Related papers: Clonal interference and Muller's ratchet in spatia…
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…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which…
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…
Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks.…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We consider the dynamics of spatially-distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
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…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
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…
In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can…
We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain…
We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic…
We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an…
Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal…