functional epistasis - senecio7の日記

Hansen TF 2013 Why epistasis is important for selection and adaptation. Evolution, in press.
doi:10.1111/evo.12214

the wide-spread misconception that it has no permanent effects on selection dynamics has restricted the search for influence to nonselective mechanisms

the importance of epistasis is mediated through changes of the additive variance (and of higher moments, which we will not consider here)

by definition selection on additive-by-additive genetic deviations cannot alter allele frequencies
the interaction terms are defined to be independent of allelic effects (i.e., orthogonal)
any phenotypic effect of allele-frequency change is by definition a part of the additive variance
the only thing that can change is the frequencies of co-occurrence of alleles, that is the linkage disequilibrium
selection on epistatic deviations thus only has the effect of increasing the frequency of co-occurrence of beneficial allele combinations above the frequency changes due to average effects of the alleles in isolation
because linkage disequilibrium is continuously broken down by recombination this change is "transitory"

their conceptualization of epistasis as independent variance components precluded them from asking how functional gene interactions may influence these changes
the missing distinction between functional and statistical epistasis invited an overgeneralization of the results
the results derived for the statistical epistatic variance components were implicitly assumed to be results about epistasis in general (as in Hill et al. 2008)

the claims by Crow (2008, 2010) that this result implies we can ignore the effects of epistasis on the selection response are only correct in a highly restricted sense, and totally misleading as general statements about evolutionary dynamics over many generations

the reason why this happened was because the orthogonality of the genetic variance components was implicitly thought to imply that they were also biologically noninteracting
the explicit theoretical results showing that epistatic variance did not have permanent effects on the selection response were therefore thought to exclude any effect of epistasis in selection dynamics
this largely implicit chain of faulty reasoning was facilitated by the missing distinction between functional and statistical epistasis
it was only toward the end of the century that quantitative geneticists started to consider the effects of (functional) epistasis on the additive variance

Hill et al. (2008) recently argued against the relevance of epistasis based on theoretical and empirical arguments that most variance should be additive
this reasoning fails to distinguish statistical and functional epistasis
even if they were right that epistatic variance components are often small, this does not rule out the possibility of strong functional epistasis in the genotype–phenotype map

the classical quantitative genetics model resembles a Taylor approximation of the genotype–phenotype map
when there is little variation, the linear (additive) part fits well and explains most of the variance
as the level of variation increases, the nonlinear (dominance and epistatic) parts become relatively more and more important and will explain larger and larger fractions of the variance

both theoretical and empirical work on epistasis should shift focus from the largely irrelevant and hard to estimate epistatic variance components of classical quantitative genetics and toward the study of systematic patterns of functional epistasis in the genotype–phenotype map

Malthusian fitnesses are naturally additive
epistasis is hence properly measured as deviation from additivity on the arithmetric scale
for Wrightian fitness on a discrete generation-to-generation time scale epistasis is more correctly measured as deviation from multiplicative interactions