There's plenty of time for evolution
Herbert S. Wilf, Warren J. Ewens
(Submitted on 25 Oct 2010)
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 $K^L$, 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.
Subjects: Populations and Evolution (q-bio.PE); Probability (math.PR); Other Quantitative Biology (q-bio.OT)
MSC classes: 60C05
Cite as: arXiv:1010.5178v1 [q-bio.PE]
Submission historyFrom: Herbert S. Wilf [view email]
[v1] Mon, 25 Oct 2010 16:17:27 GMT (5kb)
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