Coalescent processes derived from some compound Poisson population models. (English) Zbl 1367.92105

Möhle, Martin

Electron. Commun. Probab. 16, 567-582 (2011).

Summary: A particular subclass of compound Poisson population models is analyzed. The models in the domain of attraction of the Kingman coalescent are characterized and it is shown that these models are never in the domain of attraction of any other continuous-time coalescent process. Results are obtained characterizing which of these models are in the domain of attraction of a discrete-time coalescent with simultaneous multiple mergers of ancestral lineages. The results extend those obtained by T. Huillet and the author in [Stoch. Models 27, No. 3, 521–554 (2011; Zbl 1367.92074)].

MSC:

92D25	Population dynamics (general)
92D15	Problems related to evolution
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60F17	Functional limit theorems; invariance principles

Keywords:

ancestral process; Cannings model; coalescent; compound Poisson model; conditional branching process model; Dirichlet model; exchangeability; neutrality; simultaneous multiple collisions; weak convergence; Wright-Fisher model

Citations:

Zbl 1367.92074