The paradox of enrichment in an adaptive world

Paradoxically, enrichment can destabilize a predator-prey food web. While adaptive dynamics can greatly influence the stability of interaction systems, few theoretical studies have examined the effect of the adaptive dynamics of interaction-related traits on the possibility of resolution of the paradox of enrichment. We consider the evolution of attack and defence traits of a predator and two prey species in a one predator-two prey system in which the predator practises optimal diet use. The results showed that optimal foraging alone cannot eliminate a pattern of destabilization with enrichment, but trait evolution of the predator or prey can change the pattern to one of stabilization, implying a possible resolution of the paradox of enrichment. Furthermore, trait evolution in all species can broaden the parameter range of stabilization. Importantly, rapid evolution can stabilize this system, but weaken its stability in the face of enrichment.     

Enrichment can damp population cycles: a balance of inflexible and flexible interactions

Destabilization of one predator–one prey systems with an increase in nutrient input has been viewed as a paradox. We report that enrichment can damp population cycles by a food‐web structure that balances inflexible and flexible interaction links (i.e. specialist and generalist predators). We modeled six predator–prey systems involving three or four species in which the predators practice optimal foraging based on prey profitability determined by handling time. In all models, the balance of interaction links simultaneously decreased the amplitude of population oscillations and increased the minimum density with increasing enrichment, leading to a potential theoretical resolution of the paradox of enrichment in non‐equilibrium dynamics. The stabilization mechanism was common to all of the models. Important previous studies on the stability of food webs have also demonstrated that a balance of interaction strengths stabilizes systems, suggesting a general rule of ecosystem stability.     

Enrichment and ecosystem stability: effect of toxic food

Enrichment in resource availability theoretically destabilizes predator-prey dynamics (the paradox of enrichment). However, a minor change in the resource stoichiometry may make a prey toxic for the predator, and the presence of toxic prey affects the dynamics significantly. Here, theoretically we explore how, at increased carrying capacity, a toxic prey affects the oscillation or destabilization of predator-prey dynamics, and how its presence influences the growth of the predator as well as that of a palatable prey. Mathematical analysis determines the bounds on the food toxicity that allow the coexistence of a predator along with a palatable and a toxic prey. The overall results demonstrate that toxic food counteracts oscillation (destabilization) arising from enrichment of resource availability. Moreover, our results show that, at increased resource availability, toxic food that acts as a source of extra mortality may increase the abundance of the predator as well as that of the palatable prey.     

Diet choice and predator—prey dynamics

Summary We compare the dynamics of predator-prey systems with specialist predators or adaptive generalist predators that base diet choice on energy-maximizing criteria. Adaptive predator behaviour leads to functional responses that are influenced by the relative abundance of alternate prey. This results in the per capita predation risk being positively density-dependent near points of diet expansion. For a small set of parameter values, systems with adaptive predators can be locally stable whereas systems with specialist predators would be unstable. This occurs mainly when alternate prey have low enough profitability that predators cannot sustain themselves indefinitely when feeding on alternate prey. Local stability of systems with adaptive predator behaviour is inversely related to the goodness of fit to optimal diet choice criteria. Hence, typical patterns of partial prey preference are more stabilizing than perfect optimal diet selection. Locally stable systems with adaptive predators are often globally unstable, converging on limit cycles for many initial population densities. The small range of parameter combinations and initial population densities leading to stable equilibria suggest that adaptive diet selection is unlikely to be a ubiquitous stabilizing factor in trophic interactions.     

Unpalatable prey resolves the paradox of enrichment

Enrichment is an increasingly serious trend in natural ecosystems. A theoretical model of a predator–prey system with a natural assumption of satiation in predation predicts that enrichment causes the populations to fluctuate to stochastic extinction. However, this ''paradox of enrichment'' does not always occur in experimental and natural communities. Here we present a theoretical model that describes a novel mechanism for resolving the paradox in the case of a predator with optimal selective feeding. Specifically, a less profitable but edible (thus `unpalatable'') prey species sharply reduces the amplitude of population oscillations and firmly prevents the minimum abundances of species from falling below certain values. The presence of such an unpalatable prey thus guarantees the robustness of the system against enrichment.     

