A compact result for the time-dependent probability of fixation at a neutral locus.
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.
Faculty of Science and Engineering, Cockroft Building, University of Brighton, Brighton BN2 4GJ, UK. dwaxman.biology@gmail.com
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D005787:Gene Frequency / Q000235:genetics; D056426:Genetic Loci / Q000235:genetics*; D011336:Probability; D013997:Time Factors