Related papers: Evolutionary dynamics and competition stabilize th…
The dynamics of predator-prey systems influenced by intra-specific competition and additional food resources have increasingly become a subject of rigorous study in the realm of mathematical biology. In this study, we consider an additional…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…
In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates…
Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
The self-protection of alliances against external invaders is a key concept behind the maintenance of biodiversity in the face of natural selection. But since these alliances, which can be formed by different numbers of competitors, can…
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…
One of the best examples of traditional analysis of evolutionary stable strategies (ESS) is provided by the so called Dove-Hawk model. In this paper we present several enhancements to the model aimed at describing the evolution of…
Microbial communities harbor extensive fine-scale diversity: closely-related strains of the same species coexist alongside many distantly-related taxa. Yet strain coexistence remains poorly understood, largely because most studies neglect…
A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
In this letter, we investigate the population dynamics in a May-Leonard formulation of the rock-paper-scissors game in which one or two species, which we shall refer to as "weak", have a reduced predation or reproduction probability. We…
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…
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…
Using a lattice model based on Monte Carlo simulations, we study the role of the reproduction pattern on the fate of an evolving population. Each individual is under the selection pressure from the environment and random mutations. The…
A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…