On optimal diet in a patchy environment

Optimal foraging theory has dealt with the following questions independently: (1) On what prey types should an individual predator feed (optimal diet)? (2) How long should a predator stay in each patch if prey is patchily distributed (optimal allocation of time to patches) ? This paper explores optimal foraging in patches containing several different kinds of prey. Results obtained by simulation show that deviations from recent predictions are to be expected, particularly for long interpatch travel times and rapid depletion of profitable prey types. In these situations the tactics of feeding as either specialist or as a generalist can be inferior to a tactic which starts as a specialist and then expands the diet after some time in the patch. Furthermore, predators should not necessarily stay longer in a patch if interpatch travel time increases. Some experimental tests of these new predictions are proposed.     

The stability of ecosystems: A brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system,thereby collapsing the trophic interaction,a phenomenon referred to as "the paradox of enrichment". After it was first pro posed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator -prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form,inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that,although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms,which may differ among systems,need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.     

Imperfect optimal foraging and the paradox of enrichment

We show that the paradox of enrichment can be theoretically resolved in a flexible predator–prey system in which the predator practices imperfect optimal foraging. A previous study showed that perfect optimal foraging can mitigate increases in the amplitude of population oscillations associated with enrichment, but it did not show a stabilization pattern. Our results show that imperfect optimal foraging can stabilize the system and resolve the paradox of enrichment under nonequilibrium dynamics. Furthermore, the degree of stabilization with enrichment was stronger when the imperfection of optimal foraging was larger.     

Enrichment and stability: a phenomenological coupling of energy value and carrying capacity

Simple predator-prey models with a prey-dependent functional response predict that enrichment (increased carrying capacity) destabilizes community dynamics: this is the 'paradox of enrichment'. However, the energy value of prey is very important in this context. The intraspecific chemical composition of prey species determines its energy value as a food for the potential predator. Theoretical and experimental studies establish that variable chemical composition of prey affects the predator-prey dynamics. Recently, experimental and theoretical approaches have been made to incorporate explicitly the stoichiometric heterogeneity of simple predator-prey systems. Following the results of the previous experimental and theoretical advances, in this article we propose a simple phenomenological formulation of the variation of energy value at increased level of carrying capacity. Results of our study demonstrate that coupling the parameters representing the phenomenological energy value and carrying capacity in a realistic way, may avoid destabilization of community dynamics following enrichment. Additionally, under such coupling the producer-grazer system persists for only an intermediate zone of production--a result consistent with recent studies. We suggest that, while addressing the issue of enrichment in a general predator-prey model, the phenomenological relationship that we propose here might be applicable to avoid Rosenzweig's paradox.     

Numerical and dietary responses of a predator community in a temperate zone of Europe

The generalist predation hypothesis predicts that the functional responses of generalist predator species should be quicker than those of specialist predators and have a regulating effect on vole populations. New interpretations of their role in temperate ecosystems have, however, reactivated a debate suggesting generalist predators may have a destabilizing effect under certain conditions (e.g. landscape homogeneity, low prey diversity, temporary dominance of 1 prey species associated with a high degree of dietary specialization). We studied a rich predator community dominated by generalist carnivores ( Martes spp., Vulpes vulpes, Felis catus ) over a 6 yr period in farmland and woodland in France. The most frequent prey were small rodents (mostly Microtus arvalis , a grassland species, and Apodemus spp., a woodland species). Alternative prey were diverse and dominated by lagomorphs ( Oryctolagus cuniculus, Lepus europeus ). We detected a numerical response among specialist carnivores but not among generalist predators. The dietary responses of generalist predators were fairly complex and most often dependent on variation in density of at least 1 prey species. These results support the generalist predation hypothesis. We document a switch to alternative prey, an increase of diet diversity, and a decrease of diet overlap between small and medium-sized generalists during the low density phase of M. arvalis . In this ecosystem, the high density phases of small mammal species are synchronous and cause a temporary specializing of several generalist predator species. This rapid functional response may indicate the predominant role of generalists in low amplitude population cycles of voles observed in some temperate areas.     

