A Compact Result for the Time-Dependent Probability of Fixation at a Neutral Locus

D. Waxman

Journal of Theoretical Biology: 274: 131–135 (2011)

Faculty of Science and Engineering
University of Brighton
Brighton BN2 4GJ
United Kingdom

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_e) 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.