Related papers: Linking lineage and population observables in biol…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
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…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
We present a flexible branching process model for cell population dynamics in synchrony/time-series experiments used to study important cellular processes. Its formulation is constructive, based on an accounting of the unique cohorts in the…
Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
In this paper we study a two-level branching model for virus populations under cell division. We assume that the cells are carrying virus populations which evolve as a branching particle system with competition, while the cells split…
Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting…
Erythropoiesis is a mechanism for the production of red blood cells by cellular differentiation. It is based on amplification steps due to an interplay between renewal and differentiation in the successive cell compartments from stem cells…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to…
Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing…
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…
We study branching Markov chains on a countable state space (space of types) $\mathscr{X}$, with the focus on the qualitative aspects of the limit behaviour of the evolving empirical population distributions. No conditions are imposed on…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the…
Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population averaged…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…