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Creationists have reason to doubt the classical theory of evolution

January 12, 2008 by kjellstrom

Creationists have reason to doubt the theory based on Fisher’s fundamental theorem of natural selection published in 1930. It relies on the assumption that a gene (allele) may have a fitness of its own being a unit of selection. Historically this way of thinking has also influenced our view of egoism as the most important force in evolution. On the other hand, if the selection of individuals rules the enrichment of genes, then Gaussian adaptation will perhaps give a more reliable view of evolution. Creationists have reason to doubt the theory based on Fisher’s fundamental theorem of natural selection published in 1930. It relies on the assumption that a gene (allele) may have a fitness of its own being a unit of selection. Historically this way of thinking has also influenced our view of egoism as the most important force in evolution; see for instance Hamilton about kin selection, 1963, or Dawkins about the selfish gene, 1976 in

http://en.wikipedia.org/wiki/Gaussian_adaptation#References

On the other hand, if the selection of individuals rules the enrichment of genes, then
Gaussian adaptation will perhaps give a more reliable view of evolution (see the blog “Gaussian adaptation as a model of evolution”).

In modern terminology (see Wikipedia) Fisher’s theorem has been stated as:
“The rate of increase in the mean fitness of any organism at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genic variance in fitness at that time”. (A.W.F. Edwards, 1994).

A proof as given by Maynard Smith, 1998, shows the theorem to be formally correct. Its formal validity may even be extended to the mean fitness and variance of individual fitness or the fitness of digits in real numbers representing the quantitative traits.

But, if the selection of individuals rules the enrichment of genes, I am afraid there might be a risk that the theory becomes nonsense, and that this is not very well known among biologists.

A drawback is that it does not tell us the increase in mean fitness (see my blog “The definition of fitness of a DNA- or signal message”) from the offspring in one generation to the offspring in the next (which would be expected), but only from offspring to parents in the same generation. Another drawback is that the variance is a genic variance in fitness and not a variance in phenotypes. Therefore, the structure of a phenotypic landscape – which is of considerable importance to a possible increase in mean fitness - can’t be considered. So, it can’t tell us anything about what happens in phenotypic space.

The image shows two different cases (upper and lower) of individual selection, where the green points with fitness = 1 - between the two lines - will be selected, while the red points outside with fitness = 0 will not. The centre of gravity, m, of the offspring is heavy black and ditto of the parents and offspring in the new generation, m* (according to the Hardy-Weinberg law), is heavy red.
http://picasaweb.google.com/gregor744/GA_figures02?authkey=Gv1sRgCNLYgpO...
Because the fraction of green feasible points is the same in both cases, Fisher’s theorem states that the increase in mean fitness is equal in both upper and lower case. But the phenotypic variance (not considered by Fisher) in the horizontal direction is larger in the lower case, causing m* to considerably move away from the point of intersection of the lines. Thus, if the lines are pushed towards each other (due to arms races between different species), the risk of getting stuck decreases. This represents a considerable increase in mean fitness (assuming phenotypic variances almost constant). Because this gives room for more phenotypic disorder/entropy/diversity, we may expect diversity to increase according to the entropy law, provided that the mutation is sufficiently high.

So, Fisher’s theorem, the Hardy-Weinberg law or the entropy law does not prove that evolution maximizes mean fitness. On the other hand, Gaussian adaptation obeying the Hardy-Weinberg and entropy laws may perhaps serve as a complement to the classical theory, because it states that evolution may maximize two important collective parameters, namely mean fitness and diversity in parallel (at least with respect to all Gaussian distributed quantitative traits). This may hopefully show that egoism is not the only important force driving evolution, because any trait beneficial to the collective may evolve by natural selection of individuals.

Gkm