Predator–prey system with strong Allee effect in prey

Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.     

Effects of rapid prey evolution on predator–prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (1) large increases in cycle period, (2) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (3) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system (Fussmann et al. in Science 290:1358-1360, 2000; Yoshida et al. in Proc roy Soc Lond B 424:303-306, 2003) with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems (Andersson et al. in Curr Opin Microbiol 2:489-493, 1999: Gagneux et al. in Science 312:1944-1946, 2006; Yoshida et al. in Proc Roy Soc Lond B 271:1947-1953, 2004), our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.     

Analysis of a competitive prey–predator system with a prey refuge

Gauss's competitive exclusive principle states that two competing species having analogous environment cannot usually occupy the same space at a time but in order to exploit their common environment in a different manner, they can co-exist only when they are active in different times. On the other hand, several studies on predators in various natural and laboratory situations have shown that competitive coexistence can result from predation in a way by resisting any one prey species from becoming sufficiently abundant to outcompete other species such that the predator makes the coexistence possible. It has also been shown that the use of refuges by a fraction of the prey population exerts a stabilizing effect in the interacting population dynamics. Further, the field surveys in the Sundarban mangrove ecosystem reveal that two detritivorous fishes, viz. Liza parsia and Liza tade (prey population) coexist in nature with the presence of the predator fish population, viz. Lates calcarifer by using refuges.     

What determines prey selection in owls? Roles of prey traits,prey class,environmental variables,and taxonomic specialization

Ecological theory suggests that prey size should increase with predator size, but this trend may be masked by other factors affecting prey selection, such as environmental constraints or specific prey preferences of predator species. Owls are an ideal case study for exploring how predator body size affects prey selection in the presence of other factors due to the ease of analyzing their diets from owl pellets and their widespread distributions, allowing interspecific comparisons between variable habitats. Here, we analyze various dimensions of prey resource selection among owls, including prey size, taxonomy (i.e., whether or not particular taxa are favored regardless of their size), and prey traits (movement type, social structure, activity pattern, and diet). We collected pellets of five sympatric owl species (Athene noctua, Tyto alba, Asio otus, Strix aluco, and Bubo bubo) from 78 sites across the Mediterranean Levant. Prey intake was compared between sites, with various environmental variables and owl species as predictors of abundance. Despite significant environmental impacts on prey intake, some key patterns emerge among owl species studied. Owls select prey by predator body size: Larger owls tend to feed on wider ranges of prey sizes, leading to higher means. In addition, guild members show both specialization and generalism in terms of prey taxa, sometimes in contrast with the expectations of the predator–prey body size hypothesis. Our results suggest that while predator body size is an important factor in prey selection, taxon specialization by predator species also has considerable impact.     

Do unprofitable prey evolve traits that profitable prey find difficult to exploit?

Prey that are unprofitable to attack (for example, those containing noxious chemicals) are often conspicuously patterned and move in a slower and more predictable manner than species lacking these defences. Contemporary theories suggest these traits have evolved as warning signals because they can facilitate both associative and discriminative avoidance learning in predators. However, it is unclear why these particular traits and not others have tended to evolve in unprofitable prey. Here we show using a signal detection model that unprofitable prey will evolve conspicuous colours and patterns partly because these characteristics cannot readily evolve in profitable prey without close mimicry. The stability of this signal is maintained through the costs of dishonesty in profitable prey. Indeed, unprofitable prey will sometimes evolve a conspicuous form to reduce mimetic parasitism, even in the unlikely event that this form can be more closely mimicked. This is one of the first mathematical models of the evolution of warning signals to allow for the possibility of mimicry, yet our analyses suggest it may offer a general explanation as to why warning signals take the form that they do. Warning signals and mimicry may therefore be more closely related than is currently supposed.     

