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Möhle, M.

On sampling distributions for coalescent processes with simultaneous multiple collisions. (English) Zbl 1099.92052

Bernoulli 12, No. 1, 35-53 (2006).
Summary: Recursions for a class of sampling distributions of allele configurations are derived for the situation where the genealogy of the underlying population is modelled by a coalescent process with simultaneous multiple collisions of ancestral lineages. These recursions describe a new family of partition structures in terms of the composition probability function, parametrized by the infinitesimal rates of the coalescent process. For the J. F. C. Kingman coalescent process [Stochastic Processes Appl. 13, 235–248 (1982; Zbl 0491.60076)] with only binary mergers of ancestral lines, the recursion reduces to that known for the classical Ewens sampling distribution. We solve the recursion for the star-shaped coalescent. The asymptotic behaviour of the number \(K_n\) of alleles (types) for large sample size n is studied, in particular for the star-shaped coalescent and the E. Bolthausen and A.-S. Sznitman [Commun. Math. Phys. 197, No. 2, 247–276 (1998; Zbl 0927.60071)] coalescent.

Cited in 25 Documents

MSC:

92D10 Genetics and epigenetics
60J25 Continuous-time Markov processes on general state spaces
60J27 Continuous-time Markov processes on discrete state spaces

Keywords:

Bolthausen-Sznitman coalescent; composition probability function; Ewens sampling formula; mutation rate; neutral infinite alleles model; partition structure; sampling distribution; simultaneous multiple collisions; star-shaped tree

Citations:

Zbl 0491.60076; Zbl 0927.60071
PDFBibTeX XMLCite
\textit{M. Möhle}, Bernoulli 12, No. 1, 35--53 (2006; Zbl 1099.92052)
Full Text: Euclid

References:

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