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An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
How does the interplay between selection, mutation and horizontal gene transfer modify the phenotypic distribution of a bacterial or cell population? While horizontal gene transfer, which corresponds to the exchange of genetic material…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…
In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…
In this paper, by resorting to classical methods of statistical mechanics, we build a kinetic model able to reproduce the observed statistical weight distribution of many diverse species. The kinetic description of the time variations of…
Speciation is driven by many different factors. Among those are trade-offs between different ways an organism utilizes resources, and these trade-offs can constrain the manner in which selection can optimize traits. Limited migration among…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
The Yule (pure-birth) model is the simplest null model of speciation; each lineage gives rise to a new lineage independently with the same rate $\lambda$. We investigate the expected length of an edge chosen at random from the resulting…
Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist…
We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Parapatric speciation is studied using an individual--based model with sexual reproduction. We combine the theory of mutation accumulation for biological ageing with an environmental selection pressure that varies according to the…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
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…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner.…