polygenic adaptation - senecio7の日記

Thornton KR 2019 Polygenic adaptation to an environmental shift: temporal dynamics of variation under Gaussian stabilizing selection and additive effects on a single trait. Genetics 213:1513-1530.

detectable "hitchhiking" patterns are only apparent if
(i) the optimum shifts are large with respect to equilibrium variation for the trait
(ii) mutation rates to large-effect mutations are low
(iii) large-effect mutations rapidly increase in frequency and eventually reach fixation, which typically occurs after the population reaches the new optimum
partial sweeps do not appreciably affect patterns of linked variation, even when the mutations are strongly selected
populations reach the new optimum prior to the completion of any sweeps
the times to fixation are longer for this model than for standard models of directional selection

the model of Gaussian stabilizing selection around an optimal trait value differs from the standard model in that mutations affect fitness indirectly via their effects on trait values
for the additive model of gene action considered here, and considering a single segregating mutation affecting the trait, the mode of selection is under- or overdominant in a frequency-dependent manner (Robertson 1956; Kimura 1981)
this model has been extended to multiple mutations in linkage equilibrium by several authors (Barton 1986; de Vladar and Barton 2014; Jain and Stephan 2015, 2017b)
the equilibrium conditions of models of Gaussian stabilizing selection on traits have been studied extensively
the dynamics are quite complicated, with many possible equilibria existing for the case of no linkage disequilibrium

recent theoretical work has attempted to clarify when sweeps should happen and when adaptation should proceed primarily via subtle allele frequency shifts

after the directional phase, selection becomes disruptive, and mutations affecting fitness are fixed or lost to reduce the genetic load of the population

the work described above identifies the conditions where sweeps are expected
we do not have a picture of the dynamics of linked selection during adaptation to an optimum shift
the difficulty of analyzing models of continuous phenotypes with partial linkage among sites has been an impediment to a theoretical description of the process
Höllinger et al. (2019) were able to accommodate partial linkage by simplifying how mutations affect phenotype and focusing on the dynamics up until a particular mean trait value was first reached
in their simplest model, an individual is either mutant or nonmutant
there are only two phenotypes possible

I describe the physical distances over which hitchhiking during polygenic adaptation leaves detectable signatures
the key conceptual difference is that the model of adaptation is changed from constant directional selection to the sudden optimum shift models involving a continuous trait considered in de Vladar and Barton (2014) and Jain and Stephan (2015, 2017b)

I modeled a single trait under real stabilizing selection (Johnson and Barton 2005)
mutations affecting trait values arise at rate μ per haploid genome per generation according to an infinitely many sites scheme (Kimura 1969)
I evolved populations of size N = 5,000 diploids
mutations affecting trait values occur uniformly (at rate μ) in a continuous genomic interval in which recombination breakpoints arise according to a uniform Poisson process with a mean of 0.5 recombination breakpoints per diploid
the mutation rates used were 2.5 × 10⁻⁴, 10⁻³, and 5 × 10⁻³
these mutation rates corresponded to Θ = 4Nμ values of 5, 20, and 100, respectively, meaning sweeps were expected to be high frequency, mixes of partial and complete sweeps, and adaptation primarily by allele frequency changes, respectively, as the population approached the new optimum
at mutation-selection equilibrium, these parameters result in an equilibrium genetic variance given by the "House of Cards" approximation, which is ≈ 4μ for the definition of mutation rate and the V_S used here, and ignoring the contribution of genetic drift
expected genetic variance is therefore small
new mutations are more likely to have large effects relative to standing variation
I simulated all traits with V_S = 1 and did not explicitly model random effects on trait values
the evolutionary dynamics would be unaffected because the contribution of the environmental variance to V_S would be small

these simulations may be viewed as similar to the numerical calculations in de Vladar and Barton (2014) and Jain and Stephan (2017b), but with loose linkage between selected variants
previous studies assumed linkage equilibrium
I allowed for new mutation after the optimum shift
they differ from the approach of Höllinger et al. (2019) in that I simulated continuous traits and did not stop evolution once a specific mean fitness was first reached
z typically reached z_o before the first fixation had occurred
mutations with large effects on trait value fix first, as predicted by Robertson (1956)
fixations of large effect typically have origin times close to zero
large-effect mutations only exist for a relatively brief period of time after the optimum shift, after which most segregating variation reaching appreciable derived allele frequencies are of relatively small effect
for a short time following the optimum shift, several intermediate-frequency mutations with large effects on trait values may be segregating
many of these variants are adaptive (γ > 0) but will only make short-term contributions to adaption prior to their loss
the dynamics of these mutations recapitulate results from de Vladar and Barton (2014)
due to epistatic effects on fitness, some mutations that are initially beneficial later become deleterious and are removed
fixation times are rather long, in the order of N generations even for mutations with large Nγ²
the numbers of sweeps from new mutations and from standing variants are similar
fixation of smaller-effect standing variants are more common in simulations with higher μ
large-effect standing variants that fixed after the optimum shift were rare at the time of the shift
small-effect mutations were also typically rare at mutation-selection balance
fixations from variants that are common at the time of the optimum shift have small effects on trait values
the fixation of such mutations are unlikely to generate the patterns of haplotype diversity associated with "soft sweeps"
such patterns require strong selection on mutations at intermediate frequencies

