There’s plenty of time for evolution
Herbert S. Wilfa,1 and Warren J. Ewensb
Author Affiliations
Edited by Richard V. Kadison, University of Pennsylvania, Philadelphia, PA, and approved November 2, 2010 (received for review October 7, 2010)
Abstract
Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about K log L, rather than KL, where L is the length of the genomic “word,” and K is the number of possible “letters” that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there.
mutations natural selection geometric distribution
Footnotes
1To whom correspondence should be addressed. E-mail: wilf@math.upenn.edu.
Author contributions: H.S.W. and W.J.E. designed research; H.S.W. and W.J.E. performed research; and H.S.W. and W.J.E. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
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