polygenic adaptation - senecio7の日記

Sella G & Barton NH 2019 Thinking about the evolution of complex traits in the era of genome-wide association studies. Annu Rev Genom Hum Genet 20:461-493.

the genetic architecture of a trait is informative about the population genetic processes that gave rise to it
a better understanding of these processes can provide insight into practical questions, such as
why GWASs have accounted for only a modest fraction of heritable variation
the missing-heritability problem
why GWASs differ in success across traits
the design of future mapping studies
prospects for predicting phenotypes from genomes
combining information about the effects of individual loci on traits with other kinds of data—notably, changes in allele frequency across space and time—should help us learn about polygenic adaptation

Pritchard and colleagues (17, 100) have recently proposed a thought-provoking interpretation of these findings
in their omnigenic model, the value of a given trait is determined by the expression level of a few core genes in relevant tissues
the expression levels of core genes, however, can be weakly affected by the expression level of any other gene in these same tissues, and thus by any variants that affect the expression of these other genes
weak effects could arise through shared cellular machinery or by regulatory crosstalk within the RNA and protein network
even though these trans effects may be minute, their sheer number (together with the fact that, due to selection, only weak allelic effects are expected to segregate at appreciable frequencies) leads them to account, in aggregate, for most of the heritable variance in the trait
for example, active chromatin in relevant tissues, rather than specific functional annotations, seems to be the best predictor of GWAS signals
it provides an explanation for why so many loci, distributed across the genome, contribute to the heritability of a given trait

the bulk of genetic variance in quantitative, complex traits is additive
the processes that generate an individual's phenotype clearly involve highly complex and nonlinear interactions among many genes and external and internal environments
the predominance of additive variance implies that (on average) the deviation of an individual's trait value from the population mean, z, can be well approximated by a simple additive model
z = g + e = Σ_l=1^L(a_l + a'_l) + e ... 1
a_l and a'_l are the effects of the parents' alleles at site l, scaled such that the population mean contribution at each site equals 0
a_l and a'_l reflect marginal allelic effects, averaged over the distribution of genetic backgrounds and environments in the population being considered
assuming that segregating sites are biallelic, a given site with difference a in the effect of alleles and MAF x contributes 2a²x(1 − x) to genetic variance

we would like to know how well the breeding value can be approximated by polygenic scores, constructed by adding up estimated allelic effects at subsets of loci associated with a trait
the narrow-sense heritability for traits is typically substantial (~0.1–0.9) (178), suggesting that polygenic scores should, in principle, account for a substantial proportion of the phenotypic variance
a current polygenic score for height, for example, for which h² ≈ 0.8, relies on effect-size estimates for 20,000 SNPs and explains ~40% of the phenotypic variance in the self-described "white British"

the additive component can contribute the bulk of genetic variance even when dominance and epistatic interactions are included
this argument does not assume that interactions have a negligible effect
it states that even when their effect is substantial, most of it can be attributed to the marginal effects of individual alleles

many studies have reported dominance and epistatic interactions in crosses between inbred lines and between individuals from diverged populations and species
such crosses distort the allelic frequency spectrum (see 107) and bring together combinations of alleles that selection might prevent from cosegregating in the same population (akin to Dobzhansky-Muller incompatibilities in speciation)
considerable efforts to detect epistatic interactions in human GWASs have by and large come up empty-handed

contrary to the premise of the breeder's equation, covariance between fitness and a trait might not reflect selection on the trait
it could reflect a nonheritable environmental effect on both
both fitness and the trait may be strongly affected by an individual's general condition
variation in condition may be largely due to the environment
the prevalence of disruptive and stabilizing selection in meta-analyses largely reflects a combination of low statistical power and publication bias
Sanjak et al. (147) recently applied the multivariate approach, using lifetime reproductive success as a proxy for fitness in a sample size of more than 250,000 from the UK Biobank (168), orders of magnitude larger than previous studies
they found a large excess of stabilizing relative to disruptive selection

limits on the number of selected traits
consider, for example, n uncorrelated traits that are normally distributed around the optimal n-dimensional phenotype, each with variance V_P
each trait is subject to Gaussian stabilizing selection of strength V_S^{− 1}
V_S ≫ V_P
variation in all traits will reduce fitness by ~exp(−n(V_P/2V_S)) relative to the optimal phenotype
this constraint would be weaker if most selection is soft, e.g., based on competition between individuals rather than on differences in absolute fitness
or if there are negative epistatic interactions in effects on fitness

the standard deviation in relative fitness increases with the number of traits as ~exp(n(V_P/2V_S)²)
while the standard deviation in fitness is difficult to measure (but see 20), it is unlikely to exceed ~1/4 and is bound from above by offspring numbers
assuming the traditional estimated of V_P/V_S ~ 1/20 (174) would suggest an unreasonably low number of ~400 traits
although V_P/V_S is likely smaller typically, and thus the number of traits could be somewhat larger

major loci
i.e., loci that contribute substantially to genetic variance
theory suggests that the conditions in which migration-selection balance produces major loci are quite restrictive
mutations affecting the selected trait should be clustered in low-recombination regions

