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Dwarfs and giants: the dynamic interplay of size-dependent cannibalism and
competition
Claessen, D.
Publication date
2002
Link to publication
Citation for published version (APA):
Claessen, D. (2002). Dwarfs and giants: the dynamic interplay of size-dependent cannibalism
and competition. UvA-IBED.
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Summary y
Cannibalismm is an interaction between members of the same population which generallyy involves: (1) mortality of victims; (2) energy gain by cannibals; (3) a size-dependentt cannibalistic attack rate; and (4) competition between victims and cannibals.. This thesis has two aims: First, to study long-term population dynam-icss of a size-structured population model that incorporates these four aspects of cannibalism.. Second, to formulate the model such that it can be used to compare itss predictions with empirical data on population dynamics of piscivorous fish, in particularr the Eurasian perch. A general result that emerges from chapters 2, 3 and 44 is that size-dependent cannibalism, size-dependent competition and the popula-tionn size-distribution should be considered in conjunction because their interplay hass important consequences that would be overseen otherwise.
Inn Chapter 2 a size-structured population model has been developed which incorporatess size-dependent cannibalism and size-dependent competition. The de-pendencee of the cannibalistic attack rate on cannibal and victim size has been incorporatedd into two components, one that depends on cannibal size only and onee which depends on the ratio of victim and cannibal length. The former takes intoo account that the absolute attack rate increases with cannibal length, whereas thee latter takes the effect of relative victim size (i.e., relative to cannibal size) into accountt (section 1.4). The most important cannibalism-related parameters in our modell are the cannibalistic voracity (the species-specific tendency to cannibalise, denotedd by /?) and the lower and upper limits of the cannibalism window (ö and e, respectively).. Our model is the first model that takes into account that individuals cann be too small to be captured by cannibals of a given size. The model of van den Boschh and Gabriel (1997) incorporates a lower limit as well, but these authors as-sumee that it depends age rather than size, and moreover that it is independent of canniball size (or age).
Inn our model, size-dependent competition emerges from the combination of size-dependentt vital rates and exploitative foraging on a dynamic resource. The consequencess of such size-dependent competition have been investigated by Pers-sonn et al. (1998), who show that if small individuals can sustain themselves at a
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lowerr resource density than large individuals (in particular, adults), then competition-inducedd generation cycles are predicted.
Inn Chapter 2 the dependence of population dynamics on the cannibalistic vo-racityy (/?) is investigated. In the absence of cannibalism {(3 — 0) single-cohort cycless are found, which are caused by size-dependent competition for the alterna-tivee resource. Intermediate levels of cannibalism (/3 = 19 .. .45) dampen these generationn cycles, resulting in a relatively stable population size distribution with individualss of all ages present. With a higher cannibalistic voracity (/? > 45), periodss of cannibalism-induced stability and periods of competition-induced pop-ulationn cycles alternate, whereas at very high voracities (J3 > 355) only popula-tionn cycles are found. Although these cycles are mainly driven by size-dependent competition,, similar to the single-cohort cycles found in the absence of canni-balism,, cannibalism has a striking effect: the population consists of two distinct size-classes.. The smaller size class is very numerous, controls the alternative re-source,, and suffers from intra-cohort competition with retards its growth. The agee at maturation of this class determines the cycle length. The larger size-classs has a low density and has an exclusively cannibalistic diet. Due to a striking sizee difference, individuals in the former size class are referred to as 'dwarfs' and inn the latter as 'giants'. The giants survive the resource depletion by the domi-nantt dwarf cohort because they cannibalise the dwarf cohort. Thus, the interplay betweenn size-dependent cannibalism and competition can result in either stabilisa-tionn of competition-induced population cycles (cf. Cushing, 1991; van den Bosch andd Gabriel, 1997), or in population cycles with large amplitude and a period close too the generation time. In the latter case the most striking feature is the bimodal sizee distribution, consisting of dwarfs and giants.