Context-dependent effects of predator removal from experimental microcosm communities

The loss of a predator from an ecological community can cause large changes in community structure and ecosystem processes, or have very little consequence for the remaining species and ecosystem. Understanding when and why the loss of a predator causes large changes in community structure and ecosystem processes is critical for understanding the functional consequences of biodiversity loss. We used experimental microbial communities to investigate how the removal of a large generalist predator affected the extinction frequency, population abundance and total biomass of its prey. We removed this predator in the presence or absence of an alternative, more specialist, predator in order to determine whether the specialist predator affected the outcome of the initial species removal. Removal of the large generalist predator altered some species' populations but many were unaffected and no secondary extinctions were observed. The specialist predator, though rare, altered the response of the prey community to the removal of the large generalist predator. In the absence of the specialist predator, the effects of the removal were only measurable at the level of individual species. However, when the specialist predator was present, the removal of the large generalist predator affected the total biomass of prey species. The results demonstrate that the effect of species loss from high trophic levels may be very context-dependent, as rare species can have disproportionately large effects in food webs.     

Dispersal delays, predator-prey stability, and the paradox of enrichment

It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator-prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator-prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.     

Dynamics of a intraguild predation model with generalist or specialist predator

Intraguild predation (IGP) is a combination of competition and predation which is the most basic system in food webs that contains three species where two species that are involved in a predator/prey relationship are also competing for a shared resource or prey. We formulate two intraguild predation (IGP: resource, IG prey and IG predator) models: one has generalist predator while the other one has specialist predator. Both models have Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type III functional response between IG prey and IG predator. We provide sufficient conditions of the persistence and extinction of all possible scenarios for these two models, which give us a complete picture on their global dynamics. In addition, we show that both IGP models can have multiple interior equilibria under certain parameters range. These analytical results indicate that IGP model with generalist predator has “top down” regulation by comparing to IGP model with specialist predator. Our analysis and numerical simulations suggest that: (1) Both IGP models can have multiple attractors with complicated dynamical patterns; (2) Only IGP model with specialist predator can have both boundary attractor and interior attractor, i.e., whether the system has the extinction of one species or the coexistence of three species depending on initial conditions; (3) IGP model with generalist predator is prone to have coexistence of three species.     

Sustainability of exploited ecologically interdependent species

This paper examines the application of maximum sustainable yield (MSY) policy in ecosystem and indicates when the ecosystem based fisheries management approach is required for conservation purpose. To describe the possible impacts of applying global MSY policy in an ecosystem, we have considered both specialist and generalist prey–predator models with different fishing efforts. It is found that harvesting both prey and predator species in specialist prey–predator systems, to achieve global maximum sustainable total yield (MSTY) under independent efforts, will cause the extinction of the predator species. In contrast, the global MSTY may exist in a generalist prey–predator system. If global MSTY does not exist, then it is due to the extinction of predator species. Hence, the prey species never goes to extinction under independent efforts and this scenario is quite different from the one found under combined harvesting effort.     

Predator diet breadth influences the relative importance of bottom-up and top-down control of prey biomass and diversity

We investigated the effects of predator diet breadth on the relative importance of bottom-up and top-down control of prey assemblages, using microbial food webs containing bacteria, bacterivorous protists and rotifers, and two different top predators. The experiment used a factorial design that independently manipulated productivity and the presence or absence of two top predators with different diet breadths. Predators included a "specialist" predatory ciliate Euplotes aediculatus, which was restricted to feeding on small prey, and a "generalist" predatory ciliate Stentor coeruleus, which could feed on the entire range of prey sizes. Both total prey biomass and prey diversity increased with productivity in the predator-free control and specialist predator treatments, a pattern consistent with bottom-up control, but both remained unchanged by productivity in the generalist predator treatment, a pattern consistent with top-down control. Linear food chain models adequately described responses in the generalist predator treatment, whereas food web models incorporating edible and inedible prey (which can coexist in the absence of predators) adequately described responses in the specialist predator treatment. These results suggest that predator diet breadth can play an important role in modulating the relative strength of bottom-up and top-down forces in ecological communities.     

