Related papers: Slow expanders invade by forming dented fronts in …
Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of…
As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical…
Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial…
In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the…
Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from…
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…
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…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…
Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
Spatial structure is one of the simplest and most studied ecological factors that affect the evolution of cooperation. It has been shown that spatial reciprocity promotes cooperation due to the formation of cooperative clusters, which…
Mechanical interactions among cells in a growing microbial colony can significantly influence the colony's spatial genetic structure and, thus, evolutionary outcomes such as the fates of rare mutations. Here, we computationally investigate…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
We discuss a cellular automata model to study the competition between an emergent better fitted species against an existing majority species. The model implement local fights among small group of individual and a synchronous random walk on…
When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and…
We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…