Há tempo suficiente para a evolução

terça-feira, dezembro 14, 2010

There’s plenty of time for evolution 

Herbert S. Wilf a,1 and Warren J. Ewens b 

- Author Affiliations 

aDepartment of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395; and 
bDepartment of Biology, University of Pennsylvania, Philadelphia, PA 19104-6018 

Edited by Richard V. Kadison, University of Pennsylvania, Philadelphia, PA, and approved November 2, 2010 (received for review October 7, 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 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 


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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