食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。     

具有捕食正效应的捕食-食饵系统

在经典的捕食食饵系统中考虑到由于捕食效应对食饵种群带来的正向调节作用后,提出了具有捕食正效应的捕食-食饵系统.通过对模型的动力学行为的分析,从理论上说明了正向调节作用对系统的影响,并就第一象限内平衡点存在时的相图解释了捕食正效应的作用.结果表明:(1)捕食系统中适当的正向调节作用会增加系统的稳定性;(2)当捕食正效应达到一定的程度后系统拥有一个不稳定的极限环;(3)当捕食正效应过大时会使系统的稳定性发生变化,使捕食者种群与食饵种群同时趋向无穷,出现了调节放纵现象.这些结果在保护生物学中具有重要的意义.     

Effect of predator density dependent dispersal of prey on stability of a predator-prey system

This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system.     

Cannibalism in an age-structured predator-prey system

Recently, Kohlmeier and Ebenhöh showed that cannibalism can stabilize population cycles in a Lotka-Volterra type predator-prey model. Population cycles in their model are due to the interaction between logistic population growth of the prey and a hyperbolic functional response. In this paper, we consider a predator-prey system where cyclic population fluctuations are due to the age structure in the predator species. It is shown that cannibalism is also a stabilizing mechanism when population oscillations are due to this age structure. We conclude that in predator-prey systems, cannibalism by predators can stabilize both externally generated (consumer-resource) as well as internally generated (agestructure) fluctuations.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Prey patchiness, predator survival and fish recruitment

A simple mathematical model is presented for the population dynamics of fish larvae when the main food supply, in this case copepods, is spatially patchy in its distribution. Encounters by an individual predator (larva) with prey patches, and with individual prey within patches, are represented by Poisson processes. It is demonstrated analytically, and confirmed by numerical experiments, that prey patchiness fails to alter mean predator-prey encounter rates from their values for homogeneous prey distributions. Individual variance in encounter rate is, however, much affected. This has significant consequences for the (small) numbers of larvae surviving to metamorphosis and recruitment to the adult fish population.     

Testing for predator dependence in predator-prey dynamics: a non-parametric approach

The functional response is a key element in all predator-prey interactions. Although functional responses are traditionally modelled as being a function of prey density only, evidence is accumulating that predator density also has an important effect. However, much of the evidence comes from artificial experimental arenas under conditions not necessarily representative of the natural system, and neglecting the temporal dynamics of the organism (in particular the effects of prey depletion on the estimated functional response). Here we present a method that removes these limitations by reconstructing the functional response non-parametrically from predator-prey time-series data. This method is applied to data on a protozoan predator-prey interaction, and we obtain significant evidence of predator dependence in the functional response. A crucial element in this analysis is to include time-lags in the prey and predator reproduction rates, and we show that these delays improve the fit of the model significantly. Finally, we compare the non-parametrically reconstructed functional response to parametric forms, and suggest that a modified version of the Hassell-Varley predator interference model provides a simple and flexible function for theoretical investigation and applied modelling.     

Taxis-driven pattern formation in a predator-prey model with group defense

We consider a reaction-diffusion(-taxis) predator-prey system with group defense in the prey. Taxis-driven instability can occur if the group defense influences the taxis rate (Wang et al., 2017). We elaborate that this mechanism is indeed possible but biologically unlikely to be responsible for pattern formation in such a system. Conversely, we show that patterns in excitable media such as spatiotemporal Sierpinski gasket patterns occur in the reaction-diffusion model as well as in the reaction-diffusion-taxis model. If group defense leads to a dome-shaped functional response, these patterns can have a rescue effect on the predator population in an invasion scenario. Preytaxis with prey repulsion at high prey densities can intensify this mechanism leading to taxis-induced persistence. In particular, taxis can increase parameter regimes of successful invasions and decrease minimum introduction areas necessary for a successful invasion. Last, we consider the mean period of the irregular oscillations. As a result of the underlying mechanism of the patterns, this period is two orders of magnitude smaller than the period in the nonspatial system. Counter-intuitively, faster-moving predators lead to lower oscillation periods and eventually to extinction of the predator population. The study does not only provide valuable insights on theoretical spatially explicit predator-prey models with group defense but also comparisons of ecological data with model simulations.     

一类具分段常数变量的捕食-食饵系统的Neimark-Sacker分支

讨论了具时滞与分段常数变量的捕食-食饵生态模型的稳定性及Neimark-Sacker分支;通过计算得到连续模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件;以食饵的内禀增长率为分支参数,运用分支理论和中心流形定理分析了Neimark-Sacker分支的存在性与稳定性条件;通过举例和数值模拟验证了理论的正确性。     

The effect of spatial heterogeneity on the persistence of predator-prey interactions

The effect of spatially discontinuous environments on predator-prey systems is examined by using a computer simulation model. It is shown that increasing prey dispersal and decreasing predator dispersal do not necessarily have a stabilizing influence on the interaction, as had been concluded by previous workers. The stability of predator-prey interaction depends on the interaction of the dispersal process with normal reproduction and feeding of the predator and prey species.     

