polygenic adaptation - senecio7の日記

John S & Stephan W 2020 Important role of genetic drift in rapid polygenic adaptation. Ecol Evol 10:1278-1287.

it is not clear if adaptation can occur rapidly via such subtle changes in the allele frequencies

we follow this direction here to understand the evolutionary dynamics of quantitative traits from the standpoint of population genetics

we have found two distinctly different modes of rapid adaptation:
(a) through strong directional selection at a few loci when the effect sizes of the alleles at these loci are large relative to a scaled mutation rate
(b) through weak selection at many individual loci (with small effect sizes) leading to subtle allele frequency shifts in the case of polygenic adaptation
we examine to what extent these deterministic results may be generalized to populations of finite size

dp_i / dt = − sγ_ip_iq_iΔc₁ − (sγ_i² / 2) p_iq_i (q_i − p_i) − μp_i + νq_i, i = 1, ..., l ... (5)
we calculate the allele frequency changes in each locus independently based on the effect size and the allele frequency of that locus
we do binomial sampling with mutation based on allele frequency p_i(t)
we apply selection by drawing a random number from a binomial distribution whose mean is the modulus of the sum of the two selection terms in Equation (5)
this random number is added to or subtracted from the + allele frequency obtained by stochastic sampling (dependent on the sign of the sum of the selection and mutation terms in Equation (5)) to obtain the + allele frequency at locus i in the next generation

in the deterministic system (polygenic case) the trait mean may change much faster after a perturbation than the allele frequencies
after the system is pushed away from the stationary state the trait mean may quickly respond, while the allele frequencies reach the stationary state only very slowly

Δc₁ is a fast variable on the time scale of the allele frequencies p_i
Δc₁ approaches its equilibrium value [...] quickly
the allele frequencies need much longer to reach equilibrium
we obtain [the equilibrium value of Δc₁] by putting the left‐hand side of Equation (6) to zero
we may neglect the skewness term as we focus on loci with small effect sizes γ_i and c₃ is proportional to γ_i³

for large mutation rates, the stationary variance converges to lγ²
this result was also obtained for the deterministic model, for which the equilibrium allele frequencies are 0.5
for small mutation rates, such that 4β≪1, the stationary genetic variance approaches 4βlγ², a value that is much smaller than lγ²
this has important consequences for the speed of polygenic adaptation

theories with very different assumptions about mutation ([...]), all predict that the stationary distribution of the mean deviation from the optimum should have variance 1/(2Ns)
this is a quite generic property of stochastic processes best known for the Ornstein–Uhlenbeck process

the allele frequency shift at a locus depends strongly on the compound parameter γ_ip_i(0)q_i(0)
it increases with the effect size and is greatest for initial frequencies around 0.5
after an environmental change the allele frequencies are expected to shift coherently into the same direction
this appears to be an important property of polygenic selection because it may help detecting this type of selection