Related papers: A comparative study between discrete and continuum…

We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…

Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…

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…

We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem…

Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…

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?…

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…

This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the…

We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…

This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…

We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…

We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of…

Cells generally change their internal state to adapt to an environmental change, and accordingly evolve in response to the new conditions. This process involves phenotypic changes that occur over several different time scales, ranging from…

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 present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models…

We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit…

The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…

This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…

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…