compensatory evolution

Hastings A 1987 Substitution under stabilizing selection. Genetics 116:479-486.

  • one of the most interesting and important questions facing population genetics today is the relationship between selection at the level of the organism and selection at the level of the locus
  • is evolution at loci determining quantitative traits different from evolution at neutral loci?
  • can these differences be studied at the level of the single locus or are multilocus models needed?
  • as Kimura notes, the analysis above depend on the assumption that m (the deviation of the mean of the character from its optimum) is unchanged
  • this means that m, as determined by all the loci (including the one currently being examined) that contribute to the character, does not depend on the allele frequency at the single locus currently examined
  • if the mean changes as the allele frequencies change at a single locus, the fitnesses at single loci may not appear underdominant
  • Kimura then goes further by taking m to be 0
  • extensive substitutions are still possible under stabilizing selection even when S = 4Nes is as large as 8, where the rate of substitution is still 23% of the neutral rate
  • as the allele frequencies change at some given locus, the allele frequencies change at all the other loci in such a way that the overall mean phenotype remains constant
  • this is the reason that selection at each locus appears underdominant
  • another approach to studying substitution under stabilizing selection was also introduced by Kimura (1985)
  • a model with two loci A and B is studied
  • in the neutral case and for sufficiently weak selection, substitution is a single locus phenomenon
  • I mean that substitution times at a particular locus are independent of substitution times at other loci
  • for stronger selection, substitution is a two locus phenomenon
  • there is a large correlation between substitution times at different loci
  • this is because the mean of quantitative trait always remains close to the optimum with strong selection
  • the only way a substitution can occur is for two loci to substitute at nearly the same time
  • for strong selection, the time to substitute a pair of loci might be relevant for determining single locus substitution rates
  • the parameter value S = 0.4096 is one where the 2-locus model in fact says that the time until fixation of both mutants would be less than that for the neutral case, in contrast to the simulations
  • S = 4.096
  • the substitutions basically occur in pairs, even when there are 16 loci
  • with strong selection, the population mean must always lie close to the optimum
  • the mean times between substitutions differ significantly from a Poisson distribution
  • the distribution of times for substitutions which bring the population from a "0" state to a "1" state are significantly larger than the times for substitutions which bring the population from a "1 state to a "0" state
  • for strong stabilizing selection, substitution is essentially a 2-locus process
  • this is one of the first examples of the (nonlinear) dependence on the number of loci of an evolutionarily important property in models of stabilizing selection
  • analyses of the models of quantitative genetics may have to take into account the number of loci
  • differences in substitution rates of the order of magnitude observed here, or even larger, even though caused by stabilizing selection, could not be detected by observations of substitutions at a single locus
  • one cautionary note is that the results reported here are for identical diallelic loci