Math Model Diminishes Time for Evolution

December 21, 2010

By demonstrating that much less time is needed for complex organisms to evolve, a new mathematical model offers more evidence of the rightness of evolutionary theory.

Mathematician Herbert Wilf (University of Pennsylvania) and biologist Warren Ewens have put forth a model that apparently shows that large estimates of time have overlooked the so-called spying effects of natural selection. More importantly, the numbers of mutations, according to their model, are reduced significantly: from KL to about K log L, where L represents the length of a genomic “word” and K is the number of possible “letters” that can occupy any position in the word.

"If, when we guess the full string of letters [for a new species], one of the letters is correct—for instance, one that describes correctly the eyes of a butterfly—then that letter has survival value," Wilf indicated. “So although it seems at first glance that the process of random mutations will take a very long time to produce a higher organism, thanks to the spying of natural selection, the process can go very rapidly."

The theory "makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there," Wilf noted. Its ideas, described in "There's Plenty of Time for Evolution" (Proceedings of the National Academy of Sciences, December 17, 2010), are "precisely quantified, and the extent of the speedup is found. It is enormous, and shows that there is indeed plenty of time for evolution."

In 1987-1991, Herbert Wilf served as editor of the MAA's American Mathematical Monthly.

Source: PhysOrg (December 14, 2010)