PHILADELPHIA -- A new mathematical model developed by researchers at the University of Pennsylvania has offered even more evidence of the correctness of evolutionary theory.

Herbert Wilf, Penn’s Thomas A. Scott Emeritus Professor of Mathematics, and Warren Ewens, emeritus professor of biology, say their model directly challenges the long-standing contention among some doubters that evolution couldn't have happened because the small changes in species outlined by the theory simply would have taken too much time to be completed.

Their works shows that, under a very reasonable model of mutations and natural selection, the time required to evolve a very complex organism is vastly smaller than might be presumed.  As a result, the idea that evolution would require "too much time" to be true is proved false.

Wilf and Ewens’ model is described in the paper "There's Plenty of Time for Evolution," which will appear in an upcoming issue of Proceedings of the National Academy of Sciences USA.

According to Wilf, the understanding of evolution reached in the paper can best be illustrated by thinking about the two different ways a hacker might try to break into a computer.

Suppose for a moment that a computer's password is 12 letters long. Simple math dictates that because there are 12 characters in the password and 26 letters in the alphabet, there are approximately 10,000,000,000,000,000 (26 to the 12th power) possible iterations of the password.

One way to hack this password would be to guess a random string of 12 letters and keep doing so until the right combination was found. That process, however, would take an extremely long time.

A better strategy, Wilf said, would be to use a "spy."  After each guess, the spy could tell the hacker which, if any, of the 12 letters were correct. If, for instance, the spy told the hacker that two of the 12 letters were correct, it would leave only 10 letters to be discovered. Extrapolate that spying-and-guessing process over the entire hack attempt, and it's clear that the amount of time required would be greatly reduced.

"When you have this spy inside, it means that each letter is essentially operating independently in the [password] you're trying to guess," Wilf said. "Instead of trying to worry about the whole word, you just have to worry about each letter individually. When you get it right, it stays there; it doesn't change."

But what does hacking have to do with the evolution of species?

Simple, Wilf said. In the case of evolution, the hacker is evolution itself. The password is the string of codons that describes, for example, a butterfly. And the spy is natural selection.

"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," he said.

"It will not be discarded as future mutations take place because the intermediate creatures are seeing very well, and they will live and reproduce. 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.

“In the paper, these ideas are precisely quantified, according to this model, and the extent of the speedup is found.  It is enormous, and shows that there is indeed plenty of time for evolution."