Related papers: Clonal interference and Muller's ratchet in spatia…

We consider an infinite-dimensional system of stochastic differential equations describing the evolution of type frequencies in a large population. The type of an individual is the number of deleterious mutations it carries, where fitness…

Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps,…

Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…

In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…

We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness…

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics…

Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we…

Rare evolutionary events, such as the rise to prominence of deleterious mutations, can have drastic impacts on the evolution of growing populations. Heterogeneous environments may reduce the influence of selection on evolutionary outcomes…

We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates…

Cellular renewing active matter - assemblies of proliferating and apoptotic cells - underlies tissue homeostasis, morphogenesis, and clonal competition. Previous work in one-dimensional periodic systems identified a fitness advantage…

Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, $K$, at which these substitutions accumulate in the population coincides with the…

Fitness consequence of dispersal depends on property of the entire landscape, which patches are available and what are the cost of moving. These are information that are not available locally when an organism make the decision to disperse.…

We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some…

We consider the accumulation of deleterious mutations in an asexual population, a phenomenon known as Muller's ratchet, using the continuous time model proposed in Etheridge et all. \cite{epw}. We show that for any parameter $\lambda>0$…

Studies on the genetics of adaptation typically neglect the possibility that a deleterious mutation might fix. Nonetheless, here we show that, in many regimes, the first substitution is most often deleterious, even when fitness is expected…

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been…

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…

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…

Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random,…

A simple spatial computer simulation model was recently introduced to study the evolution of the linguistic diversity. The model considers processes of selective geographic colonization, linguistic anomalous diffusion and mutation. In the…