Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The evolution of the spatial distribution of species is governed by iterated invasions between the neighboring predator-prey pairs with species specific rates and by site exchange between the neutral pairs with a probability $X$. This dynamical rule yields the formation of five associations composed of two or three species with proper spatiotemporal patterns. For large $X$ a cyclic dominance can occur between the three two-species associations whereas one of the two three-species associations prevails in the whole system for low values of $X$ in the final state. Within an intermediate range of $X$ all the five associations coexist due to the fact that cyclic invasions between the two-species associations reduce their resistance temporarily against the invasion of three-species associations.
We study the degree of success of a single predator hunting a herd of prey on a two dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into direct escap…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are characterized with predation efficiency and death rates, to which Darwinian evolutionary adaptation is introduced. Competition for limited prey abundance drives the populations' optimization with respect to predation efficiency and death rates. We study the influence of various ecological elements on the final state, finding that both indirect competition and …
We show, within the context of the standard class of deterministic ODE predator-prey mathematical models, that predator culling does not produce a long term decrease in the predator population.
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type functionals involved. Here we study the effects of intraspecific cooperation and competition on diffusion-driven instability in a predator-prey system with a different structure. We conduct the analysis on a generalized population dynamics that bounds intraspecific and interspecific interactions with Verhulst-type saturation terms instead of Holling-type func…
In freshwater ecosystems, aquatic insects that ontogenetically shift their habitat from aquatic to terrestrial play vital roles as prey subsidies that move nutrients and energy from aquatic to terrestrial food webs. As a result, these subsidies negatively affect alternative terrestrial prey by enhancing predator density. However, these aquatic insects can also transport contamination to the terrestrial community that is primarily produced in aquatic ecosystems. Which can reduce insectivore abundance and biomass, lower insectivore reproductive success, and increase predation pressure on alterna…
This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the stability of the solution, we make use of the Jacobian matrix and the resultant characteristic polynomial. Particularly, the sign of the eigenvalue is used to determine the stability of a solution. We then provide proof for stability of the interior solution. Finally, we verify our results numerically in MATLAB by plotting: (1) predator-prey intersection graphs; (2)…
Eco-evolutionary frameworks can explain certain features of communities in which ecological and evolutionary processes occur over comparable timescales. Here, we investigate whether an evolutionary dynamics may interact with the spatial structure of a prey-predator community in which both species show limited mobility and predator perceptual ranges are subject to natural selection. In these conditions, our results unveil an eco-evolutionary feedback between species spatial mixing and predators perceptual range: different levels of mixing select for different perceptual ranges, which in turn re…
Foraging movements of predator play an important role in population dynamics of prey-predator interactions, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches…
The war of attrition in game theory is a model of a stand-off situation between two opponents where the winner is determined by its persistence. We model a stand-off between a predator and a prey when the prey is hiding and the predator is waiting for the prey to come out from its refuge, or when the two are locked in a situation of mutual threat of injury or even death. The stand-off is resolved when the predator gives up or when the prey tries to escape. Instead of using the asymmetric war of attrition, we embed the stand-off as an integral part of the predator-prey model of Rosenzweig and M…
In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain constant. Such derivation permits an explicit interpretation of the structure and parameters of the functional response in terms of individual behaviour. The same method is also used here to derive the corresponding numerical response of the predator as well as of the prey.
A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of equilibria are investigated with several illustrating examples. In addition, several periodic solutions were achieved. Furthermore, high degree of fractality of the prey-predator population trajectories is observed when the system is sufficiently delayed. This system has turned out to be a cooperative system, which is depicted using fractal dimension.
We consider a nonautonomous eco-epidemiological model with general functions for predation on infected and uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We obtain persistence and extinction results for the infected prey based on assumptions on systems related to the dynamics in the absence of infected preys. We apply our results to eco-epidemiological models constructed from predator-prey models existent in the literature. Some illustrative simulation is undertaken.
Trait-mediated indirect effects are increasingly acknowledged as important components in the dynamics of ecological systems. The hamiltonian form of the LV equations is traditionally modified by adding density dependence to the prey variable and functional response to the predator variable. Enriching these non-linear elements with a trait-mediation added to the carrying capacity of the prey creates the dynamics of critical transitions and hysteretic zones.
