Coalescent Theory of Migration Network Motifs

Coalescent Theory

Random variation in reproduction causes random fluctuation in allele frequencies. Can describe this process as diffusion: (Wright 1931) showed that the equilibrium distribution of the allele frequency of p, where alleles mutate: P → Q at rate µ and Q → P at rate υ, can be described by:) 1 4 () 1 4 () Pr(− − = µ υ e e N N q cp p (c is a constant that normalizes the area under the curve to one) D...

Coalescent Theory

The coalescent process is a powerful modeling tool for population genetics. The allelic states of all homologous gene copies in a population are determined by the genealogical and mutational history of these copies. The coalescent approach is based on the realization that the genealogy is usually easier to model backward in time, and that selectively neutral mutations can then be superimposed a...

Hamilton's rule: Game theory meets coalescent theory.

Extending Coalescent Theory to Autotetraploids

We develop coalescent models for autotetraploid species with tetrasomic inheritance. We show that the ancestral genetic process in a large population without recombination may be approximated using Kingman's standard coalescent, with a coalescent effective population size 4N. Numerical results suggest that this approximation is accurate for population sizes on the order of hundreds of individua...

Recent Progress in Coalescent Theory

Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and other fields such as spin glass models. The emphasis is on recent work concerning in particular the connection of these...