The population genealogy of the infinitely-many neutral alleles model
The author introduces a process \(M_ t\) analogous to Kingman's coalescent to describe the genealogy of populations evolving according to the infinitely-many neutral alleles model. The process \(M_ t\) is defined by \({\mathfrak M}_{D_ t}\), \({\mathfrak M}_ t\) is a Markov chain on \(N_{\infty}\times \Delta\), \[ N_{\infty}=\{0,1,2,3,...\infty \},\quad \Delta =\{(x_ 1,x_ 2,...): 0\leq x_ i\leq 1,\quad \sum x_ i=1\}, \] and \(D_ t\) is an independent death process on \(N_{\infty}\), \(D_ 0=\infty\). Using this process K-allele models are considered. Its marginal distribution is explicitly calculated.
scientific article; zbMATH DE number 4037660
scientific article