How to analyse prey preference when prey density varies? A new method to discriminate between effects of gut fullness and prey type composition

Summary State-dependent changes in prey preference are among the phenomena to be expected in studies of predator behaviour. For example, the rate of attack on each prey type is well known to be affected by the state of satiation, the dynamics of which is often assumed to parallel that of gut fullness. An interesting question is whether satiation alone is the determinant of the attack rate or whether the particular mixture of prey types in the predator's direct environment has an additional influence by itself. To detect examples of the latter type the predictive method proposed by Cock (1978) may be useful. In the present paper the predictive tool is a model built on the assumption that gut fullness is the sole internal state variable determining the attack rate. It is provided with parameter estimates from observations in monocultures of each type and then used to predict predation in mixtures of prey types. When measured predation on these prey types differs from what is predicted, the model may be too simple in various respects, one of which is that predators change prey preference in response to their own sample estimates of the densities of each prey type and their (innate or sample) estimate of the profitability of each prey type in terms of reproductive success. Thus, the lack of fit of the model poses a challenging problem, for to explain it one must identify underlying causes, such as differences in prey quality with respect to scarce nutrients or noxious chemicals that need to be detoxified or rendered harmless in other ways. The predictive approach is illustrated by analysis of preference of predatory mites (Phytoseiulus persimilis Athias-Henriot and Typhlodromus occidentalis Nesbitt) with respect to various stages of development of their prey, the two-spotted spider mite (Tetranychus urticae Koch). The results show that the relation between attack rate and gut fullness might well explain prey stage preference of predatory mites when the prey stages are presented together rather than each alone. In another paper by Dicke et al. (1989) marked deviations between predicted and measured diet are reported when the predatory mite, Typhlodromus pyri Scheuten, was offered a choice between two prey species, i.e. apple rust mites and (larvae of) European red spider mites. The underlying causes are to be revealed by further research, the impetus of which is born out by use of the method proposed by Cock (1978) and extended in this paper.     

Effects of the probability of a predator catching prey on predator–prey system stability

To understand the effect of the probability of a predator catching prey, P_catch, on the stability of the predator–prey system, a spatially explicit lattice model consisting of predators, prey, and grass was constructed. The predators and prey randomly move on the lattice space, and the grass grows according to its growth probability. When a predator encounters prey, the predator eats the prey in accordance with the probability P_catch. When a prey encounters grass, the prey eats the grass. The predator and prey give birth to offspring according to a birth probability after eating prey or grass, respectively. When a predator or prey is initially introduced or newly born, its health state is set at a high given value. This health state decreases by one with every time step. When the state of an animal decreases to less than zero, the individual dies and is removed from the system. Population densities for predator and prey fluctuated significantly according to P_catch. System stability was characterized by the standard deviation ? of the fluctuation. The simulation results showed that ? for predators increased with an increase of P_catch; ? for prey reached a maximum at P_catch = 0.4; and ? for grass fluctuated little regardless of P_catch. These results were due to the tradeoff between P_catch and the predator–prey encounter rate, which represents the degree of interaction between predator and prey and the average population density, respectively.     

Can species‐specific prey responses to chemical cues explain prey susceptibility to predation?

The perception of danger represents an essential ability of prey for gaining an informational advantage over their natural enemies. Especially in complex environments or at night, animals strongly rely on chemoreception to avoid predators. The ability to recognize danger by chemical cues and subsequent adaptive responses to predation threats should generally increase prey survival. Recent findings suggest that European catfish (Silurus glanis) introduction induce changes in fish community and we tested whether the direction of change can be attributed to differences in chemical cue perception. We tested behavioral response to chemical cues using three species of freshwater fish common in European water: rudd (Scardinius erythrophthalmus), roach (Rutilus rutilus), and perch (Perca fluviatilis). Further, we conducted a prey selectivity experiment to evaluate the prey preferences of the European catfish. Roach exhibited the strongest reaction to chemical cues, rudd decreased use of refuge and perch did not alter any behavior in the experiment. These findings suggest that chemical cue perception might be behind community data change and we encourage collecting more community data of tested prey species before and after European catfish introduction to test the hypothesis. We conclude that used prey species can be used as a model species to verify whether chemical cue perception enhances prey survival.     

