Effect of hunting cooperation and fear in a predator-prey model

Dynamics of predator-prey systems under the influence of cooperative hunting among predators and the fear thus imposed on the prey population is of great importance from ecological point of view. The role of hunting cooperation and the fear effect in the predator-prey system is gaining considerable attention by the researchers recently. But the study on combined effect of hunting cooperation and fear in the predator-prey system is not yet studied. In the present paper, we investigate the impact of hunting cooperation among predators and predator induced fear in prey population by using the classical predator-prey model. We consider that predator populations cooperate during hunting. We also consider that hunting cooperation induces fear among prey, which has far richer and complex dynamics. We observe that without hunting cooperation, the unique coexistence equilibrium point is globally asymptotically stable. However, an increase in the hunting cooperation induced fear may destabilize the system and produce periodic solution via Hopf-bifurcation. The stability of the Hopf-bifurcating periodic solution is obtained by computing the Lyapunov coefficient. The limit cycles thus obtained may be supercritical or subcritical. We also observe that the system undergoes the Bogdanov-Takens bifurcation in two-parameter space. Further, we observe that the system exhibits backward bifurcation between predator-free equilibrium and coexisting equilibrium. The system also exhibits two different types of bi-stabilities due to subcritical Hopf-bifurcation (between interior equilibrium and stable limit cycle) and backward bifurcation (between predator-free and interior equilibrium points). Further, we observe strong demographic Allee phenomenon in the system. To visualize the dynamical behavior of the system, extensive numerical experiments are performed by using MATLAB and MATCONT softwares.     

Effects of sterile insect releases on a population under predation or parasitism

A continuous-time differential equation model was constructed which describes the population dynamics of a predator prey system in which sterile prey are released in a program designed to eradicate or reduce the prey population. It was found that the dynamics of the system behave quite differently when predators are present. Two conditions were found which have differing implications for the control program. If the predators still exist when the wild prey population declines to extinction, then the SIRM is assisted by the predators, sometimes to a considereble extent. If the predators decline to extinction before the wild prey population goes extinct, then the predators may or may not assist the SIRM depending on the parameters of the system. If the predators do assist the SIRM, then a potentially dangerous situation exists in which an explosion of the prey population could occur after the predators go extinct. Predator polyphagy would probably minimize this danger of an explosion since it would stabilize the predator population.     

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate,predator's reproductive gain and preference

Parasites are considered as an important factor in regulating their host populations through trait-mediated effects. On the other hand, predation becomes particularly interesting in host–parasite systems because predation can significantly alter the abundance of parasites and their host population. The combined effects of parasites and predator on host population and community structure therefore may have larger effect. Different field experiments confirm that predators consume disproportionately large number of infected prey in comparison to their susceptible counterpart. There are also substantial evidences that predator has the ability to distinguish prey that have been infected by a parasite and avoid such prey to reduce fitness cost. In this paper we study the predator–prey dynamics, where the prey species is infected by some parasites and predators consume both the susceptible and infected prey with some preference. We demonstrate that complexity in such systems largely depends on the predator's selectivity, force of infection and predator's reproductive gain. If the force of infection and predator's reproductive gain are low, parasites and predators both go to extinction whatever be the predator's preference. The story may be totally different in the opposite case. Survival of species in stable, oscillatory or chaotic states, and their extinction largely depend on the predator's preference. The system may also show two coexistence equilibrium points for some parameter values. The equilibrium with lower susceptible prey density is always stable and the equilibrium with higher susceptible prey density is always unstable. These results suggest that understanding the consequences of predator's selectivity or preference may be crucial for community structure involving parasites.     

A reinforcement learning-based predator-prey model

Classic population models can often predict the dynamics of biological populations in nature. However, the adaptation process and learning mechanism of species are rarely considered in the study of population dynamics, due to the complex interaction of species, seasonal variation, spatial distribution or other factors. We use reinforcement learning algorithms to improve the existing individual-based ecosystem simulation algorithms, which allows species to spontaneously adjust their strategies according to a short period of experience and then feed back to improve their abilities to make action decisions. Our results show that the reinforcement learning of predators is beneficial to the stability of the ecosystem, and predators can learn to spontaneously form hunting patterns that surround their prey. The learning of prey makes the ecosystem oscillate and meanwhile leads to a higher risk of extinction for predators. When individuals are more likely to die, these herbivores rely on reproductive behavior to maintain their populations; when individuals live longer, herbivores spend more time eating to maintain their own survival. The co-reinforcement learning of predators and prey helps predators to find a more suitable way to survive with their prey, that is, the number of predators is more stable and larger than when only predator or only prey learns.     

