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Selection models

``Selection" is the differential survival and reproduction (aka ``fitness") of individuals. From an evolutionary perspective, we are most often interested in the fitness associated with particular genotypes, and a simple parametrization of single-locus genotypic fitnesses might be:

Different values of s (usually called the selection coefficient) and h (the dominance coefficient) produce the familiar dominance, recessive, additive, overdominant, and underdominant relationships. Kimura[8] used the following parametrization (equivalent to the additive case above)

and showed that the probability of fixation of an allele under this type of genic selection is approximately

in an otherwise ideal population. As this probability approaches , as expected from our discrete-process analysis. For small (positive) s and large N, we can approximate . There are a few interesting consequences of this result. The first is that even an advantageous mutation is not guaranteed to increase in frequency, and in fact, the probability that it does may be quite small. Notice also that now, the rate of substitution of advantageous alleles is . Many people who are willing to assume a constant mutation rate in order to be able to construct a phylogenetic tree balk (with good reason) at the prospect of the number of simultaneous, delicately balanced, suppositions that would have to be made to construct a tree of selected substitutions along the same lines. On the other hand, it has become increasingly clear that the statement that most evolution at the molecular level is neutral is, at best, an oversimplification.



Simon Cawley
Tue May 12 11:50:21 PDT 1998