Constructive effects of environmental noise in an excitable prey–predator plankton system with infected prey

An excitable model of fast phytoplankton and slow zooplankton dynamics is considered for the case of lysogenic viral infection of the phytoplankton population. The phytoplankton population is split into a susceptible (S) and an infected (I) part. Both parts grow logistically, limited by a common carrying capacity. Zooplankton (Z) is grazing on susceptibles and infected, following a Holling-type III functional response. The local analysis of the S–I–Z differential equations yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the behaviour under multiplicative noise, modelled by stochastic differential equations. The external noise can enhance the survival of susceptibles and infected, respectively, that would go extinct in a deterministic environment. In the parameter range of excitability, noise can induce prey–predator oscillations and coherence resonance (CR). In the spatially extended case, synchronized global oscillations can be observed for medium noise intensities. Higher values of noise give rise to the formation of stationary spatial patterns.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

Geometric optimization for prey–predator strategies

This paper investigates several strategies for prey and predator in both bounded and unbounded domains, assuming they have the same speed. The work describes how the prey should move to escape from the predator and how predator should move to catch the prey. The approach is agent-based and explicitly tracks movement of individuals as prey and predator. We show that the prey escapes one or two competing predators, while might be caught in the case of three predators. The paper also describes a strategy for finding a well camouflaged static prey which emits signals.     

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.     

Are all prey created equal? A review and synthesis of differential predation on prey in substandard condition

Our understanding of predator-prey interactions in fishes has been influenced largely by research assuming that the condition of the participants is normal. However, fish populations today often reside in anthropogenically altered environments and are subjected to many kinds of stressors, which may reduce their ecological performance by adversely affecting their morphology, physiology, or behaviour. One consequence is that either the predator or prey, or both, may be in a substandard condition at the time of an interaction. We reviewed the literature on predator-prey interactions in fishes where substandard prey were used as experimental groups. Although most of this research indicates that such prey are significantly more vulnerable to predation, prey condition has rarely been considered in ecological theory regarding predator-prey interactions. The causal mechanisms for increased vulnerability of substandard prey to predation include a failure to detect predators, lapses in decision-making, poor fast-start performance, inability to shoal effectively, and increased prey conspicuousness. Despite some problems associated with empirical predator-prey studies using substandard prey, their results can have theoretical and applied uses, such as in ecological modelling or justification of corrective measures to be implemented in the wild. There is a need for more corroborative field experimentation, a better understanding of the causal mechanisms behind differential predation, and increased incorporation of prey condition into the research of predator-prey modellers and theoreticians. If the concept of prey condition is considered in predator-prey interactions, our understanding of how such interactions influence the structure and dynamics of fish communities is likely to change, which should prove beneficial to aquatic ecosystems.     

Does prey preference change as a result of prey species being presented together? Analysis of prey selection by the predatory mite Typhlodromus pyri (Acarina: Phytoseiidae)

Summary Prey-selection behaviour of the phytoseiid mite Typhlodromus pyri Scheuten was analysed with a Markovtype model of feeding-state dynamics and feeding-state dependent searching behaviour (Sabelis 1981, 1986, 1989; Metz and Van Batenburg 1985a, b). All behavioural characteristics of the predator which are independent of the feeding state were represented by one parameter. The remaining feeding-state dependent characteristics were represented by a function of the feeding state, with one parameter. The best parameter values to describe a predator-prey interaction were determined by fitting the model to the predation rates in monocultures. Under the assumption that the parameter values are not dependent on the composition of prey species supply, the diet of the predators in mixed cultures was predicted from parameters estimated in monoculture experiments.Two prey types, apple rust mite (Aculus schlechtendali (Nalepa)) adults and European red spider mite (Panonychus ulmi (Koch)) larvae were studied. A large discrepancy was observed between calculated and experimentally determined predation rates of T. pyri in mixed cultures: the predators actually killed 3–7 times more P. ulmi larvae than was predicted by the model.The large difference between observed and predicted predation rates in mixed cultures cannot be explained by changes in the behaviour of the prey species as a result of being together. Therefore, it seems likely that the prey selection behaviour of the predator was different when prey species were presented together than when presented singly. Apparently the predatory mite T. pyri prefers P. ulmi to S. schlechtendali.     

