The evolution of a population under recombination: how to linearise the dynamics

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 Bennett, for the dynamics of an infinite population where offspring are the product of two parents sampled independently from the population.