balistic system (e.g., Persson et al. 2003). This restruc-turing of the model represented more than a ‘‘fine tun-ing’’ of previous models. It meant a qualitative changein modeling perspective regarding which interactionswere driving the system—for example, a shift from afocus on inter-cohort competition between YOY perchand perch $2 yr old to a focus on inter-cohort com-petition between YOY perch and 1-yr-old perch.

ACKNOWLEDGMENTS

We thank J. Andersson, C. Halvarsson, J. Hjelm J. Karls-son, E. Lindgren, P. Nilsson, P. Nordin, A. Persson. K. Sa-muelsson, F. Staffans, and R. Wallin for help with extensivefield sampling. We thank two anonymous reviewers and OsSchmitz for valuable comments on the manuscript. The studywas supported by a grant from the Swedish Research Counciland the Swedish Research Council for Environment, Agri-cultural Sciences and Spatial Planning to L. Persson and agrant from the Dutch Science foundation to A. M. De Roos.This paper was to a large extent written when L. Persson wasa visiting Killam professor at University of Calgary, Canada.The long-term use of the experimental lake area is providedthrough Aman’s Fish Cooperative, which is gratefully ac-knowledged.

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