Predator group size distributions in predator–prey systems

The grouping behavior is common in nature, e.g., fish school, bird flocks and insects swarms. Indeed, numerous theoretical and empirical predator-prey models have demonstrated the impact of group-living animals on ecosystems. To examine the interactions between individuals in the same group or competition between groups, we introduced different models based on Monte Carlo simulation and mean-field theory and found that the predator group sizes follow the geometric distribution and logarithmic distribution, as in previous empirical and theoretical cases. Our models also provide an intuitive explanation for these distributions. A new distribution based on the Holling-III functional response is presented; this distribution is heavy tailed in some specific cases.     

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.     

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.     

Viable populations in a prey–predator system

 Lotka–Volterra equations are considered a dynamical game, where the phenotypes of the predator and of the prey can vary. This differs from the usual procedure of specifying as a priori laws according to which strategies are supposed to change. The question at stake is the survival of each of the species, instead of the maximization of a given pay-off by each player, as it is commonly discussed in games. The predator needs the prey, while the prey can survive without the predator. These obvious and simplistic constraints are enough to shape the regulation of the system: notably, the largest closed set of initial conditions can be delineated, from which there exists at least one evolutionary path where the population can avoid extinction forever. To these so-called viable trajectories, viable strategies are associated, respectively for the prey or for the predator. A coexistence set can then be defined. Within this set and outside the boundary, strategies can vary arbitrarily within given bounds while remaining viable, whereas on the boundary, only specific strategies can guarantee the viability of the system. Thus, the largest set can be determined, outside of which strategies will never be flexible enough to avoid extinction. Received 2 May 1995; received in revised form 15 August 1995     

On the Neimark–Sacker bifurcation in a discrete predator–prey system

A two-parameter family of discrete models describing a predator–prey interaction is considered, which generalizes a model discussed by Murray, and originally due to Nicholson and Bailey, consisting of two coupled nonlinear difference equations. In contrast to the original case treated by Murray, where the two populations either die out or may display unbounded growth, the general member of this family displays a somewhat wider range of behaviour. In particular, the model has a nontrivial steady state which is stable for a certain range of parameter values, which is explicitly determined, and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter space and a repelling one in others.     

Can prey exhibit threat-sensitive generalization of predator recognition? Extending the Predator Recognition Continuum Hypothesis

Despite the importance of predator recognition in mediating predator-prey interactions, we know little about the specific characteristics that prey use to distinguish predators from non-predators. Recent experiments indicate that some prey who do not innately recognize specific predators as threats have the ability to display antipredator responses upon their first encounter with those predators if they are similar to predators that the prey has recently learned to recognize. The purpose of our present experiment is to test whether this generalization of predator recognition is dependent on the level of risk associated with the known predator. We conditioned fathead minnows to chemically recognize brown trout either as a high or low threat and then tested the minnows for their responses to brown trout, rainbow trout (closely related predator) or yellow perch (distantly related predator). When the brown trout represents a high-risk predator, minnows show an antipredator response to the odour of brown trout and rainbow trout but not to yellow perch. However, when the brown trout represents a low-risk predator, minnows display antipredator responses to brown trout, but not to the rainbow trout or yellow perch. We discuss these results in the context of the Predator Recognition Continuum Hypothesis.     

Predator hunting modes and predator–prey space games

Predators and prey are often engaged in a game where their expected fitnesses are affected by their relative spatial distributions. Game models generally predict that when predators and prey move at similar temporal and spatial scales that predators should distribute themselves to match the distribution of the prey's resources and that prey should be relatively uniformly distributed. These predictions should better apply to sit-and-pursue and sit-and-wait predators, who must anticipate the spatial distributions of their prey, than active predators that search for their prey. We test this with an experiment observing the spatial distributions and estimating the causes of movements between patches for Pacific tree frog tadpoles (Pseudacris regilla), a sit-and-pursue dragonfly larvae predator (Rhionaeschna multicolor), and an active salamander larval predator (Ambystoma tigrinum mavortium) when a single species was in the arena and when the prey was with one of the predators. We find that the sit-and-pursue predator favors patches with more of the prey's algae resources when the prey is not in the experimental arena and that the prey, when in the arena with this predator, do not favor patches with more resources. We also find that the active predator does not favor patches with more algae and that prey, when with an active predator, continue to favor these higher resource patches. These results suggest that the hunting modes of predators impact their spatial distributions and the spatial distributions of their prey, which has potential to have cascading effects on lower trophic levels.     

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.     

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.     