Continuous-time predator-prey models with parasites

We study a deterministic continuous-time predator-prey model with parasites, where the prey population is the intermediate host for the parasites. It is assumed that the parasites can affect the behavior of the predator-prey interaction due to infection. The asymptotic dynamics of the system are investigated. A stochastic version of the model is also presented and numerically simulated. We then compare and contrast the two types of models.     

The discrete Rosenzweig model

Discrete time versions of the Rosenweig predator-prey model are studied by analytic and numerical methods. The interaction of the Hopf bifurcation leading to periodic orbits and the period-doubling bifurcation is investigated. It is shown that for certain choices of the parameters there is stable coexistence of both species together with a local attractor at which the prey is absent.     

Predation across spatial scales in heterogeneous environments

A hierarchy of scales is introduced to the spatially heterogeneous Lotka-Volterra predator-prey diffusion model, and its effects on the model's spatial and temporal behavior are studied. When predators move on a large scale relative to prey, local coupling of the predator-prey interaction is replaced by global coupling. Prey with low dispersal ability become narrowly confined to the most productive habitats, strongly amplifying the underlying spatial pattern of the environment. As prey diffusion rate increases, the prey distribution spreads out and predator abundance declines. The model retains neutrally stable Lotka-Volterra temporal dynamics: different scales of predator and prey dispersal do not stabilize the interaction. The model predicts that, for prey populations that are limited by widely ranging predators, species with low dispersal ability should be restricted to discrete high density patches, and those with greater mobility should be more uniformly distributed at lower density.     

Impact of spatial heterogeneity on a predator-prey system dynamics

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.     

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.     

Systems analysis of an acarine predator-prey system II: Interactions in discontinuous environment

An acarine predator-prey system in a circular stepping-stone environment was described with a simulation model to elucidate the factors responsible for persistence of the system. The main assumptions in this model are: (1) The prey are inevitably eliminated in patches in which predators exist. (2) The density of prey declines and becomes extinct by plant defoliation due to feeding by prey. In this regard this model is different from the models which mimickedHuffaker's (1958) experiments and assumed stable plant-prey relations. Analyses showed that the critical factor in persistence of the predator-prey system was the plant-prey relations, at any combination of other parameters involved in the model. The predator-prey system did not persist long under the unstable relationship of prey and plant. Otherwise the system persisted longer especially when I used a larger number of patches, a larger amount of plant in each patch, and long-distance-migrations of the prey. In particular, frequent emigration of the prey regardless of plant conditions was most effective.     

An emerging infectious disease triggering large-scale hyperpredation

Hyperpredation refers to an enhanced predation pressure on a secondary prey due to either an increase in the abundance of a predator population or a sudden drop in the abundance of the main prey. This scarcely documented mechanism has been previously studied in scenarios in which the introduction of a feral prey caused overexploitation of native prey. Here we provide evidence of a previously unreported link between Emergent Infectious Diseases (EIDs) and hyperpredation on a predator-prey community. We show how a viral outbreak caused the population collapse of a host prey at a large spatial scale, which subsequently promoted higher-than-normal predation intensity on a second prey from shared predators. Thus, the disease left a population dynamic fingerprint both in the primary host prey, through direct mortality from the disease, and indirectly in the secondary prey, through hyperpredation. This resulted in synchronized prey population dynamics at a large spatio-temporal scale. We therefore provide evidence for a novel mechanism by which EIDs can disrupt a predator-prey interaction from the individual behavior to the population dynamics. This mechanism can pose a further threat to biodiversity through the human-aided disruption of ecological interactions at large spatial and temporal scales.     

Availability of prey resources drives evolution of predator-prey interaction

Productivity is predicted to drive the ecological and evolutionary dynamics of predator-prey interaction through changes in resource allocation between different traits. Here we report results of an evolutionary experiment where prey bacteria Serratia marcescens was exposed to predatory protozoa Tetrahymena thermophila in low- and high-resource environments for approximately 2400 prey generations. Predation generally increased prey allocation to defence and caused prey selection lines to become more diverse. On average, prey became most defensive in the high-resource environment and suffered from reduced resource use ability more in the low-resource environment. As a result, the evolution of stronger prey defence in the high-resource environment led to a strong decrease in predator-to-prey ratio. Predation increased temporal variability of populations and traits of prey. However, this destabilizing effect was less pronounced in the high-resource environment. Our results demonstrate that prey resource availability can shape the trade-off allocation of prey traits, which in turn affects multiple properties of the evolving predator-prey system.     

Should "handled" prey be considered? Some consequences for functional response, predator-prey dynamics and optimal foraging theory

Predator-prey models consider those prey that are free. They assume that once a prey is captured by a predator it leaves the system. A question arises whether in predator-prey population models the variable describing prey population shall consider only those prey which are free, or both free and handled prey together. In the latter case prey leave the system after they have been handled. The classical Holling type II functional response was derived with respect to free prey. In this article we derive a functional response with respect to prey density which considers also handled prey. This functional response depends on predator density, i.e., it accounts naturally for interference. We study consequences of this functional response for stability of a simple predator-prey model and for optimal foraging theory. We show that, qualitatively, the population dynamics are similar regardless of whether we consider only free or free and handled prey. However, the latter case may change predictions in some other cases. We document this for optimal foraging theory where the functional response which considers both free and handled prey leads to partial preferences which are not observed when only free prey are considered.     

Predator migration in response to prey density: What are the consequences?

A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically.