Ontogenetic scaling of foraging rates and the dynamics of a size-structured consumer-resource model

Size-dependent interactions inhibit coexistence in intraguild predation systems with life-history omnivory

Growth in body size during ontogeny often results in changes in diet, leading to life-history omnivory. In addition, growth is often dependent on food density. Using a physiologically structured population model, we investigated the effects of these two aspects of individual growth in a system consisting of two size-structured populations, an omnivorous top predator and an intermediate consumer. With a single shared resource for both populations, we found that life-history omnivory decreases the likelihood of coexistence between top predator and intermediate consumer in this intraguild predation (IGP) system. This result contrasts with previous unstructured models and stage-structured models without food-dependent development. Food-dependent development and size-dependent foraging abilities of the predator resulted in a positive feedback between foraging success on the shared resource at an early life stage and foraging success on the intermediate consumer later in life. By phenomenologically incorporating this feedback in an unstructured IGP model, we show that it also demotes coexistence in this simple setting, demonstrating the robustness of the negative effect of this feedback.

THE INFLUENCE OF SIZE-SPECIFIC INDIRECT INTERACTIONS IN PREDATOR–PREY SYSTEMS

Nonlethal indirect interactions between predators often lead to nonadditive effects of predator number on prey survival and growth. Previous studies have focused on systems with at least two different predator species and one prey species. However, most predators undergo extreme ontological changes in phenotype such that interactions between different-sized cohorts of a predator and its prey could lead to nonadditive effects in systems with only two species. This may be important since different-sized individuals of the same species can differ more in their ecology than similar-sized individuals of different species. This study examined trait-mediated indirect effects in a two-species system including a cannibalistic predator with different-sized cohorts and its prey. I tested for these effects using larvae of two stream salamanders, Gyrinophilus porphyriticus (predator) and Eurycea cirrigera (prey), by altering the densities and combinations of predator size classes in experimental streams. Results showed that the presence of large individuals can significantly reduce the impact of density changes of smaller conspecifics on prey survival through nonlethal means. In the absence of large conspecifics, an increase in the relative frequency of small predators significantly increased predation rates, thereby reducing prey survival. However, with large conspecifics present, increasing the density of small predators did not decrease prey survival, resulting in a 14.3% lower prey mortality than predicted from the independent effects of both predator size classes. Small predators changed their microhabitat use in the presence of larger conspecifics. Prey individuals reduced activity in response to large predators but did not respond to small predators. Both predators reduced prey growth. These results demonstrate that the impact of a predator can be significantly altered by two different types of trait-mediated indirect effects in two-species systems: between different-sized cohorts and between different cohorts and prey. This study demonstrates that predictions based on simple numerical changes that assume independent effects of different size classes or ignore size structure can be strongly misleading. We need to account for the size structure within predator populations in order to predict how changes in predator abundance will affect predator-prey dynamics.

Variation in predation pressure as a mechanism underlying differences in numerical abundance between populations of the poeciliid fish Heterandria formosa

We explored whether a variation in predation and habitat complexity between conspecific populations can drive qualitatively different numerical dynamics in those populations. We considered two disjunct populations of the least killifish, Heterandria formosa, that exhibit long-term differences in density, top fish predator species, and dominant aquatic vegetation. Monthly censuses over a 3-year period found that in the higher density population, changes in H. formosa density exhibited a strong negative autocorrelation structure: increases (decreases) at one census tended to be followed by decreases (increases) at the next one. However, no such correlation was present in the lower density population. Monthly census data also revealed that predators, especially Lepomis sp., were considerably more abundant at the site with lower H. formosa densities. Experimental studies showed that the predation by Lepomis gulosus occurred at a much higher rate than predation by two other fish and two dragonfly species, although L. gulosus and L. punctatus had similar predation rates when the amount of vegetative cover was high. The most effective predator, L. gulosus, did not discriminate among life stages (males, females, and juveniles) of H. formosa. Increased predation rates by L. gulosus could keep H. formosa low in one population, thereby eliminating strong negative density-dependent regulation. In support of this, changes in H. formosa density were positively correlated with changes in vegetative cover for the population with a history of lower density, but not for the population with a history of higher density. Our results are consistent with the hypothesis that the observed differences among natural populations in numerical abundance and dynamics are caused in part by the differences in habitat complexity and the predator community.

