A compact result for the time-dependent probability of fixation at a neutral locus

D. Waxman (1)

1 Faculty of Science and Engineering

A result is derived, in the form of a sum, for the time-dependent probability of fixation of an unlinked neutral locus. The result captures many of the key features of the probability of fixation in a highly compact form. For 'small' times (t≲4N) a single term of the sum accurately determines the time-dependent probability of fixation. This is in contrast to the well-known result of Kimura, which requires the contribution of many terms in a different sum, for 'small' times. Going beyond small times, an approximation is derived for the time-dependent probability of fixation which applies for all times when the initial relative allele frequency is small.

Mots clés: Gene fixation; Random genetic drift; Diffusion approximation; Neutral theory; Wright-Fisher model

Domaines: Sciences du Vivant [q-bio]

D. Waxman. A compact result for the time-dependent probability of fixation at a neutral locus. Journal of Theoretical Biology, 2011, 274 (1), pp.131. ⟨10.1016/j.jtbi.2011.01.019⟩. ⟨hal-00671833⟩