Inn section 2.4 these results are compared with empirical data. First, it is argued thatt the data presented by LeCren (1992) on the dynamics of the perch population inn Lake Windermere and the occurrence of 'exceptionally big' individuals are in agreementt with the dwarfs-and-giants dynamics found in our model. Second, a moree thorough comparison was made of model predictions with empirical data onn time series of perch abundance, size-distributions, growth curves, diets and zooplanktonn dynamics from Lake Abborrtjarn 3. This comparison showed both agreementt and discrepancies between model predictions and data. Particularly, the timingg of the acceleration of giant cannibals with perch and zooplankton densities wass in accordance with the model, but in the dynamics following the moment of accelerationn discrepancies were found. Nevertheless, our model provides novel insightt in the dynamics of populations in which both size-dependent cannibalism andd competition occur. In particular this includes the appearance of giant cannibals ass an emergent property of these two interactions.
Chapterr 3 continues the study of the model developed in Chapter 2, focusing on thee effect of the size-dependent nature of cannibalism itself. Specifically, we in-vestigatee the effect of the lower (S) and upper (e) limits of the cannibalism window. Contraryy to the results of van den Bosch and Gabriel (1997), who found that "the positionn of the stability boundary is influenced by the position of the cannibalism
windoww to a minor extend only", it appears that both parameters have great im-portancee for individual life histories, the population size distribution, and/or pop-ulationn dynamics. Strikingly, the two parameters have entirely different effects. Thee lower limit of the cannibalism window (6) determines whether cannibalism hass the capacity to dampen competition-induced population cycles. If Ö is below a criticall value, competition-induced population cycles like the single-cohort cycles neverr occur. If Ö is above a second critical value (larger than the first), single-cohortt cycles are the only possible type of population dynamics. In the range in betweenn the two critical values, the dynamics resemble a mixture of the cohort cy-cless and the population state stabilised by cannibalism. This is the range in which dwarfs-and-giantss dynamics occur (Chapter 2).
Thee latter critical value of 5 can be understood as follows. Reproducing indi-vidualss can counter the competitive superiority of recruits only if they manage to decimatee the latter's density before they are outcompeted by the recruits. New-bornn individuals are within the cannibalism window of reproducing individuals if
88 is sufficiently small. If, however, 6 is above the critical value, the reproducing
individualss are dead before they get the chance to decimate the YOY. By approx-imation,, this requires that S < L^/Li where Lf, is the length at first feeding of larvae,, and L\ is the length at first reproduction. A similar reasoning applies to the secondd critical value of 6.
Thee upper limit of the cannibalism window (e) has a limited effect on popula-tionn dynamics, but a drastic one on population size distribution. Essentially, it de-pendss on e whether or not individuals manage to enter the 'piscivory niche', which iss defined as the size range in which individuals feed exclusively on conspecifics. Iff they do not manage (which occurs if e is below a critical value) the population is characterisedd by a small ultimate length, and hence referred to as stunted. If they doo manage, they reach giant sizes on a cannibalistic diet and the population size distributionn is accordingly very wide. The transition between these two states of thee population occurs abruptly, and resembles a catastrophic bifurcation. Yet, no bistabilityy is found.
Thee results are compared to empirical data on population dynamics of a num-berr of piscivorous fish species for which data on 6 and e exist. Eurasian perch and yelloww perch (Perca fiavescens) differ in their value of 6 (Mittelbach and Persson,
1998).. A comparison between these two perch species, using data on population
dynamicsdynamics from Persson et al. (2000) and Sanderson et al. (1999), confirms the resultss we found with our model.
Inn Chapter 4 a second population model of size-dependent cannibalism has been formulatedd which can be regarded as a simplification of the first model. It has fewerr state variables and fewer parameters, and it assumes that reproduction oc-curss continuously rather than in pulses. This model was analysed with both nu-mericall simulations and numerical continuation of equilibria. The latter method allowss one to study both stable and unstable equilibria, and reveals how different equilibriaa are connected with each other (or not). Using the continuation method wee gained insight into this system which would have been very hard to obtain
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withh simulations alone. The most striking result revealed with this method was thee coexistence of two stable states, associated with two saddle-node or fold bifur-cations.. For certain parameters, the population can either converge to a 'stunted' statee or a 'piscivorous' state, depending on initial conditions. In the stunted state thee population contains small individuals only, whereas in the piscivorous state the populationn contains individuals of giant sizes that consume conspecifics only. The stuntedd state is characterised by small ultimate size, little gain from cannibalism, andd a high alternative resource density. Inversely, the piscivorous state is charac-terisedd by large ultimate sizes, a high gain and a low resource. We argue that the drivingg force of the bistability is the 'Hansel and Gretel' effect. This effect is based onn the dependence of the 'mean yield' of cannibalism on the size distribution of cannibals.. Due to the cannibalism window, if cannibals are larger they have a largerr gain from cannibalism because on average they consume victims when they aree larger and hence contain more energy. The effect has been named after the tale which,, to our knowledge, is the first account of the idea to postpone cannibalism untill the victim has become more nutritious.
