Related papers: Wright-Fisher diffusions for evolutionary games wi…
We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…
We study voter models defined on large sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright-Fisher diffusion only involves certain averages of…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
This paper is concerned with the death-birth updating process. This model is an example of a spatial game in which players located on the~$d$-dimensional integer lattice are characterized by one of two possible strategies and update their…
The Moran discrete process and the Wright-Fisher modelare the most popular models in population genetics. It is common tounderstand the dynamics of these models to use an approximating diffusionprocess, called Wright-Fisher diffusion. Here,…
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended…
We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are defined by a degenerate second order operator on the interval [0, 1], where the coefficient of the second order term…
Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The…
We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
The Wright--Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation, and genetic drift. Simulating paths of…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to…