Related papers: Small populations corrections for selection-mutati…
The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a…
We analyse the asymptotic behaviour of integro-differential equations modelling $N$ populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total…
Nowadays, in our globalized world,the local and intercountry movements of population have been increased. This situation makes it important for host countries to do right predictions for the future population of their native people as well…
Complex adaptive systems have been the subject of much recent attention. It is by now well-established that members (`agents') tend to self-segregate into opposing groups characterized by extreme behavior. However, while different social…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…
Species-rich communities, such as the microbiota or microbial ecosystems, provide key functions for human health and climatic resilience. Increasing effort is being dedicated to design experimental protocols for selecting community-level…
We study the stationary state of a population evolving under the action of random genetic drift, selection and recombination in which both deleterious and reverse beneficial mutations can occur. We find that the equilibrium fraction of…
We present an individual-based model for two interacting populations diffusing on lattices in which a strong natural selection develops spontaneously. The models combine traditional local predator-prey dynamics with random walks.…
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models arise in a variety of contexts from climate change to…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over…
In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
The dynamics of populations is rich, taking into account that both, the individual's actions and the population's fitness are coupled. The way in which an individual chooses a strategy depends off course on the interaction with other…
We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…