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic coevolution of prey and predators. The community evolves as a multi-type birth and death process with mutations. We first consider the infinite particle approximation of the process without mutation. In this limit, the process can be approximated by a system of differential equations. We prove the existence of a unique globally asymptotically stable equilibriu…
Effects of rapid prey evolution on predator-prey cycles
我们研究了遗传变异允许猎物当代快速进化的捕食者-猎物系统中种群周期的定性性质。先前的数值研究发现，猎物进化对捕食风险变化的反应可能对捕食者-猎物循环产生重大的定量和定性影响，包括：（i）周期的大幅增加，（ii）相位关系的变化（因此捕食者和猎物的循环完全是反相的，而不是经典的四分之一周期相位滞后），和（iii）“隐”循环，其中总猎物密度保持几乎恒定，而捕食者密度和猎物性状循环。在这里，我们专注于恒化器模型的动机，我们的实验系统[Fussmann et al. 2000，Yoshida et al. 2003]与藻类（猎物）和轮虫（捕食者），其中的猎物表现出快速进化的防御水平对捕食。我们表明，快速猎物进化的影响是强大的和普遍的，而且它们发生在一个特定的，但生物相关的参数空间区域：当能大大降低捕食风险的特性相对便宜时，（在其他适应度分量的减少方面），当两种猎物类型和捕食者之间共存时，当捕食者和不设防的猎物之间的相互作用会产生循环时。由于在许多系统中，防御被证明是廉价的，甚至是无成本的[Andersson and Levin 1999，Gagneux et al. 2006，Yoshida et al. 2004]，我们的发现很可能在其他模型系统和自然界中重现。最后，我们的一些关键结果被扩展到一个一般的模型，其中函数形式的捕食率和猎物出生率没有指定。
我们考虑了一类广泛的随机格型捕食模型，其主要特点进行了概述。特别是，这篇文章的目的是绘制一幅图片的空间波动的影响，这是不占的确定性速率方程，随机模型的属性。在这里，我们概述了强大的情况下服从的大多数格点捕食模型与互动“一个' la Lotka-Volterra”。我们还展示了如何一个截然不同的行为可以出现作为一个微妙的相互作用的结果之间的远程相互作用和最近的邻居交换过程。
We consider a modified Rosenzweig-MacArthur predator-prey model, based on the premise that the search rate of predators is dependent on the prey density, rather than constant. A complete analysis of the global behavior of the model is presented, and shows that the model exhibits a dichotomy similar to the classical Rosenzweig-MacArthur model: either the coexistence steady state is globally stable; or it is unstable, and then a unique, globally stable limit cycle exists. We discuss the similarities, but also important differences between our model and the Rosenweig-MacArthur model. The main dif…
Cannibalism, which is the act of killing and at least partial consumption of conspecifics, is ubiquitous in nature. Mathematical models have considered cannibalism in the predator primarily, and show that predator cannibalism in two species ODE models provides a strong stabilizing effect. There is strong ecological evidence that cannibalism exists among prey as well, yet this phenomenon has been much less investigated. In the current manuscript, we investigate both the ODE and spatially explicit forms of a Holling-Tanner model, with ratio dependent functional response. We show that cannibalism…
Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction
包括空间结构和随机噪声失效的经典Lotka-Volterra图片出现在捕食者-猎物相互作用的模型中的稳定的定期人口周期。生长限制条款的猎物诱导连续灭绝阈值的捕食者人口的关键属性是在定向渗透普适类。在这里，我们讨论了这种情况下的鲁棒性，考虑生态启发的随机格捕食者-被捕食者模型的变体，其中捕食过程包括下一个最近邻的相互作用。我们发现，相应的随机模型再现了上述情况的尺寸1< d \leq 4，与平均场理论预测的一阶相变。然而，平均场的功能恢复后，允许最近的邻居粒子交换过程，提供这些是足够快的。
A common idiom in biology education states, "Eyes in the front, the animal hunts. Eyes on the side, the animal hides." In this paper, we explore one possible explanation for why predators tend to have forward-facing, high-acuity visual systems. We do so using an agent-based computational model of evolution, where predators and prey interact and adapt their behavior and morphology to one another over successive generations of evolution. In this model, we observe a coevolutionary cycle between prey swarming behavior and the predator's visual system, where the predator and prey continually adapt …
We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions of the Lotka-Volterra predator-prey model, by analogy to the damped harmonic oscillator. The analogy deepens with the use of Lyapunov functions, which allow us to characterize their dynamics and even make some estimates.
A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We give conditions for the existence of some local and global bifurcations at the coexistence equilibrium. We also show that fear can induce extinction of the prey population from a coexistence zone in finite time. Our numerical simulations reveal that varying the strength of fear of predators with suitable choice of parameters can stabilize and destabilize the…
Predator-prey networks originating from different aqueous and terrestrial environments are compared to assess if the difference in environments of these networks produce any significant difference in the structure of such predator-prey networks. Spectral graph theory is used firstly to discriminate between the structure of such predator-prey networks originating from aqueous and terrestrial environments and secondly to establish that the difference observed in the structure of networks originating from these two environments are precisely due to the way edges are oriented in these networks and…
The present paper deals with a prey-predator model with prey refuge proportion to both species and independent harvesting of each species. Our study shows that using refuge as control, it can break the limit circle of the system and reach the required state of equilibrium level. It is established the optimal harvesting policy. The boundedness, feasibility of interior equilibria, bionomic equilibrium have been determined. The main observation is that coefficient of refuge plays an important role in regulating the dynamics of the present system. Moreover the variation of the coefficient of refug…