Immigration can destabilize tri-trophic interactions: implications for conservation of top predators

Top predators often have large home ranges and thus are especially vulnerable to habitat loss and fragmentation. Increasing connectance among habitat patches is therefore a common conservation strategy, based in part on models showing that increased migration between subpopulations can reduce vulnerability arising from population isolation. Although three-dimensional models are appropriate for exploring consequences to top predators, the effects of immigration on tri-trophic interactions have rarely been considered. To explore the effects of immigration on the equilibrium abundances of top predators, we studied the effects of immigration in the three-dimensional Rosenzweig-MacArthur model. To investigate the stability of the top predator equilibrium, we used MATCONT to perform a bifurcation analysis. For some combinations of model parameters with low rates of top predator immigration, population trajectories spiral towards a stable focus. Holding other parameters constant, as immigration rate is increased, a supercritical Hopf bifurcation results in a stable limit cycle and thus top predator populations that cycle between high and low abundances. Furthermore, bistability arises as immigration of the intermediate predator is increased. In this case, top predators may exist at relatively low abundances while prey become extinct, or for other initial conditions, the relatively higher top predator abundance controls intermediate predators allowing for non-zero prey population abundance and increased diversity. Thus, our results reveal one of two outcomes when immigration is added to the model. First, over some range of top predator immigration rates, population abundance cycles between high and low values, making extinction from the trough of such cycles more likely than otherwise. Second, for relatively higher intermediate predator migration rates, top predators may exist at low values in a truncated system with impoverished diversity, again with extinction more likely.     

Revealing the role of predator interference in a predator–prey system with disease in prey population

Predation on a species subjected to an infectious disease can affect both the infection level and the population dynamics. There is an ongoing debate about the act of managing disease in natural populations through predation. Recent theoretical and empirical evidence shows that predation on infected populations can have both positive and negative influences on disease in prey populations. Here, we present a predator–prey system where the prey population is subjected to an infectious disease to explore the impact of predator on disease dynamics. Specifically, we investigate how the interference among predators affects the dynamics and structure of the predator–prey community. We perform a detailed numerical bifurcation analysis and find an unusually large variety of complex dynamics, such as, bistability, torus and chaos, in the presence of predators. We show that, depending on the strength of interference among predators, predators enhance or control disease outbreaks and population persistence. Moreover, the presence of multistable regimes makes the system very sensitive to perturbations and facilitates a number of regime shifts. Since, the habitat structure and the choice of predators deeply influence the interference among predators, thus before applying predators to control disease in prey populations or applying predator control strategy for wildlife management, it is essential to carefully investigate how these predators interact with each other in that specific habitat; otherwise it may lead to ecological disaster.     

A mechanistic model for interference and Allee effect in the predator population

We present the results of simulations in an individual-based model describing spatial movement and predator-prey interaction within a closed rectangular habitat. Movement of each individual animal is determined by local conditions only, so any collective behavior emerges owing to self-organization. It is shown that the pursuit of prey by predators entails predator interference, manifesting itself at the population level as the dependency of the trophic function (individual ration) on predator abundance. The stabilizing effect of predator interference on the dynamics of a predator-prey system is discussed. Inclusion of prey evasion induces apparent cooperation of predators and further alters the functional response, giving rise to a strong Allee effect, with extinction of the predator population upon dropping below critical numbers. Thus, we propose a simple mechanistic interpretation of important but still poorly understood behavioral phenomena that underlie the functioning of natural trophic systems.     

Induced changes in island fox (Urocyon littoralis) activity do not mitigate the extinction threat posed by a novel predator

Prey response to novel predators influences the impacts on prey populations of introduced predators, bio-control efforts, and predator range expansion. Predicting the impacts of novel predators on native prey requires an understanding of both predator avoidance strategies and their potential to reduce predation risk. We examine the response of island foxes (Urocyon littoralis) to invasion by golden eagles (Aquila chrysaetos). Foxes reduced daytime activity and increased night time activity relative to eagle-na?ve foxes. Individual foxes reverted toward diurnal tendencies following eagle removal efforts. We quantified the potential population impact of reduced diurnality by modeling island fox population dynamics. Our model predicted an annual population decline similar to what was observed following golden eagle invasion and predicted that the observed 11% reduction in daytime activity would not reduce predation risk sufficiently to reduce extinction risk. The limited effect of this behaviorally plastic predator avoidance strategy highlights the importance of linking behavioral change to population dynamics for predicting the impact of novel predators on resident prey populations.     

