gregor

O. k., in the following I will continue my believing-in-evolution-story.

Our artificial process was climbing an artificial landscape defined by the math-model of the signal processing system. A corresponding phenotypic landscape would be defined by the fitness of the individual, defined by Hartl as the probability s(x) that the individual having the n characteristic parameters xT = (x1, x2, ..., xn) – where xT is the transpose of x - will survive, i. e. become selected as a parent of new individuals in the progeny.
Hartl, D. L. A Primer of Population Genetics. Sinauer, Sunderland, Massachusetts, 1981.

From my point of view it was an issue of interest if the natural evolution was able to make use of the theorem of Gaussian (normal) adaptation for the maximisation of mean fitness. So, I looked in some textbooks of biology and noted that many phenotypes were Gaussian distributed in a large population, or nearly so. There was also a strong indication that the ontogeny was a modified stepwise replay of the phylogeny and the central limit theorem stating that the sum of many steps tends to become Gaussian distributed.

If m is the centre of gravity of the Gaussian and m* is the centre of gravity of phenotypes of survivors, could evolution make the centers of gravity, m and m*, coincide for the maximization of mean fitness?

Yes, if mating is random, then the Hardy Weinberg law seemed to do the job. The law states that If mating takes place at random, then the allele frequencies in the next generation are exactly the same as they were for the parents. Thus we would expect m = m* in every generation. Selection will move m*, but the process will always strive towards a selective equilibrium with m = m*, thus mean fitness will be maximized as far as Gaussian phenotypes are considered.

Thus, Gaussian adaptation seemed to be a fairly good model of evolution.