Related papers: Fixation properties of subdivided populations with…
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a…
Background: Speciation corresponds to the progressive establishment of reproductive barriers between groups of individuals derived from an ancestral stock. Since Darwin did not believe that reproductive barriers could be selected for, he…
We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the environment follows a Markovian process, resulting in a…
In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here,…
A steady influx of a single deleterious multilocus genotype will impose genetic load on the resident population and leave multiple descendants carrying various numbers of the foreign alleles. Provided that the foreign types are rare at…
Evolutionary dynamics on graphs can lead to many interesting and counterintuitive findings. We study the Moran process, a discrete time birth-death process, that describes the invasion of a mutant type into a population of wild-type…
This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
The accumulation of beneficial mutations on many competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the…
We present an individual-based model for two interacting populations diffusing on lattices in which a strong natural selection develops spontaneously. The models combine traditional local predator-prey dynamics with random walks.…
Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape…
Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not…
Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of natural selection, and those that suppress the spreading of fitter mutants are…
Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…