epistasis

Crow JF 2010 On epistasis: why it is unimportant in polygenic directional selection. Phil Trans R Soc Lond B 365:1241-1244.

  • epistatic variance has minimum effect, since the selected population soon arrives at a state in which the rate of change is given by the additive variance or covariance
  • in its original introduction by Bateson, the word epistasis was defined as the masking of the effect of an allele by another at a different locus
  • Fisher further extended the usage to a second definition
  • he coined the word epistacy to mean any departure from additivity—or on a different scale, multiplicativity—of allelic effects
  • Fisher's word did not catch on—users preferred epistasis—but the concept did
  • retaining Fisher's word might have averted some confusion
  • three genome-wide association tests have documented the large number of loci involved
  • the three studies identified a total of 54 loci (Visscher 2008)
  • these 54 loci accounted for about 9 per cent of the genetic variance
  • hence the total number of loci must be roughly 54 × (100 / 9) = 600
  • this is a minimum estimate
  • only those loci contributing at least 0.3 per cent of the variance would have been detected
  • human height fits the picture of a trait determined by a large number of genes, each with a very small effect
  • Nagylaki (1993) was able to develop the theory under very general conditions
  • the number of loci, linkage map, dominance and epistasis are arbitrary
  • no one had previously treated such a realistic model
  • the important results hold under weak selection, where the selection coefficient, s (defined as the relative selective difference between the most and least fit genotype) is small relative to the smallest two-locus recombination frequency, c
  • after a short time period, approximately (ln s) / ln(1 − c), the population evolves approximately as if in linkage equilibrium
  • after twice this time interval, the linkage disequilibria are nearly constant
  • then Fisher's Fundamental Theorem holds to order s2
  • for a quantitative character correlated with fitness, the variance is replaced by the covariance of the character and fitness
  • the accuracy is of order s
  • the covariance is between the effect on the character and the excess of fitness, to use Fisher's terms (1930, p. 30; 1941)
  • this result was foreshadowed in a more restricted study by Kimura (1965), one effect of which was to stimulate Nagylaki to address the problem
  • what this means is that the change of fitness or of a character correlated with fitness is, after a short time and through most of the period of gene frequency change, given by the additive genetic variance or covariance
  • for a two-locus numerical example, see Crow & Kimura (2009, p. 222)
  • quantitative genetics has a contrasting view
  • any attempt to include epistatic terms in prediction formulae is likely to do more harm than good