Continuous time multi-allelic stepping stone models in population genetics

One dimensional stepping stone models, sardine genetics, and Brownian local time

Consider a one dimensional stepping stone model with colonies of size M and per generation migration probability ν, or a voter model on Z in which interactions occur over a distance of order K. Sample one individual at the origin and one at L. We show that if Mν/L and L/K2 converge to positive finite limits, then the genealogy of the sample converges to a pair Brownian motions that coalesce aft...

Genetic demixing and evolution in linear stepping stone models.

Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for populati...

Competition and cooperation in one-dimensional stepping-stone models.

Mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well known, their effects on mutualism are not fully understood. With range expansions of microbes in mind, we show that, even when mutualism confers a selective advantage, it persists only in populations with high density and frequent migratio...

Isolation-by-distance-and-time in a stepping-stone model.

With the great advances in ancient DNA extraction, genetic data are now obtained from geographically separated individuals from both present and past. However, population genetics theory about the joint effect of space and time has not been thoroughly studied. Based on the classical stepping-stone model, we develop the theory of Isolation by distance and time. We derive the correlation of allel...

Stepping Stone Detection Analysis