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The evolution of a population under recombination: how to linearise the dynamics. (English) Zbl 1003.92023
Summary: A system of recursions is derived for the dynamics of an infinitely large population, evolving under a very general process of recombination, whereby an individual can inherit genes from an arbitrary number of parents, sampled independently from the population in the proceeding generation. In general, the number of parents sampled is itself a random variable. A procedure is presented for linearising this system of recursions. This generalises the linearisation procedure introduced by J.H. Bennett [Ann. Human Genetics 18, 311-317 (1954)] for the dynamics of an infinite population where offspring are the product of two parents sampled independently from the population.

MSC:
92D15 Problems related to evolution
60C05 Combinatorial probability
05A18 Partitions of sets
92D10 Genetics and epigenetics
15A99 Basic linear algebra
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