Related papers: Effect of population size in a Prey-Predator model
We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin)…
Animal grouping behaviors have been widely studied due to their implications for understanding social intelligence, collective cognition, and potential applications in engineering, artificial intelligence, and robotics. An important…
This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
The classical two-species non-linear Predator-Prey system, often used in population dynamics modeling, is expressed in terms of a single positive coupling parameter $\lambda$. Based on standard logarithmic transformations, we derive a novel…
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
We construct a model of speciation from evolution in an ecosystem consisting of a limited amount of energy recources. The species posses genetic information, which is inherited according to the rules of the Penna model of genetic evolution.…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
The internal behaviour of a population is an important feature to take account of when modelling their dynamics. In line with kin selection theory, many social species tend to cluster into distinct groups in order to enhance their overall…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate…
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…