×

The general coalescent with asynchronous mergers of ancestral lines. (English) Zbl 0962.92026

Summary: Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral process. We describe a class of asymptotic structures for the ancestral process via a convergence criterion. One of the basic conditions of the criterion prevents simultaneous mergers of ancestral lines. Another key condition implies that the marginal distribution of the family size is attracted by an infinitely divisible distribution. If the latter is normal the coalescent allows only for pairwise mergers (Kingman’s coalescent). Otherwise multiple mergers happen with positive probability.

MSC:

92D15 Problems related to evolution
60E07 Infinitely divisible distributions; stable distributions
60F05 Central limit and other weak theorems
PDFBibTeX XMLCite
Full Text: DOI