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J Theor Biol. 2011 Apr 7;274(1):131-5. doi: 10.1016/j.jtbi.2011.01.019. Epub 2011 Jan 20.

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

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Faculty of Science and Engineering, Cockroft Building, University of Brighton, Brighton BN2 4GJ, UK.


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.

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