Related papers: On a stochastic Ricker competition model
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
Branching processes are widely used to model evolutionary and population dynamics as well as the spread of infectious diseases. To characterize the dynamics of their growth or spread, the basic reproduction number $R_0$ has received…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
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…
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. We introduce theclimate shift due to {\it Global Warming} and discuss the dynamicsof the…
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
In this paper we develop an SIR model for coinfection. We discuss how the underlying dynamics depends on the carrying capacity $K$: from a simple dynamics to a more complicated. This can help in understanding of appearance of more…
We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two…
The Tangled Nature Model of biological and cultural evolution features interacting agents which compete for limited resources and reproduce in an error prone fashion and at a rate depending on the `tangle' of interactions they maintain with…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field…
We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space in regular lattices. Individuals of one species can invade a…