Predator-prey interactions in a nonequilibrium context: the metapopulation approach to modeling "hide-and-seek" dynamics in a spatially explicit tri-trophic system

Predators and prey are usually heterogeneously distributed in space so that the ability of the predators to respond to the distribution of their prey may have a profound influence on the stability and persistence of a predator‐prey system. A special type of dynamics is “hide‐and‐seek” characterized by a high turnover rate of local populations of prey and predators, because once the predators have found a patch of prey they quickly overexploit it, whereupon the starving predators either should move to better places or die. Continued persistence of prey and predators thus hinges on a long‐term balance between local extinctions and founding of new subpopulations. The colonization rate depends on the rate of emigration from occupied patches and the likelihood of successfully arriving at a suitable new patch, while extinction rate depends on the local population dynamics. Since extinctions and colonizations are both discrete probabilistic events, these phenomena are most adequately modeled by means of a stochastic model. In order to demonstrate the qualitative differences between a deterministic and stochastic approach to population dynamics, a spatially explicit tritrophic predator‐prey model is developed in a deterministic and a stochastic version. The model is parameterized using data for the two‐spotted spider mite (Tetranychus urticae) and the phytoseiid mite predator Phytoseiulus persimilis inhabiting greenhouse cucumbers.
Simulations show that the deterministic and stochastic approaches yield different results. The deterministic version predicts that the populations will exhibit violent fluctuations, implying that the system is fundamentally unstable. In contrast, the stochastic version predicts that the two species will be able to coexist in spite of frequent local extinctions of both species, provided the system consists of a sufficiently large number of local populations. This finding is in agreement with experimental results. It is therefore concluded that demographic stochasticity in combination with dispersal is capable of producing and maintaining sufficient asynchrony between local populations to ensure long‐term regional (metapopulation) persistence.     

Spatial dynamics of specialist seed predators on synchronized and intermittent seed production of host plants

Masting, the synchronized and intermittent seed production by plant populations, provides highly variable food resources for specialist seed predators. Such a reproductive mode helps minimize seed losses through predator satiation and extinction of seed predator populations. The seed predators can buffer the resource variation through dispersal or extended diapause. We developed a spatially explicit resource-consumer model to understand the effect of masting on specialist seed predators. The masting dynamics were assumed to follow a resource-based model for plant reproduction, and the population dynamics of the predator were represented by a spatially extended Nicholson-Bailey model. The resultant model demonstrated that when host plants reproduce intermittently, seed predator populations go locally extinct, but global persistence of the predator is facilitated by dispersal or extended diapause. Global extinction of the predator resulted when the intermittent reproduction is highly synchronized among plants. An approximate invasion criterion for the predators showed that negative lag-1 autocorrelation in seeding reduces invasibility, and positive lag-1 cross-correlation enhances invasibility. Spatial synchronization in seeding at local scale caused by pollen coupling (or climate forcing) further prevented invasion of the predators. If the predators employed extended diapause, extremely high temporal variability in reproduction was required for plants to evade the predators.     

Heterogeneous landscapes and the role of refuge on the population dynamics of a specialist predator and its prey

How, and where, a prey species survives predation by a specialist predator during low phases of population fluctuations or a cycle, and how the increase phase of prey population is initiated, are much-debated questions in population and theoretical ecology. The persistence of the prey species could be due mainly to habitats that act as refuges from predation and/or due to anti-predatory behaviour of individuals. We present models for the former conjecture in two (and three) habitat systems with a specialist predator and its favoured prey. The model is based on dispersal of prey between habitats with high reproductive output but high risk of predation, and less productive habitats with relatively low risk of predation. We illustrate the predictions of our model using parameters from one of the most intriguing vertebrate predator–prey systems, the multi-annual population cycles of boreal voles and their predators. We suggest that cyclic population dynamics could result from a sequence of extinction and re–colonization events. Field voles (Microtus agrestis), a key vole species in the system, can be hunted to extinction in their preferred meadow habitat, but persist in sub-optimal wet habitats where their main predator, the least weasel (Mustela nivalis nivalis) has a low hunting efficiency. Re–colonization of favourable habitats would occur after the predator population crashes. At the local scale, the model suggests that the periodicity and amplitude of population cycles can be strongly influenced by the relative availability of risky and safe habitats for the prey. Furthermore, factors like intra-guild predation may lead to reduced predation pressure on field voles in sub-optimal habitats, which would act as a refuge for voles during the low phase of their population cycles. Elasticity analysis suggested that our model is quite robust to changes in most parameters but sensitive to changes in the population dynamics of field voles in the optimal grassland habitat, and to the maximum predation rate of weasels.     