Predicting shifts in dynamics of cannibalistic field populations using individual-based models

The occurrence of qualitative shifts in population dynamical regimes has long been the focus of population biologists. Nonlinear ecological models predict that these shifts in dynamical regimes may occur as a result of parameter shifts, but unambiguous empirical evidence is largely restricted to laboratory populations. We used an individual-based modelling approach to predict dynamical shifts in field fish populations where the capacity to cannibalize differed between species. Model-generated individual growth trajectories that reflect different population dynamics were confronted with empirically observed growth trajectories, showing that our ordering and quantitative estimates of the different cannibalistic species in terms of life-history characteristics led to correct qualitative predictions of their dynamics.

Population dynamic theory of size-dependent cannibalism

Cannibalism is characterized by four aspects: killing victims, gaining energy from victims, size-dependent interactions and intraspecific competition. In this review of mathematical models of cannibalistic populations, we relate the predicted population dynamic consequences of cannibalism to its four defining aspects. We distinguish five classes of effects of cannibalism: (i) regulation of population size; (ii) destabilization resulting in population cycles or chaos; (iii) stabilization by damping population cycles caused by other interactions; (iv) bistability such that, depending on the initial conditions, the population converges to one of two possible stable states; and (v) modification of the population size structure. The same effects of cannibalism may be caused by different combinations of aspects of cannibalism. By contrast, the same combination of aspects may lead to different effects. For particular cannibalistic species, the consequences of cannibalism will depend on the presence and details of the four defining aspects. Empirical evidence for the emerged theory of cannibalism is discussed briefly. The implications of the described dynamic effects of cannibalism are discussed in the context of community structure, making a comparison with the community effects of intraguild predation.

Gigantic cannibals driving a whole-lake trophic cascade

Trophic cascades have been a central paradigm in explaining the structure of ecological communities but have been demonstrated mainly through comparative studies or experimental manipulations. In contrast, evidence for shifts in trophic cascades caused by intrinsically driven population dynamics is meager. By using empirical data of a cannibalistic fish population covering a 10-year period and a size-structured population model, we show the occurrence of a dynamic trophic cascade in a lake ecosystem, in which the community over time alternates between two different configurations. The intrinsically driven change in the size structure of the fish population from a dominance of stunted individuals to a dominance of gigantic cannibals among adult individuals is the driving force behind distinct abundance switches observed in zooplankton and phytoplankton. The presence of the phase with gigantic cannibals depends critically on the energy they extract from their victims, allowing strong reproduction for a number of years.

Competition in size-structured populations: mechanisms inducing cohort formation and population cycles

In this paper we investigate the consequences of size-dependent competition among the individuals of a consumer population by analyzing the dynamic properties of a physiologically structured population model. Only 2 size-classes of individuals are distinguished: juveniles and adults. Juveniles and adults both feed on one and the same resource and hence interact by means of exploitative competition. Juvenile individuals allocate all assimilated energy into development and mature on reaching a fixed developmental threshold. The combination of this fixed threshold and the resource-dependent developmental rate, implies that the juvenile delay between birth and the onset of reproduction may vary in time. Adult individuals allocate all assimilated energy to reproduction. Mortality of both juveniles and adults is assumed to be inversely proportional to the amount of energy assimilated. In this setting we study how the dynamics of the population are influenced by the relative foraging capabilities of juveniles and adults. In line with results that we previously obtained in size-structured consumer-resource models with pulsed reproduction, population cycles primarily occur when either juveniles or adults have a distinct competitive advantage. When adults have a larger per capita feeding rate and are hence competitively superior to juveniles, population oscillations occur that are primarily induced by the fact that the duration of the juvenile period changes with changing food conditions. These cycles do not occur when the juvenile delay is a fixed parameter. When juveniles are competitively superior, two different types of population fluctuations can occur: (1) rapid, low-amplitude fluctuations having a period of half the juvenile delay and (2) slow, large-amplitude fluctuations characterized by a period, which is roughly equal to the juvenile delay. The analysis of simplified versions of the structured model indicates that these two types of oscillations also occur if mortality and/or development is independent of food density, i.e. in a situation with a constant juvenile developmental delay and a constant, food-independent background mortality. Thus, the oscillations that occur when juveniles are more competitive are induced by the juvenile delay per se. When juveniles exert a larger foraging pressure on the shared resource, maturation implies an increase not only in adult density, but also in food density and consequently fecundity. Our analysis suggests that this correlation in time between adult density and fecundity is crucial for the occurrence of population cycles when juveniles are competitively superior.

