The existence of beyond mean field quasi-cycle oscillations in a simple spatial model of predator prey interactions is derived from a path integral formalism. The results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation. In all of these analyses, the discrete nature of predator prey populations and finite size effects lead to persistent oscillations in time, but spatial patterns fail to form. The path integral formalism goes beyond mean field theory and provides a focus on individual realizations of the stochastic time evolution of population not captured in the standard master equation approach.
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。
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…
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…
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.
The use of predator-prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka-Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be subject to an Allee effect, where the per capita growth rate increases with the population density. Including an Allee effect has been shown to fundamentally change predator-prey dynamics and strongly impact species persistence, but previous studies mos…
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。
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…
Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference
相互干扰和猎物避难所是捕食者-猎物动力学的重要驱动因素。相互干扰的“指数”或程度在理论生态学中一直备受争议。本文研究了一类具有广义Holling型功能反应的捕食-食饵模型中相互干扰指数的相互作用。我们调查系统的稳定性，并推导出鞍结和Hopf分岔发生的条件。对于该模型，还得到了食饵种群灭绝的一个充分条件.此外，我们调查的猎物避难所对模型的种群动力学的影响，并推导出的猎物避难所，将产生持久性的人口的条件。我们通过数值模拟提供了额外的验证我们的分析结果。我们的研究结果与Gauss G. F（1934），这表明捕食者和猎物种群的灭绝是可能的在一个有限的时间段内-但引入避难所可以有效地导致持久性。
Dynamics of a non-autonomous system with age-structured growth and harvesting of prey and mutually interfering predator with reliance on alternative food