Antipredator Responses by Native Mosquitofish to Non-Native Cichlids: An Examination of the Role of Prey Naiveté

The strong impact of non‐native predators in aquatic systems is thought to relate to the evolutionary naiveté of prey. Due to isolation and limited dispersal, this naiveté may be relatively high in freshwater systems. In this study, we tested this notion by examining the antipredator response of native mosquitofish, Gambusia holbrooki, to two non‐native predators found in the Everglades, the African jewelfish, Hemichromis letourneuxi, and the Mayan cichlid, Cichlasoma urophthalmus. We manipulated prey naiveté by using two mosquitofish populations that varied in their experience with the recent invader, the African jewelfish, but had similar levels of experience with the longer‐established Mayan cichlid. Specifically, we tested these predictions: (1) predator hunting modes differed between the two predators, (2) predation rates would be higher by the novel jewelfish predator, (3) particularly on the naive population living where jewelfish have not invaded yet, (4) antipredator responses would be stronger to Mayan cichlids due to greater experience and weaker and/or ineffective to jewelfish, and (5) especially weakest by the naive population. We assayed prey and predator behavior, and prey mortality in lab aquaria where both predators and prey were free‐ranging. Predator hunting modes and habitat domains differed, with jewelfish being more active search predators that used slightly higher parts of the water column and less of the habitat structure relative to Mayan cichlids. In disagreement with our predictions, predation rates were similar between the two predators, antipredator responses were stronger to African jewelfish (except for predator inspections), and there was no difference in response between jewelfish‐savvy and jewelfish‐naive populations. These results suggest that despite the novelty of introduced predators, prey may be able to respond appropriately if non‐native predator archetypes are similar enough to those of native predators, if prey rely on general antipredator responses or predation cues, and/or show neophobic responses.     

Modeling the Fear Effect in Predator–Prey Interactions with Adaptive Avoidance of Predators

Recent field experiments on vertebrates showed that the mere presence of a predator would cause a dramatic change of prey demography. Fear of predators increases the survival probability of prey, but leads to a cost of prey reproduction. Based on the experimental findings, we propose a predator–prey model with the cost of fear and adaptive avoidance of predators. Mathematical analyses show that the fear effect can interplay with maturation delay between juvenile prey and adult prey in determining the long-term population dynamics. A positive equilibrium may lose stability with an intermediate value of delay and regain stability if the delay is large. Numerical simulations show that both strong adaptation of adult prey and the large cost of fear have destabilizing effect while large population of predators has a stabilizing effect on the predator–prey interactions. Numerical simulations also imply that adult prey demonstrates stronger anti-predator behaviors if the population of predators is larger and shows weaker anti-predator behaviors if the cost of fear is larger.     

Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics

Most classical prey-predator models do not take into account the behavioural structure of the population. Usually, the predator and the prey populations are assumed to be homogeneous, i.e. all individuals behave in the same way. In this work, we shall take into account different tactics that predators can use for exploiting a common self-reproducing resource, the prey population. Predators fight together in order to keep or to have access to captured prey individuals. Individual predators can use two behavioural tactics when they encounter to dispute a prey, the classical hawk and dove tactics. We assume two different time scales. The fast time scale corresponds to the inter-specific searching and handling for the prey by the predators and the intra-specific fighting between the predators. The slow time scale corresponds to the (logistic) growth of the prey population and mortality of the predator. We take advantage of the two time scales to reduce the dimension of the model and to obtain an aggregated model that describes the dynamics of the total predator and prey densities at the slow time scale. We present the bifurcation analysis of the model and the effects of the different predator tactics on persistence and stability of the prey-predator community are discussed.     