V_M/V_E, known as the mutational heritability, are typically ~0.0006–0.006
V_M ≅ 2U ⋅ E(a²), [...], is likely smaller than 0.1 ⋅ V_P
the estimates of V_M/V_E suggest remarkably high mutation rates of ~0.006–0.06 per gamete per generation affecting a variety of traits
assuming a typical mutation rate of ~10⁻⁸ per base pair per generation for multicellular eukaryotes, these values suggest mutational target sizes of ~0.15–1.5 Mb, echoing the evidence for high polygenicity based on the response to artificial selection and human GWASs

V_A/V_M
this ratio, also referred to as persistence time, is a measure of the number of generations required for mutation to replenish quantitative genetic variation
if most variation is effectively neutral, the persistence time is much longer, on the order of twice the effective population size, 2N_e
estimates of the persistence time are typically on the order of 100 generations (72, 115), much lower than for any species, suggesting that the bulk of quantitative genetic variation is selected against (as opposed to being neutral or under balancing selection) and lending strong support to the dominant role of mutation-selection balance in maintaining quantitative genetic variation

one of the early fault lines, the so-called Gaussian versus house of cards debate (174), centered on whether the distribution of allelic effect sizes should be modeled as Gaussian (83, 92) or rather reflects an (unknown) distribution for newly arising mutations (141, 174, 194)
one might expect an approximate Gaussian distribution if segregating variation at a locus consisted of (largely) nonrecombining haplotypes carrying many mutations affecting the trait
this would occur if the per-site mutation rate, u, far exceeds the recombination rate, r
typically u/r ~ 1 or less for all mutations
for mutations affecting a given trait, it is likely to be at least an order of magnitude smaller
e.g., in humans, only ~10% of mutations are under selection
for this reason and others, the Gaussian assumption has been largely abandoned
LD is now thought to play a minor role in mutation–selection balance
models of mutation-selection balance over the past three decades disagree primarily in their assumptions about the relationship between allelic effects on a trait and on fitness

in the Eyre-Walker model, mutations with large effect sizes and small selection coefficients are too rare to contribute substantially to genetic variance
strongly selected mutations with large effect sizes have the greatest contribution to variance
in the Caballero et al. model (first presented in 80), the distribution of effect sizes conditional on a given selection coefficient can have thicker tails
weakly selected mutations with larger effect sizes make the greatest contribution
their diverging predictions suggest that we need to understand more about the statistical relationship between selection coefficients and effect sizes to know what to expect

3.2.1. possible extensions
one would be to relax the assumption that the (effective) number of traits affected by mutations is fixed
another generalization would be to relax the assumption that all selected traits are subject to stabilizing selection
one might also envision mutational effects on a focal trait to partially reflect contributions that are not selected
such effects can be incorporated by adding an underlying neutral trait
one might consider the effects of selected traits that are not highly polygenic

the number of strongly selected mutations that entered the population was high
the expected number per generation is 2NU
their initial frequencies were low, i.e., 1/2N
the total, strongly selected variance is approximately unaffected
the two effects cancel out
the distribution of the variance among sites is profoundly affected, with many more sites segregating but at proportionally lower MAFs, and thus with lower per-site contributions to genetic variance
weakly deleterious variation, by contrast, would have largely arisen before or during the out-of-Africa bottleneck, which implies a lower input of mutations and stronger genetic drift that accelerated the loss of most mutations and boosted the frequency of those remaining
we would therefore expect fewer weakly selected segregating sites, but with greater MAFs and per-site contributions to variance
more generally, we expect the total contribution of strongly or weakly selected mutations to variance to be fairly insensitive to changes in population size (and instead depend primarily on their mutational input)
the number of segregating sites and the distribution of their contributions to variance should be markedly influenced, with strongly selected variation more affected by the more recent population sizes than weakly selected variation

when GWS associations are represented in terms of their estimated frequencies and effect sizes, they are often distributed tightly above the variance threshold
the question about missing heritability can be recast as asking where the remaining loci reside on such plots
are they mostly strongly selected loci with relatively large effects, which evade identification because their minor alleles are so rare
or are they relatively weakly selected loci with relatively small effect sizes, which evade detection because of their small contributions to variance
fitting evolutionary models to GWAS findings can help to answer these questions

Agarwala et al. (2) took a pioneering step in this direction
they used forward population genetic simulations to generate samples of genomes
they ascribed liabilities to these genomes under a range of models that vary both in their mutational target size for the disease (which determined how many of the selected sites were picked to be causal) and in the coupling between selection and effect size, assuming Eyre-Walker's model (which determined how effect sizes were ascribed to these causal sites)
they performed GWASs on their simulated data sets and compared the numbers of GWS associations with the one observed for type 2 diabetes
they were able to rule out the pleiotropic and direct selection extremes of Eyre-Walker's model
they were left with a wide range of possible genetic architectures.