Community-driven dispersal in an individual-based predator–prey model

We present a spatial, individual-based predator–prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynamics of the model is described in terms of this threshold. We compare this dynamics with the one obtained through density-independent dispersal and find marked differences. In the community-driven scenario, the spatial correlations in the population density do not vary in a linear fashion as we increase the tolerance threshold. Instead we find the system to cross different dynamical regimes as the threshold is raised. Spatial patterns evolve from disordered, to scale-free complex patterns, to finally becoming well-organized domains. This model therefore predicts that natural populations, the dispersal strategies of which are likely to be influenced by their local environment, might be subject to complex spatiotemporal dynamics.     

Environmental fluctuations restrict eco-evolutionary dynamics in predator–prey system

Environmental fluctuations, species interactions and rapid evolution are all predicted to affect community structure and their temporal dynamics. Although the effects of the abiotic environment and prey evolution on ecological community dynamics have been studied separately, these factors can also have interactive effects. Here we used bacteria–ciliate microcosm experiments to test for eco-evolutionary dynamics in fluctuating environments. Specifically, we followed population dynamics and a prey defence trait over time when populations were exposed to regular changes of bottom-up or top-down stressors, or combinations of these. We found that the rate of evolution of a defence trait was significantly lower in fluctuating compared with stable environments, and that the defence trait evolved to lower levels when two environmental stressors changed recurrently. The latter suggests that top-down and bottom-up changes can have additive effects constraining evolutionary response within populations. The differences in evolutionary trajectories are explained by fluctuations in population sizes of the prey and the predator, which continuously alter the supply of mutations in the prey and strength of selection through predation. Thus, it may be necessary to adopt an eco-evolutionary perspective on studies concerning the evolution of traits mediating species interactions.     

Cooperative hunting in a discrete predator–prey system II

ABSTRACT

We investigate a discrete-time predator–prey system with cooperative hunting in the predators proposed by Chow et al. by determining local stability of the interior steady states analytically in certain parameter regimes. The system can have either zero, one or two interior steady states. We provide criteria for the stability of interior steady states when the system has either one or two interior steady states. Numerical examples are presented to confirm our analytical findings. It is concluded that cooperative hunting of the predators can promote predator persistence but may also drive the predator to a sudden extinction.     

Effects of perturbation on the predator–prey system in a heterogeneous landscape

Environmental perturbations occur in ecosystems as the result of disturbance, which is closely related to ecosystem stability and resilience. To understand how perturbations can affect ecosystems, we constructed a spatially explicit lattice model to simulate the integrative predator–prey–grass relationships. In this model, a predator (or prey) gives birth to offspring, according to a specific birth probability, when it is able to feed on prey (or grass). When a predator or prey animal was initially introduced or newly born, its health state was set at a given high value. This state decreased by 1 with each time step. When the state of an animal decreased to zero, the animal was considered dead and was removed from the system. In this model, the perturbation was defined as the sudden death of some portion of the population. The heterogeneous landscape was characterized by a parameter, H, which controlled the degree of heterogeneity. When H ≥ 0.6, the predator population size was positively influenced by the perturbation. However, the perturbation had little effect upon the population sizes of prey or grass, regardless of the value of H.     

Asexual reproduction changes predator population dynamics in a life predator–prey system

Many organisms display oscillations in population size. Theory predicts that these fluctuations can be generated by predator–prey interactions, and empirical studies using life model systems, such as a rotifer-algae community consisting of Brachionus calyciflorus as predator and Chlorella vulgaris as prey, have been successfully used for studying such dynamics. B. calyciflorus is a cyclical parthenogen (CP) and clones often differ in their sexual propensity, that is, the degree to which they engage into sexual or asexual (clonal) reproduction. Since sexual propensities can affect growth rates and population sizes, we hypothesized that this might also affect population oscillations. Here, we studied the dynamical behaviour of B. calyciflorus clones representing either CPs (regularly inducing sex) or obligate parthenogens (OPs). We found that the amplitudes of population cycles to be increased in OPs at low nutrient levels. Several other population dynamic parameters seemed unaffected. This suggests that reproductive mode might be an important additional variable to be considered in future studies of population oscillations.     

Spatiotemporal behavior of a prey–predator system with a group defense for prey

Group defense is a strategy widely employed by various species. We consider the effect of grouping on population persistence when animals join together in herds in order to provide a self-defense from predators. In literature, group defense is usually addressed in terms of individual behavioral responses. In this paper, we consider an alternative ‘mean-field’ approach which uses prey and predator densities as the dynamical variables. The model is essentially a predator–prey system but with an unconventional parametrization for the predation term. We discuss the outcomes of the ecosystem dynamics in terms of persistence and prey survival. In the spatially distributed model some specific spatio-temporal features are discovered.     

Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species

In this paper, a predator–prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.