polygenic adaptation

Hayward LK & Sella G 2019 Polygenic adaptation after a sudden change in environment. bioRχiv 792952.
doi:10.1101/792952

  • hard sweeps were rare, at least over the past ~500,000 years of human evolution (13, 14)
  • for many traits, estimates of the heritability contributed by chromosomes are approximately proportional to their length (17), suggesting that the contributing variants are numerous and roughly uniformly distributed across the genome
  • recent studies pooled signatures of frequency changes over the hundreds to thousands of alleles that were found to be associated with an increase (or decrease) in a given trait
  • quantitative traits are unlikely to be subject to long-term continuous change in one direction
  • they are often subject to long-term stabilizing selection (3), with intermittent shifts of the optimum in different directions
  • the second scenario therefore assumes that a sudden change in the environment induces an instantaneous shift in the optimum of a trait under stabilizing selection
  • with GWASs now enabling us, at least in principle, to learn about the genetic basis of the phenotypic response, we would like to understand the allelic dynamics that underlie it
  • we follow previous work in considering the phenotypic and allelic responses of highly polygenic traits after a sudden change in optimal phenotype
  • we do so in finite populations and employ a combination of analytic and simulation approaches to characterize how the responses varies across a broad range of evolutionary parameters
  • we assume a Gaussian (absolute) fitness function:
  • W(z) = exp(− z2/2VS) ... (2)
  • [absolute?]
  • parents are randomly chosen to reproduce with probabilities proportional to their fitness
  • i.e., Wright-Fisher sampling with fertility selection
  • [fertility?]
  • √(2NU)≫1
  • U = Lu≫1
  • the mutational target size, L, would have to exceed ~5 Mb
  • se = a2/VS≪1
  • we assume that a substantial proportion of mutations are not effectively neutral
  • quantitative genetic variance is not predominantly neutral
  • δ2 = VS/2N
  • √VA≫δ
  • Λ > δ
  • Λ < √VS
  • a≪√VS
  • sd = 2Λ⋅a/VS≪1
  • the closest previous work assumed an infinite population size (36, 37, 40, 43)
  • relaxing this assumption leads to entirely different behavior
  • variation in allele frequencies due to genetic drift, which is absent in infinite populations, critically affects the allelic response to selection
  • an allele’s contribution to phenotypic change is proportional to its contribution to phenotypic variance before the shift
  • alleles with moderate and large effect sizes make the greatest per site contributions to phenotypic change
  • alleles with moderate effect sizes experience the greatest frequency changes
  • the transient contributions of large effect alleles are supplanted by contributions of fixed moderate, and to a lesser extent, small effect alleles
  • this process takes on the order of 4Ne generations, after which the steady state architecture of genetic variation around the new optimum is restored
  • our finding that large effect alleles almost never sweep to fixation appears at odds with the results of previous studies of similar models
  • these discrepancies are largely explained by earlier papers considering settings that violate our assumptions, notably about evolutionary parameter ranges
  • some studies assume that large effect alleles segregate at high frequencies before the shift in optimum (e.g., (65)), which is presumably uncommon in natural populations and in any case, violates our assumption that the trait is at steady state before the shift
  • Thornton (38) observes sweeps in cases in which the trait is not highly polygenic (violating our assumption that √(2NU)≫1)
  • Chevin and Hospital (66) observe sweeps in cases in which a single newly arising mutation of large effect contributes substantially to genetic variance, which violates our assumptions that genetic variation is highly polygenic and is not predominantly effectively neutral
  • quantitative genetic variation is not predominantly neutral
  • Stetter et al. (39) considered a huge shift in the optimal trait value (e.g., of ~90 phenotypic standard deviations), resulting in a massive drop in fitness (violating our assumption that Λ < √VS)
  • little is known about the magnitude of shifts in optimal trait values over the time scales of large effect, beneficial fixations
  • the response to such larger shifts is not covered by our analysis and clearly warrants further study
  • pleiotropy is therefore likely to affect which alleles contribute to phenotypic change at the different phases of polygenic adaptation
  • after a shift in the optimal trait value, the number of fixations of alleles whose effects are aligned to the shift are nearly equal to the number of alleles that are opposed (Fig. 6)
  • the alleles that fix are a largely random draw from the vastly greater number of alleles that affect the trait
  • in this plausible scenario, it becomes meaningless to say that any given fixation was adaptive, and arguably uninteresting to focus on the particular subset of alleles that happened to reach fixation
  • identifying the traits that experienced adaptive changes promises to provide important insights