Related papers: Pattern formation through genetic drift at expandi…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
The ecological dynamics of interacting predator and prey populations can display sustained oscillations, as for instance predicted by the Rosenzweig-MacArthur predator-prey model. The presence of demographic stochasticity, due to the…
When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in…
Our purpose in this paper is to determine the limiting distribution and the evolution rate of particles near the frontier of branching Brownian motions. Here the branching rate is given by a Kato class measure with compact support in…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…
In an increasingly interconnected world, a key scientific challenge is to examine mechanisms that lead to the widespread propagation of contagions, such as misinformation and pathogens, and identify risk factors that can trigger large-scale…
The ubiquitous existence of microbial communities marks the importance of understanding how species interact within the community to coexist and their spatial organization. We study a two-species mutualistic cross-feeding model through a…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
Many theoretical and experimental studies suggest that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly…
Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative…
We investigate the effect of spatial range expansions on the evolution of fitness when beneficial and deleterious mutations co-segregate. We perform individual-based simulations of a uniform linear habitat and complement them with…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…