Kestrel-Prey Dynamic in a Mediterranean Region: The Effect of Generalist Predation and Climatic Factors

Background

Most hypotheses on population limitation of small mammals and their predators come from studies carried out in northern latitudes, mainly in boreal ecosystems. In such regions, many predators specialize on voles and predator-prey systems are simpler compared to southern ecosystems where predator communities are made up mostly of generalists and predator-prey systems are more complex. Determining food limitation in generalist predators is difficult due to their capacity to switch to alternative prey when the basic prey becomes scarce.

Methodology

We monitored the population density of a generalist raptor, the Eurasian kestrel Falco tinnunculus over 15 years in a mountainous Mediterranean area. In addition, we have recorded over 11 years the inter-annual variation in the abundance of two main prey species of kestrels, the common vole Microtus arvalis and the eyed lizard Lacerta lepida and a third species scarcely represented in kestrel diet, the great white-toothed shrew Crocidura russula. We estimated the per capita growth rate (PCGR) to analyse population dynamics of kestrel and predator species.

Principal Findings

Multimodel inference determined that the PCGR of kestrels was better explained by a model containing the population density of only one prey species (the common vole) than a model using a combination of the densities of the three prey species. The PCGR of voles was explained by kestrel abundance in combination with annual rainfall and mean annual temperature. In the case of shrews, growth rate was also affected by kestrel abundance and temperature. Finally, we did not find any correlation between kestrel and lizard abundances.

Significance

Our study showed for the first time vertebrate predator-prey relationships at southern latitudes and determined that only one prey species has the capacity to modulate population dynamics of generalist predators and reveals the importance of climatic factors in the dynamics of micromammal species and lizards in the Mediterranean region.     

The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs

This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.     

How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses

In Rosenzweig-MacArthur models of predator-prey dynamics, Allee effects in prey usually destabilize interior equilibria and can suppress or enhance limit cycles typical of the paradox of enrichment. We re-evaluate these conclusions through a complete classification of a wide range of Allee effects in prey and predator's functional response shapes. We show that abrupt and deterministic system collapses not preceded by fluctuating predator-prey dynamics occur for sufficiently steep type III functional responses and strong Allee effects (with unstable lower equilibrium in prey dynamics). This phenomenon arises as type III functional responses greatly reduce cyclic dynamics and strong Allee effects promote deterministic collapses. These collapses occur with decreasing predator mortality and/or increasing susceptibility of the prey to fall below the threshold Allee density (e.g. due to increased carrying capacity or the Allee threshold itself). On the other hand, weak Allee effects (without unstable equilibrium in prey dynamics) enlarge the range of carrying capacities for which the cycles occur if predators exhibit decelerating functional responses. We discuss the results in the light of conservation strategies, eradication of alien species, and successful introduction of biocontrol agents.     

When is overkill optimal? Tritrophic interactions reveal new insights into venom evolution

Organisms embedded within food webs must balance arms races with their predators and prey. For venom users, venom may mediate each arms race, but the dynamical evolutionary changes in venom production in response to the two arms races are still poorly understood. Here, we use a simple model to evaluate the evolutionary response of a venomous consumer to the presence of an apex generalist predator and evolution of the consumer’s prey. We find that introduction of the apex predator can weaken the arms race between the two lower trophic levels. In addition, when consumer prey capture and predator defense venoms functionally overlap, a reduced evolutionary response in the prey population can drive investment in venom used for prey capture going beyond what is optimal for subduing prey. These dynamics suggest that interactions with multiple trophic levels can substantially alter the venom complexity in predatory venomous animals and may explain the paradox of the overkill hypothesis.