Mancuso et al. (108) applied a similar approach to the study of prostate cancer in men of African ancestry
they relied on targeted sequencing at 63 loci found to affect disease risk in a larger GWAS and estimated that rare variants at these loci (with MAFs of 0.1–1%) account for ~12% of the heritability in risk (on the liability scale) compared with ~17% for common variants
the contribution of rare variants far exceeds the neutral expectation, indicating that variation affecting disease risk is subject to purifying selection
Mancuso et al. (108) then used their heritability estimate as a summary statistic to infer the coupling between selection and effect size, again assuming Eyre-Walker's model
as in the study by Agarwala et al. (2), they were left with a wide range of possible architectures

Simons et al. (157) took a step in this direction by asking whether the distribution of variances among the loci identified in GWASs for height and BMI in Europeans accords with their theoretical predictions
assuming the loci are highly pleiotropic and under moderate to strong selection (because otherwise they contribute much less to variance), the distribution of variances among them is well approximated by a closed form that depends on a single parameter, v_S
they used the observed distribution for the ~700 GWS associations for height and ~80 for BMI to estimate this parameter
the theoretical distribution provided a good fit for either trait
models with low pleiotropy did not
moderately and strongly selected mutations affecting height have a target size of ~5 Mb and account for ~50% of the heritable variance
for BMI these values are ~1 Mb and only ~15%, respectively
they do not account for the effects of historical changes in population size
simulations that incorporate changes in the population sizes of Europeans suggest that only moderately selected loci (s ~ 10⁻³) would be identified by these GWASs
the contribution to variance per segregating, strongly selected locus has been reduced by population growth after the out-of-Africa bottleneck
their estimates should be attributed only to moderately selected loci
the heritability that they do not account for could be due to loci under stronger and/or weaker selection

current GWS loci likely reflect a fairly narrow range of selection effects
further progress therefore depends on moving beyond these GWS associations

most approaches rely on strong assumptions about genetic architecture and are sensitive to varying these assumptions
earlier work assumed that the contributions of SNPs to genetic variance are normally distributed and do not depend on their frequency
E(a²|x) ∝ [x(1 − x)]⁻¹
more recent work assumed the more flexible α model
E(a²|x) ∝ [x(1 − x)]^α
estimates of α are generally negative
mutations with larger effect sizes are more strongly selected against
there is little reason to think that selection produces genetic architectures that are well approximated by the α model

4. polygenic adaptation
many selected traits are highly polygenic
the adaptive response to changing selective pressures must often involve shifts in such traits, accomplished through changes to allele frequencies at the many segregating loci that affect them
we would therefore expect polygenic adaptation in complex traits to be ubiquitous

models of polygenic adaptation
a sudden change of environment induces an instantaneous shift in the optimum of a trait under stabilizing selection
this simple scenario provides a sensible starting point for thinking about polygenic adaptation in nature

polygenic adaptation can be so rapid because it requires only tiny changes to allele frequencies at the numerous loci contributing to genetic variation

E(Δx) ≅ 1/(2V_S) D(t)ax(1 − x) − 1/(4V_S) a²x(1 − x)(1/2 − x) ... 3.
the first term on the right-hand side corresponds to directional selection
it pushes alleles with effects that are aligned with the shift to higher frequencies
its strength weakens as the distance to the new optimum, D, decreases
the second term corresponds to stabilizing selection
it acts to reduce the frequency of minor alleles regardless of the direction of their effect, and dominates when D is small
it shapes the genetic architecture at mutation–selection–drift balance, prior to the shift in optimum
when D = 0
the expected contribution to variance is then greatest for sites with intermediate and large effects, where it is approximately constant at E(2a²x(1 − x)) ≅ v_S
for such sites, on average, x(1 − x) declines roughly as 1/a²
immediately after the shift in optimum, the change in allele frequency due to directional selection is proportional to ax(1 − x) and thus is greater for alleles with intermediate effect sizes than for alleles with large effects
the contribution of an allele to phenotypic change is proportional to a²x(1 − x) and is therefore fairly insensitive to its effect sizes
once the population mean has largely caught up with the new optimum (and D is small), stabilizing selection dominates the allelic dynamics
large-effect alleles started at low frequencies and are not likely to have neared a frequency of 1/2 by this time
they are highly unlikely to further increase in frequency, let alone fix, with stabilizing selection now acting against them
alleles with intermediate effects that are aligned with the shift reach higher frequencies by this time and are therefore more likely to increase in frequency at this second stage, eventually leading to an excess fixation of intermediate-effect, aligned alleles
as a result, and counterintuitively, over longer timescales, the contribution of intermediate-effect alleles to phenotypic change supplants the contribution of alleles with large effect
eventually, the contribution of all transient frequency changes is replaced by fixations at a small subset of loci