Impact of Allee effect on an eco-epidemiological system

In this paper, we propose a general ratio-dependent prey-predator model with disease in predator subject to the strong Allee effect in prey. We obtain the complete dynamics of both models: (a) full model with Allee effect; (b) full model without Allee effect. Model (a) may have more than one interior equilibrium point, but model (b) has only one interior equilibrium point. Numerical results reveal that the coexistence of all the populations at the endemic state is possible for both the models. But for the model with Allee effect, the coexistence can be destroyed by an increased supply of alternative food for the predators. It can also be proved that for the full model with Allee effect, the disease can be suppressed under certain parametric conditions. Also by comparing models (a) and (b), we conclude that Allee effect can create or destroy the interior attractor. Finally, we have studied the disease free-submodel (prey and susceptible predator model) with and without Allee effect. The comparative study between these two submodels leads to the following conclusions: 1) In the presence of Allee effect, the number of interior equilibrium points can change from zero to two whereas the submodel without Allee effect has unique interior equilibrium point; 2) Both with and without Allee effect, initial conditions play an important role on the survival and extinction of prey as well as its corresponding predator; 3) In the presence of Allee effect, bi-stability occurs with stable or periodic coexistence of prey and susceptible predator and the extinction of prey and susceptible predator; 4) Allee effect can generate or destroy the interior equilibrium points.     

The role of prey taxis in biological control: a spatial theoretical model

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large-scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator-pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density.     

Ecological stability and social hierarchy

We have examined a predator-prey model in which the predator is assumed to have a social structure of the dominance hierarchy or “peck order” type in which the feeding success of an individual is related both to the availability of food and to his social rank. We find such a social structure to be a strongly beneficial influence on population stability so long as the rewards of social dominance are not too extreme. We also show that an optimally hierarchical predator population can stably achieve a much larger depression of the prey below its carrying capacity than is possible for a simple predator population composed of identical individuals. This strongly suggests that socially structured predator populations may be more effective agents of biological control than simpler predators with no such population structure.     

The re-emergence of felid camouflage with the decay of predator recognition in deer under relaxed selection

When a previously common predator disappears owing to local extinction, the strong source of natural selection on prey to visually recognize that predator becomes relaxed. At present, we do not know the extent to which recognition of a specific predator is generalized to similar looking predators or how a specific predator-recognition cue, such as coat pattern, degrades under prolonged relaxed selection. Using predator models, we show that deer exhibit a more rapid and stronger antipredator response to their current predator, the puma, than to a leopard displaying primitive rosettes similar to a locally extinct predator, an early jaguar. Presentation of a novel tiger with a striped coat engendered an intermediate speed of predator recognition and strength of antipredator behaviour. Responses to the leopard model slightly exceeded responses to a non-threatening deer model, suggesting that thousands of years of relaxed selection have led to the loss of recognition of the spotted coat as a jaguar-recognition cue, and that the spotted coat has regained its ability to camouflage the felid form. Our results shed light on the evolutionary arms race between adoption of camouflage to facilitate hunting and the ability of prey to quickly recognize predators by their formerly camouflaging patterns.     

Impact of vigilance on the density variations in a food chain model

Anti-predator behavior in the form of vigilance greatly influences the dynamics of a predator-prey system. In the present work, we investigate the impact of prey vigilance in a three-species food chain model where both prey and middle predator use vigilance as a survival strategy in the presence of their respective predators. We present basic mathematical results such as local and global stability, bifurcation behavior of the system. We explore the variation of the densities of the populations in different bi-parameter spaces and observe that vigilance plays a crucial role in the survival and extinction of the populations.     

Scrounging behavior regulates population dynamics

The integration of behavioral and population ecology is necessary when behavior both feeds into demographic parameters and depends on population parameters. We show that scrounging behavior, the exploitation of others' resources, can affect both demographic parameters and population dynamics, including the stability of interactions with prey. Scrounging is a common tactic and its pay-offs exhibit both density- and frequency-dependence. We demonstrate that scrounging can act as a population regulator through its effects on individuals' reproductive rate and mortality. We also explore its effects on predator-prey population dynamics and show that the presence of scrounging predators allows an increased predator population size and contributes to the regulation of both predator and prey populations. Behavioral ecologists will appreciate that although scrounging is often pictured as imposing a social foraging cost to group membership, at the population level it also allows higher numbers of both prey and predators to coexist at equilibrium.