Coalescent processes obtained from supercritical Galton-Watson processes

Jason Schweinsberg

Stochastic Processes and their Applications, 2003, vol. 106, issue 1, 107-139

Abstract: Consider a population model in which there are N individuals in each generation. One can obtain a coalescent tree by sampling n individuals from the current generation and following their ancestral lines backwards in time. It is well-known that under certain conditions on the joint distribution of the family sizes, one gets a limiting coalescent process as N-->[infinity] after a suitable rescaling. Here we consider a model in which the numbers of offspring for the individuals are independent, but in each generation only N of the offspring are chosen at random for survival. We assume further that if X is the number of offspring of an individual, then P(X[greater-or-equal, slanted]k)~Ck-a for some a>0 and C>0. We show that, depending on the value of a, the limit may be Kingman's coalescent, in which each pair of ancestral lines merges at rate one, a coalescent with multiple collisions, or a coalescent with simultaneous multiple collisions.

Keywords: Coalescence; Galton-Watson; processes; Ancestral; processes; Poisson-Dirichlet; distribution (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (20)

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