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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,…

This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type…

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…

We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also…

There is a gap between single-species model predictions, and empirical studies, regarding the effect of habitat fragmentation per se, i.e., a process involving the breaking apart of habitat without loss of habitat. Empirical works indicate…

We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…

The establishment of protected areas or parks has become an important tool for wildlife conservation. However, frequent occurrences of human-wildlife conflict at the edges of these parks can undermine their conservation goals. Many African…

A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…

We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…

Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…

Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…

In this work we suggest and consider an original, simple mathematical model of a "quasi-rapid" extinction population dynamics. It describes a decrease and final extinction of the population of one prey species by a "quasi-rapid" interaction…

We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one,…

Using as a narrative theme the example of Darwin's finches, a microscopic agent-based model is introduces to study sympatric speciation as a result of competition for resources in the same ecological niche. Varying competition among…

Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…

The modelling of evolutionary game dynamics in finite populations requires microscopic processes that determine how strategies spread. The exact details of these processes are often chosen without much further consideration. Different types…

Economic incentives to harvest a species usually diminish as its abundance declines, because harvest costs increase. This prevents harvesting to extinction. A known exception can occur if consumer demand causes a declining species' harvest…

The relationships which characterise the outcomes of the interactions between firms in the economy appear to follow power law behaviour. In particular, there is evidence that the empirical power laws which relate the size of an extinction…

We construct two ordinary-differential-equation models of a predator feeding adaptively on two prey types, and we evaluate the models' ability to fit data on freshwater plankton. We model the predator's switch from one prey to the other in…

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…