Stepping-stone model with circular Brownian migration
نویسنده
چکیده
In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the stepping-stone model using Arratia flow and circular coalescing Brownian motion. Such a representation enables us to carry out some explicit computation. In particular, we find the Laplace transform for the time when there is only a single type left across the circle.
منابع مشابه
N ov 1 99 8 CONTINUUM – SITES STEPPING – STONE MODELS , COALESCING EXCHANGEABLE PARTITIONS , AND RANDOM TREES
Analogues of stepping–stone models are considered where the site– space is continuous, the migration process is a general Markov process, and the type–space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative represent...
متن کاملContinuum{sites Stepping{stone Models, Coalescing Exchangeable Partitions, and Random Trees
Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative representat...
متن کاملOne 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...
متن کاملImpacts of seed and pollen flow on population genetic structure for plant genomes with three contrasting modes of inheritance.
The classical island and one-dimensional stepping-stone models of population genetic structure developed for animal populations are extended to hermaphrodite plant populations to study the behavior of biparentally inherited nuclear genes and organelle genes with paternal and maternal inheritance. By substituting appropriate values for effective population sizes and migration rates of the genes ...
متن کاملThe coalescent and the genealogical process in geographically structured population.
We shall extend Kingman's coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005