epistasis

Barton N 2017 How does epistasis influence the response to selection? Heredity 118:96–109.

• stabilising selection can maintain many traits close to their optima, even when the underlying alleles are weakly selected
• the number of traits that can be optimised is apparently limited to ~4N_e by the 'drift load'
• this is hard to reconcile with the apparent complexity of many organisms
• most variance in fitness may be because of alleles with large N_es
• substantial amounts of adaptation may be because of alleles in the infinitesimal regime, in which epistasis has modest effects

• epistasis has surprisingly little effect on the response to either directional or stabilising selection, even when substantial fractions of the genetic variance are because of gene interactions, and the underlying fitness landscape is rugged

• assume that fitness falls away from the optimum as a Gaussian function, exp (−(z − z_opt)² / (2V_s)), of the individual trait value
• the mean moves towards the optimum at a rate ∂_tz = −(z − z_opt) V_A / V_s, and fluctuates because of random sampling, with variance E[δz²] = V_A / N_e
• very many loci affect the trait
• the genetic variance evolves slowly
• V_A can be taken as constant
• the variance of the mean around the optimum is var(z) = E[δz²] / (2V_A / V_s) = V_s / (2N_e)
• the loss of fitness due to this variation is 1 / (4N_e) (Lande, 1976)

• epistasis in the infinitesimal limit
• strong interactions among loci may have little effect in aggregate
• this point is illustrated by the contrasting analyses of Weber et al. (1999) of the same cross between populations of Drosophila selected for different wing shape
• a model of 11 interacting loci with strong interactions fit best
• yet because these interactions varied in sign, the overall data fit closely to an additive infinitesimal model
• a large meta-analysis of twin studies in humans found 69% of cases to be consistent with additivity (Polderman et al., 2015)
• even when the underlying genes interact strongly, most variance is additive (Hill et al., 2008)
• in particular, deleterious mutations are rare, and rare alleles necessarily contribute mostly additive variance
• Huang et al. (2012) argue that there is widespread epistasis for behavioural traits in Drosophila
• their estimates are for variance among inbred lines, rather than an outcrossed population, which amplifies nonadditive variance
• variation in estimated allelic effects across backgrounds may also be because of statistical error rather than epistasis (Maki-Tanila and Hill, 2014, pp 363–364)

• the strength of selection relative to drift
• the survey of Kingsolver and Diamond (2011) of 143 studies found an average directional selection gradient of 0.08 on survival, 0.19 on fecundity and 0.17 on mating success, standardised relative to phenotypic s.d.
• stabilising selection is also typically strong but, surprisingly, is as often negative (that is, disruptive) as positive
• larger studies gave systematically smaller estimates
• publication bias may inflate estimate
• long-term studies find that trait means often remain constant, despite high heritability and strong directional selection
• despite these difficulties, traits do typically seem to be associated with strong fitness differences
• possibly, measured traits are correlated with a small number of strongly selected traits, such as body size (Barton, 1990)

• the strength of selection against deleterious mutations can be estimated from the ratio between the rate of increase of additive variance due to mutation and the standing genetic variance, V^A_m / V_g
• this suggests selection coefficients of s ~ 10⁻³ or more, estimates being remarkably consistent across diverse traits and species
• Charlesworth (2014) [2015] ... concludes that the selection on the mutations that sustain fitness variance is relatively strong, averaging a few percent
• Charlesworth (2014) [2015] also concludes that genomic mutation rates are not high enough to explain observed levels of fitness variance, suggesting a substantial component contributed by balancing selection

• how many degrees of freedom can be maintained despite random drift?
• the success of domestication shows that populations of just a few hundred can adapt well to radically new conditions
• over longer timescales, it would seem that a substantial and possibly catastrophic fitness decline must ensue, as random drift fixes slightly deleterious mutations
• Charlesworth (2013a) has criticised such arguments on the grounds that compensatory mutations prevent decline
• stabilising selection can be effective even when individual alleles are dominated by drift
• small populations should ultimately be unable to maintain more than ~4N_e traits close to their optima
• genetic variation will decrease, but even in the most extreme case, will fix a genotype that is ~√V_a s.d. from the optimum
• not far outside the initial range of phenotypic variation
• a new equilibrium is reached when the marginal selection becomes strong enough to make fixation of deleterious mutations unlikely
• functional complexity will only be lost over the timescale of molecular evolution

• it is argued that epistasis makes the marginal effects of alleles unpredictable
• selection becomes ineffective
• if epistasis is strong enough that allelic effects change sign, then populations may be trapped at suboptimal 'adaptive peaks'
• pleiotropic allelic effects, and tradeoffs between different fitness components, prevent response to selection
• from the quantitative genetic viewpoint, these are all arguments that there may be no additive variance for selected traits—and are most obviously countered by the observation that there is almost always ample heritable variance, much of it additive
• many of these arguments are supported by models of a few interacting loci under strong selection that typically do lead to a rugged fitness landscape on which selection is ineffective
• I have argued that if traits depend on very large numbers of loci, so that alleles are influenced by drift as well as selection, then epistasis is no longer a constraint
• traits evolve under the infinitesimal model in which the additive variance is not eroded by selection
• my argument is not that epistasis is irrelevant to evolution
• it does not significantly constrain the way populations respond to selection on complex traits
• populations typically contain abundant additive variance that allows them to follow a moving optimum in a high-dimensional trait space