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Zbl 1064.92034
Möhle, M.
The coalescent in population models with time-inhomogeneous environment. (English)
[J] Stochastic Processes Appl. 97, No. 2, 199-227 (2002). ISSN 0304-4149

Summary: The coalescent theory, well developed for the class of exchangeable population models with time-homogeneous reproduction law, is extended to a class of population models with time-inhomogeneous environment, where the population size is allowed to vary deterministically with time and where the distribution of the family sizes is allowed to change from generation to generation. A new class of time-inhomogeneous coalescent limit processes with simultaneous multiple mergers arises. Its distribution can be characterized in terms of product integrals.

MSC 2000:: *92D15 Problems related to evolution
60J70 Appl. of diffusion theory
60F17 Functional limit theorems

Keywords: ancestors; coalescent; diffusion approximation; population genetics; product integral; Stirling numbers

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