Title Author Date

Variance and probability in Nilsson and Pelger Wein, Richard Sep 23, 2003

David Berlinski writes: "What is at issue is whether changes in a population from one generation to another arise as the expression of an underlying stochastic process. It is, of course, the only point at issue."

On the contrary, it is not at all the point at issue! Nilsson and Pelger take for granted the fact that such changes can arise. The justification for that assumption is outside the scope of their paper. The issue they address is whether such changes can accumulate to produce an eye, and how long such a process is likely to take.

Berlinski appears to believe that a stochastic process cannot be represented by a deterministic model. If so, he is clearly wrong. Deterministic algorithms are often used to model stochastic processes. Does a casino manager use cards, dice or other randomizers in estimating his future takings? I doubt it. Due to the large number of random events, he makes the approximating assumption that his takings will be in accordance with the statistical expectation, which he calculates by means of a purely deterministic algorithm. Similarly, Nilsson and Pelger make the approximating assumption that the quantitative change in each generation will be the statistically expectated value estimated by Falconer's formula.

Berlinski is too concerned with whether Nilsson and Pelger's model can be labelled "Darwinian". I'm not even sure what he means by this. If he means that their algorithm is not Darwinian, then I agree. But just as one can use a non-stochastic algorithm to model a stochastic process, one can use a non-Darwinian algorithm to model a Darwinian process. Berlinski is chasing a red herring. The real issue is not how we label the model, but whether the assumptions and approximations it makes are justifiable.

His failure to appreciate that a model is an abstraction leads Berlinski into further blunders: "...there is absolutely no reason to suppose that the MV will rise monotonically throughout the course of 330,000 generations." Indeed, but the model does not require that it do so. It merely assumes that it will do so for the purposes of approximation. All the model reqires is that the mean value rises on average by roughly the calculated amount. Sometimes it may fall, other times it may rise faster and catch up.

[Regarding my allegation of argument by innuendo, I will respond to Berlinski in the column where I originally made that allegation (titled "James Downard").]

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