Effects of epibiosis on consumer–prey interactions

In many benthic communities predators play a crucialrole in the population dynamics of their prey. Surfacecharacteristics of the prey are important forrecognition and handling by the predator. Because theestablishment of an epibiotic assemblage on thesurface of a basibiont species creates a new interfacebetween the epibiotized organism and its environment,we hypothesised that epibiosis should have an impacton consumer–prey interactions. In separateinvestigations, we assessed how epibionts onmacroalgae affected the susceptibility of the latterto herbivory by the urchin Arbacia punctulataand how epibionts on the blue mussel Mytilusedulis affected its susceptibility to predation bythe shore crab Carcinus maenas.Some epibionts strongly affected consumer feedingbehavior. When epibionts were more attractive thantheir host, consumer pressure increased. Whenepibionts were less attractive than their host or whenthey were repellent, consumer pressure decreased. Insystems that are controlled from the top-down,epibiosis can strongly influence community dynamics.For the Carcinus/Mytilus system that westudied, the in situ distribution of epibiontson mussels reflected the epibiosis-determinedpreferences of the predator. Both direct and indirecteffects are involved in determining theseepibiont-prey–consumer interactions.     

Prolonged prey suppression by carnivores — predator-removal experiments

Summary The hypothesis that carnivores can significantly suppress prey populations after they collapse during drought was tested by predator-removal experiments. Low populations of rabbits (Oryctolagus cuniculus) responded with significantly accelerated growth where foxes (Vulpes vulpes) and feral cats (Felis catus) were continually shot. Experiments in years of good pasture and poor were confirmatory. After only 14 months, the rabbits were well on their way to another eruption whereas untreated populations had remained low for 2.5 yrs until a second drought. These studies confirm the impact of carnivores found for low populations of cyclical prey but there was no measurable effect of predator-removal on the population declines in our studies. They were due to aridity and poor pastures. The concept of Environmentally Modulated Predation is presented. Only after the intervention of a widespread environmental event is such limiting predation possible. Drought is also the cause in arid Australia for dingoes (Canis familiaris dingo) preying seqenntially on rodents, rabbits and red kangaroos, while wildfire was the cause in temperate forests. Such environmental intervention may be more widespread than usually considered, triggering some apparent predator-prey cycles. The major factors limiting rabbits in inland Australia are: adequacy of green herbage during breeding, food scarcity during average summers, critical shortages of food and its low quality (including moisture content) during crashes in drought, followed by limiting predation. Contrasting life-histories are one cause for the ultimate escape of rabbit populations from limiting predation as rabbits can breed continuously but carnivores seasonally only. Patchy predation and alternate prey may also play a part.     

Are scared prey as good as dead?

Predators affect prey and their resources by changing the density and traits (e.g. morphology and behavior) of those prey. Ecological studies and models of community dynamics, however, typically only incorporate how changes in prey densities, rather than their traits, affect community dynamics. In a recent meta-analysis, Preisser et al. show that trait effects are as large, if not larger than density effects. This strongly suggests that trait effects should be integrated into empirical and theoretical studies.     

Individual behavioral variation in predator–prey models

The role of individual behavioral variation in community dynamics was studied. Behavioral variation in this study does not refer to differences in average responses (e.g., average response between presence and absence of antipredator behavior). Rather it refers to the variation around the average response that is not explained by trivial experimental treatments. First, the effect of behavioral variation was examined based on Jensen’s inequality. In cases of commonly used modeling framework with type II functional response, neglecting behavioral variation (a component of encounter rate) causes overestimation of predation effects. The effect of this bias on community processes was examined by incorporating the behavioral variation in a commonly used consumer-resource model (Rosenzweig–MacArthur model). How such a consideration affects a model prediction (paradox of enrichment) was examined. The inclusion of behavioral variation can both quantitatively and qualitatively alter the model characteristics. Behavioral variation can substantially increase the stability of the community with respect to enrichment.