as the mutation rate increases, the genetic background of these fixing variants becomes more polygenic
the initial rate of frequency change of the fixation lessens because other mutations are involved in the response to the optimum shift, some of which may contribute to adaptation but not fix in the long-term
for all replicates, the fixations are at different loci (separated by ≥ 50 cM) with one exception

the partial sweeps occurring at intermediate mutation rates (middle collumn of Figure 6) are not associated with strong signals of hitchhiking, at least when the sample size is relatively small
the time when a given statistic shows its maximum departure from equilibrium values differs for each statistic
the maximum departure may occur ≈ 100 generations after the time to adaptation
Figure 6 and Figure 7 suggest that patterns of strong hitchhiking are more likely at loci where large-effect mutations fix
such mutations must arise on average before the mean time to adaptation

patterns of variation due to strong sweeps from standing variation overlap considerably with those of older sweeps from new mutations

the conditions for a selective sweep are consistent with predictions made using theoretical results from Jain and Stephan (2017b) and Höllinger et al. (2019)
the simulations presented here are comparable to the "most effects are large" case from Jain and Stephan (2017b)
the trait variance increases during adaptation [also see de Vladar and Barton (2014)] due to large-effect mutations moving from low to intermediate frequency
mutations with large effects on trait values at the time of the optimum shift are most likely to rise in frequency
mutations that eventually fix are not necessarily those with the largest effect size
when several large-effect mutations cosegregate, those with the highest initial frequencies tend to reach fixation
faster sweeps are more likely at lower mutation rates
regimes where the genetic variance decreases during adaptation are not possible for any of the simulations presented here

when considering the pattern of hitchhiking at a locus, the presence or absence of a large-effect fixation at a locus is a reliable predictor of the magnitude of hitchhiking patterns
such fixations are more common when the mutation rate is smaller
thus strong departures from equilibrium patterns of variation are not expected for more polygenic traits
for the optimum shift model considered here, the strength of selection is not constant over time
genotypes containing variants that were initially strongly favored by selection are subject to much weaker selection by the time the population has reached the new optimum
this weakening of selection increases fixation times to the order of the population size

the partial linkage among sites in this work leads to some negative linkage disequilibrium (Figure S18), which is a signal of interference
this interference has little effect on the mean time to adaptation, but fixation times are increased
once the population is close to the new optimum, selection on individual genotypes is much weaker (Figure 5), setting up the conditions for interference to affect fixation times

the stabilizing selection around the initial optimum keeps large-effect mutations rare
sweeps from such standing variants start at low frequencies
it is not possible to tune the model parameters to obtain sweeps from large-effect, but common, variants with high probability
it is tempting to involve a need for pleiotropic effects to have large-effect mutations segregating at intermediate frequencies at the time of the optimum shift

I also allowed for partial linkage among sites, which is a key difference from the work based on the Barton (1986) framework, which assumes free recombination
partial linkage affects the long-term dynamics of selected mutations

the only test statistic based on patterns of SNP variation for detecting polygenic adaptation that I am aware of is the singleton density score (Field et al. 2016)
I have not explored this statistic here
it would be more fruitful to do so using simulations of much larger genomic regions applying tree sequence recording (Kelleher et al. 2018)

a more thorough understanding of the dynamics of linked selection during polygenic adaptation will require investigation of models with pleiotropic effects
the question in a pleiotropic model is the role that large-effect mutations may play, which is an unresolved question

acknowledging the focus on the standard additive model, the current work is best viewed as an investigation of a central concern in molecular population genetics (the effect of natural selection on linked neutral variation) having replaced the standard model of that subdiscipline with the standard model of evolutionary quantitative genetics
there are considerable theoretical and empirical challenges remaining in the understanding of the genetics of rapid adaptation
for models of phenotypic adaptation, our standard "tests of selection" are likely to fail, and are highly underpowered even when the assumptions of the phenotype model are close to that of the standard model