Related papers: Long-term analysis of phenotypically structured mo…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
Biological organisms exhibit diverse strategies for adapting to varying environments. For example, a population of organisms may express the same phenotype in all environments (`unvarying strategy'), or follow environmental cues and express…
We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of…
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population…
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…
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,…
In this work we propose a physical model of organismal evolution, where phenotype, organism life expectancy, is directly related to genotype i.e. the stability of its proteins which can be determined exactly in the model. Simulating the…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
This paper shows that differentiating the lifetimes of two phenotypes independently from their fertility can lead to a qualitative change in the equilibrium of a population: since survival and reproduction are distinct functional aspects of…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…
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…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual…
We consider the cell population dynamics with $n$ different phenotypes. Both the Markovian branching process model (stochastic model) and the ordinary differential equation (ODE) system model (deterministic model) are presented, and…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Genetic information and environmental factors determine the path of an individuals life and therefore, the evolution of its entire species. We have succeeded in proposing and studying a model that captures this idea. In our model, a…