Dynamics of a non-autonomous system with age-structured growth and harvesting of prey and mutually interfering predator with reliance on alternative food
N. S. N. V. K. Vyshnavi Devi, Debaldev Jana, M. Lakshmanan
We perform a detailed analysis of the behaviour of a non-autonomous prey-predator model where age based growth with age discriminatory harvesting in prey and predator's reliance upon alternative food in the absence of that particular prey are considered. We begin by deriving certain sufficient conditions for permanence and positive invariance and then proceed to construct a Lyapunov function to derive some constraints for global attractivity. With the help of continuation theorem we arrive at the best fit criterion to prove the occurrence of a positive periodic solution. Moreover, using Arzela-Ascoli theorem we formulate a proof for a unique positive solution to be almost periodic and we carry out numerical simulation to verify the analytical findings. With the aid of graphs and tables we show the nature of the prey-predator system in response to the alternative food and delays.
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…
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.
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)…
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 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…
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.
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。
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 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…
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…
Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, on the behavior of a predator-prey model with a generalized Holling type functional response. We investigate stability properties of the system and derive conditions for the occurrence of saddle-node and Hopf-bifurcations. A sufficient condition for extinction of the prey species has also been derived for the model. In addition…
In this investigation we study the effects of climate change on predator-prey population dynamics. The interaction of predator and prey is described by the Variable Territory (VT) model with Allee effects in an Ordinary Differential Equation (ODE) framework. Climate influence is modeled in this ODE framework as an exogenous driver which affects the prey growth rate. Mathematically, this exogenous driver is a function of time, the climate function, that describes how favorable is the climate, on a scale from $-1$ to $+1$. Climate change has a number of effects; in this work, we focus on changes…
