ID critics often complain that ID advocates go ON AND ON (and ON) worrying about Weasel-type models of evolution, as illustrations of how undirected variation and selection can rapidly converge to apparently designed outcomes. No one takes such models seriously as biology, the critics say. Weasels are toys with a strictly limited teaching purpose.
Over to the latest issue of the Proceedings of the National Academy of Sciences (PNAS). Looks like a weasel in the tall grass:
Suppose that we are trying to find a specific unknown word of L letters, each of the letters having been chosen from an alphabet of K letters. We want to find the word by means of a sequence of rounds of guessing letters. A single round consists in guessing all of the letters of the word by choosing, for each letter, a randomly chosen letter from the alphabet. If the correct word is not found, a new sequence is guessed, and the procedure is continued until the correct sequence is found. Under this paradigm the mean number of rounds of guessing until the correct sequence is found is indeed K^L.
But a more appropriate model is the following: After guessing each of the letters, we are told which (if any) of the guessed letters are correct, and then those letters are retained. The second round of guessing is applied only for the incorrect letters that remain after this first round, and so forth. This procedure mimics the “in parallel” evolutionary process.
See Herbert S. Wilf and Warren J. Ewens, “There’s plenty of time for evolution,” PNAS Early Edition. For those who cannot access PNAS behind its paywall, an earlier version of the same paper is available here.