Related papers: On the long-time behaviour of age and trait struct…
We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in…
We study the dynamics of an age-structured population in which the life expectancy of an offspring may be mutated with respect to that of its parent. When advantageous mutation is favored, the average fitness of the population grows…
This paper is devoted to the analysis of the long-time behavior of a phenotypic-structured model where phenotypic changes do not occur. We give a mathematical description of the process in which the best adapted trait is selected in a given…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
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…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…
We give a direct proof of well-posedness of solutions to general selection-mutation and structured population models with measures as initial data. This is motivated by the fact that some stationary states of these models are measures and…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…
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,…
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…