Size-dependent life-history traits promote catastrophic collapses of top predators

Catastrophic population collapses such as observed in many exploited fish populations have been argued to result from depensatory growth mechanisms (i.e., reduced reproductive success at low population densities, also known as Allee effect). Empirical support for depensation from population-level data is, however, hard to obtain and inconclusive. Using a size-structured, individual-based model we show that catastrophic population collapses may nonetheless be an intrinsic property of many communities, because of two general aspects of individual life history: size- and food-dependent individual growth and individual mortality decreasing with body size. Positive density dependence, characteristic for depensatory growth mechanisms and catastrophic behavior, results as a direct and robust consequence of the interplay between these individual life-history traits, which are commonly found in many species.

Ecological bistability and evolutionary reversals under asymmetrical competition

How does the process of life-history evolution interplay with population dynamics? Almost all models that have addressed this question assume that any combination of phenotypic traits uniquely determine the ecological population state. Here we show that if multiple ecological equilibria can exist, the evolution of a trait that relates to competitive performance can undergo adaptive reversals that drive cyclic alternation between population equilibria. The occurrence of evolutionary reversals requires neither environmentally driven changes in selective forces nor the coevolution of interactions with other species. The mechanism inducing evolutionary reversals is twofold. First, there exist phenotypes near which mutants can invade and yet fail to become fixed; although these mutants are eventually eliminated, their transitory growth causes the resident population to switch to an alternative ecological equilibrium. Second, asymmetrical competition causes the direction of selection to revert between high and low density. When ecological conditions for evolutionary reversals are not satisfied, the population evolves toward a steady state of either low or high abundance, depending on the degree of competitive asymmetry and environmental parameters. A sharp evolutionary transition between evolutionary stasis and evolutionary reversals and cycling can occur in response to a smooth change in ecological parameters, and this may have implications for our understanding of size-abundance patterns.

Single-species models for many-species food webs

Most species live in species-rich food webs; yet, for a century, most mathematical models for population dynamics have included only one or two species. We ask whether such models are relevant to the real world. Two-species population models of an interacting consumer and resource collapse to one-species dynamics when recruitment to the resource population is unrelated to resource abundance, thereby weakening the coupling between consumer and resource. We predict that, in nature, generalist consumers that feed on many species should similarly show one-species dynamics. We test this prediction using cyclic populations, in which it is easier to infer underlying mechanisms, and which are widespread in nature. Here we show that one-species cycles can be distinguished from consumer resource cycles by their periods. We then analyse a large number of time series from cyclic populations in nature and show that almost all cycling, generalist consumers examined have periods that are consistent with one-species dynamics. Thus generalist consumers indeed behave as if they were one-species populations, and a one-species model is a valid representation for generalist population dynamics in many-species food webs.

A theoretical investigation into the direct and indirect effects of state on the risk of predation

As well as there being a direct physical effect of the state (for example fat reserves, or size) of an animal on the risk of being caught by a predator, state also has an effect on predation risk indirectly through changes in behaviour. We present a mathematical model which looks at these two components of the effect of state on predation risk. We focus on two different models, (i) where the animal must achieve a fixed state and its fitness depends on the time at which this state is reached and (ii) where the animal must survive until a fixed time and its fitness depends on its final state. We investigate conditions under which the indirect effect of increased state is to increase or decrease predation risk, and give some numerical illustrations. Under certain conditions in the fixed-state model, the indirect effect of state is to increase predation risk, whereas under certain conditions in the fixed-time model the indirect effect of state is to decrease predation risk. We discuss the implications of our results for empirical investigations into the effect of state on predation risk.

Dwarfs and Giants: Cannibalism and Competition in Size-Structured Populations

Cannibals and their victims often share common resources and thus potentially compete. Smaller individuals are often competitively superior to larger ones because of size-dependent scaling of foraging and metabolic rates, while larger ones may use cannibalism to counter this competition. We study the interplay between cannibalism and competition using a size-structured population model in which all individuals consume a shared resource but in which larger ones may cannibalize smaller conspecifics. In this model, intercohort competition causes single-cohort cycles when cannibalism is absent. Moderate levels of cannibalism reduce intercohort competition, enabling coexistence of many cohorts. More voracious cannibalism, in combination with competition, produces large-amplitude cycles and a bimodal population size distribution with many small and few giant individuals. These coexisting ``dwarfs'' and ``giants'' have very different life histories, resulting from a reversal in importance of cannibalism and competition. The population structure at time of birth determines whether individuals suffer severe cannibalism, with the few survivors reaching giant sizes, or whether they suffer intense intracohort competition, with all individuals remaining small. These model results agree remarkably well with empirical data on perch population dynamics. We argue that the induction of cannibalistic giants in piscivorous fish is a population-dynamic emergent phenomenon that requires a combination of size-dependent cannibalism and competition.