Related papers: Phenotypic Equilibrium as Probabilistic Convergenc…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes linear diffusion, while the other proliferates in…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
Cells with the same genome can exist in different phenotypes. and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation)…
This paper considers the probabilistic representation of the solutions of ordinary differential equations (ODEs) by the generation of marked random trees in which marks can be interpreted as mutant types in population genetics models. We…
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…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…