markovian
Crow JF 1987 Twenty-five years ago in Genetics: Motoo Kimura and molecular evolution. Genetics 116:183-184.
- Fisher (1930) had called attention to the considerable chance of stochastic loss of an new mutant
- even a favorable one
- yet, in any large population, mutations at the same locus occur repeatedly
- the chances of fixation of one or another of them is near certainty
- Wright (1931, 1942, 1945) was mainly interested in the steady-state distribution of allele frequencies
- these being relevant to his shifting-balance theory
- the only serious use for the fixation probability was in animal breeding theory
- Kimura's work turned out to be pre-adapted for the later study of molecular evolution
- Kimura had the happy insight that the average rate of nucleotide substitutions in a long evolutionary period does not depend on the time required for an individual mutation to be fixed
- rather it depends on the frequency of occurrence of ultimately fixed mutations
- this requires that the mutation rate be small
- the simplest and oldest hypothesis for molecular evolution is that it is a succession of substitutions of selectively favored mutations
- that the rate should be proportional to μ and s is reasonable
- the proportionality to N is dubious
- it is contrary to fact
- carnivores with small populations evolve molecularly just as rapidly as do herbivores with large ones
- those invertebrates with enormous population numbers change no more rapidly than do mammals
- this argue strongly against the result of successive incorporation of favorable mutations
- Kimura's well known alternative is that molecular substitutions are mainly neutral
- the process becomes mutation-driven rather than selection-driven
- I first heard of Kimura's mathematical work in the early 1950s through a student, Newton Morton, who was temporarily working in Hiroshima