Inn the models presented in chapters 2, 3 and 4, the diet history of individuals is ann emergent property of the dynamics of individual state and their environment, i.e.,, the alternative resource and their own population. Individuals that become giantt cannibals in dwarfs-and-giants cycles (Chapter 2) feed on zooplankton dur-ingg their first year and make a very abrupt switch to piscivory shortly after the birthh of the next cohort. For the age of one year and onward, 'giants' feed exclu-sivelyy on conspecifics. In the 'piscivorous' population state, however, the switch fromm planktivory to piscivory is rather gradual (Fig. 3.9, Fig. 4.2b), and reflects thee size-dependent attack rate on the alternative resource. In less stable population dynamics,, the diet of individuals may switch back and forth between planktivory andd piscivory. Nevertheless, in general the diet of smaller individuals tends to be planktivorouss and the diet of larger individuals piscivorous.
Adaptivee dynamics of an ontogenetic niche shift
Chapterr 5 investigates the evolutionary consequences of such and ontogenetic nichee shift with a population model in which the niche shift is more or less 'hard wired'.. Although the actual diet still depends on the densities of the two different resources,, the gradual shift from exploitation of the first to the second resource is partt of the definition of an individual life history. This is in part analogous to the diett shift observed in the model of size-dependent cannibalism, but in this chapter itt is assumed that both the first and the second resources are heterospecific. On an ecologicall time scale the model always predicts a stable equilibrium in which the twoo resource densities depend on the ontogenetic niche shift of the individuals in thee population. On an evolutionary time scale it is assumed that the size at the niche shiftt is an evolutionary trait which changes by mutation from parent to offspring. Ann essential feedback in this model is that the equilibrium resource densities re-spondd to evolutionary changes in the ontogenetic 'strategies' (i.e., switch sizes)
presentt within the consumer population. Incorporation of this ecological feedback intoo the evolution of ontogenetic niche shifts is new - previous theory considered optimisationn of the switch size under given resource densities (e.g., Werner and Gilliam,, 1984; Leonardsson, 1991).
Thee adaptive dynamics of a monomorphic population (i.e., all individuals with thee same switch size) always converge to a resident strategy which exploits both resourcess equally by switching to the second niche at an intermediate body size. Thiss strategy is hence best qualified as an ontogenetic generalist. Once the gener-alistt has established itself, it depends on the size-scaling of the functional response whetherr the generalist is a continuously stable strategy (CSS) or an evolutionary branchingg point (EBP). In the former case the model predicts that the population remainss indefinitely monomorphic with only the generalist strategy present. In the latterr case it is predicted that mutants that are more specialised (i.e., that switch eitherr sooner or later than the resident to the second niche) can invade, and that thee population 'branches' into two subpopulations which diverge genetically from eachh other. Eventually, two specialist populations result, each consuming only a singlee resource throughout its life. The conditions under which the generalist strat-egyy is a CSS or an EBP can be expressed in terms of parameters of the allometric scalingg of attack rates and/or handling times.
Inn chapter 6 it is shown that the observed effects of the interplay of size-dependent cannibalismm and competition depend on the ecological interactions between indi-viduals,, rather than on the specific bioenergetics at the individual level. This is donee by comparing the results obtained with the model presented in Chapters 2 andd 3 and the model presented in Chapter 4. It appears that very similar results are foundd with both models. Yet subtle but important differences exist, but these can bee attributed to the timing of reproduction (i.e., pulsed versus continuous), rather thann bioenergetics. This result means that the finding in this thesis about the ef-fectss of the interplay of size-dependent cannibalism and competition have general implications,, since they may apply to a wide range of cannibalistic species, even thoughh these species may differ by their bioenergetics.
