The concept of evolutionary potential is central to many questions in evolutionary biology and key in particular to our understanding of adaptation prospects to ongoing global changes. I will illustrate how understanding limits to adaptation necessitates to integrate together genetic and demographic constraints. I will deal with structured heterogeneous populations, where different...
We present a population model structured by a quantitative trait, based on the infinitesimal model of quantitative genetics.
The model combines sexual reproduction, selection, and competition in a nonlocal partial differential equation.
The talk focuses on the modeling assumptions and on the interpretation of the small-variance regime.
This talk is based on a joint work with Matthieu...
This is joint work with Coralie Fritsch, Cristóbal Quiñinao, Leonardo Videla and Nicolás Zalduendo-Vidal.
We consider an individual-based model of niche construction based on birth-death processes of d interacting (sub)species immersed in an environment which is influenced by the population state and evolves according to a slower dynamic. Under the above hypothesis, extinction and/or...
Time-inhomogeneous Branching Brownian motion (BBM and its discrete counterpart, time-inhomogeneous branching random walks (BRW) may be considered as models for populations undergoing reproduction and dispersion, in an environment that changes slowly over a large time scale T. They have also been studied intensely by physicists and mathematicians as toy models for so-called spin glasses. In...
The theory of life-history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens. It assumes, however, that host populations are large and that one can neglect the effects of demographic stochasticity. Here, we expand the theory to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic...
We study the evolution of a population with a phenotypic trait structure, where the dynamics is ruled by births, deaths and mutations. We are interested in following populations in logarithmic scales of size and time, and derive a limiting Hamilton-Jacobi equation (with state constraints) from the stochastic individual based model. The limiting partial differential equation takes into account...
n this presentation we study an integro-differential equation which describes the evolutionary dynamics of a population structured by a phenotypic trait. This population undergoes asexual reproduction, competition, selection, and mutation. We provide an asymptotic analysis of the model, assuming that the mutations have small effects. A standard approach for the analysis of the qualitative...
The speed of evolution of a phenotypic trait increases with the proportion of its variation that is transmitted to the next generation. The genetic variance for the trait is thus considered a good measure of evolutionary potential. The former can be computed from the joint distribution of the different gene copies that determine the trait value in the population. Evolutionary forces such as...
In this talk I am considering a model for the dynamics of a population—distributed according to a phenotypic trait—that reproduces sexually and is subject to selection and competition. Sexual reproduction is modeled via a nonlinear integral term, known as Fisher's “infinitesimal model”, which prescribes that the phenotypic trait of the offspring follows a Gaussian distribution around the mean...
We propose a new approach to discretize the von Neumann equation, which is efficient in the semi-classical limit. This method is first based on the so called Weyl's variables to address the stiffness associated with the equation. Then, by applying a truncated Hermite expansion of the density operator, we successfully handle this stiffness. Additionally, we develop a finite volume approximation...
In natural populations, individuals may have different vital rates depending on their age, size, location, infection status, or immunity. This demographic heterogeneity has important ecological and evolutionary consequences. In evolutionary epidemiology, two important sources of heterogeneity are imperfect vaccination and infection age structure. As a result of this heterogeneity, hosts do not...
Telomeres are repetitive sequences situated at both ends of the chromosomes of eukaryotic cells. At each cell division, they are eroded until they reach a critical length that triggers a state in which the cell stops to divide: the senescent state. In this work, we are interested in the link between the initial distribution of telomere lengths and the distribution of senescence times. We...
In this talk I will present a joint and ongoing work with Madeleine Kubasch and Nicolas Loeuille. We are interested in the question of how does spatial heterogeneity of an agricultural landscape impact conservation and yield goal. We developed a model for the ecological dynamics of a meta-community in an agricultural landscape and study both theoretically and numerically which strategies allow...