our current understanding provides a basis for a few useful, educated guesses
polygenic adaptation likely has minimal effects on the genetic architecture of a trait
at most loci it causes only tiny changes to allele frequencies and thus only weakly perturbs the distribution of allele frequencies
polygenic adaptation arises predominantly from standing variation and primarily from variants that were segregating at relatively high MAFs, which would suggest modest effects on levels of neutral genetic variation at linked sites
identifying polygenic adaptation is likely to require pooling the evidence for changes in frequencies across many loci affecting a given trait

4.2. identifying polygenic adaptation in humans
all the methods recently proposed for identifying polygenic adaptation in humans are based on combining signals of changes in allele frequency across many loci that affect a given trait and testing whether these changes tend to affect the trait in a given direction
the reliance on subtle signals aggregated over many loci identified in GWASs renders tests extremely sensitive to systematic biases
the first set of methods relies on frequency differences of trait-increasing alleles among extant populations
the second set instead leverages genealogical footprints of past increases in the frequency of trait-increasing (or trait-decreasing) alleles in a single population
all current GWASs employ controls for population structure
it is currently not known how well these correct for biases in tests of polygenic adaptation
much of the existing evidence for polygenic adaptation is driven by subtle biases in GWAS estimates

the first approach relies on allele-frequency differences among extant populations
or, by extension, in archaic ones
the second set of methods relies on genealogical signatures of past increases in the frequency of trait-increasing (or trait-decreasing) alleles in a single population
Field et al. (45) introduced the first method in this vein
they reasoned that a recent and rapid change in allele frequency driven by selection would result in shorter terminal branches in the genealogy of the favored allele
the haplotypes flanking the beneficial alleles should carry fewer mutations that are singletons in the sample
they relied on the distribution of distances to the nearest singleton across individuals carrying each genotype in order to estimate the (log) ratio of the mean tip-branch lengths corresponding to the two alleles
they then standardized these estimates within bins of derived allele frequencies to define the singleton density score (SDS)
two recent methods take the same general approach but rely on explicit inferences of the genealogies of SNPs associated with a trait rather than summaries of tip-branch lengths
Edge & Coop (39) relied on estimated genealogical trees to approximate the time course of allele frequencies at SNPs associated with a trait and used them to approximate the time course of the polygenic score
in principle, the test should be well powered farther back in time than one based on SDS, with power increasing with sample size
the reliability of the estimated time course inevitably degrades substantially farther back in time
the number of lineages remaining in the genealogy of the sample decreases
thus so does power
in practice, the performance of this method strongly depends on the quality of the genealogical inference
Speidel et al. (166) introduced a promising and computationally efficient method for reconstructing genealogical trees in large samples, alongside a new test for polygenic adaptation
they considered the number of lineages at the time of the most recent common ancestor of the focal allele and tested whether the branching rate that led to the current frequency of the allele is significantly greater than that of the other lineages present when the allele first arose
significance levels were derived based on the symmetry of branching rates expected under neutrality and thus depend only on the topology of the inferred tree

much of the reported evidence for polygenic adaptation in height, and plausibly in other traits, was driven by subtle, systematic biases in GWASs

assuming these problems are overcome and polygenic adaptation in multiple traits and populations is identified, what is next?
one challenge will be to place adaptation events in a given trait in the context of human evolutionary history
another challenge will be to home in on targets of selection
e.g., to infer whether signals of adaptation for multiple traits in a given population reflect selection on each of the traits or rather selection on fewer traits that are genetically correlated with the others
Berg et al. (15) tested for correlations between polygenic scores in extant populations and ecological variables, controlling for the relatedness among populations

we now think that ubiquitous heritable variation in complex traits is maintained primarily by a balance between mutation and selection
we also think that polygenic adaptation via complex traits should be ubiquitous and a major mode of adaptation
we can learn about polygenic adaptation in recent human evolution by combining GWAS data with population genetic analyses

we could envision relating the processes that shape heritable variation with the cellular processes that translate this variation into phenotypic differences
we also have evolutionary models that relate mutational effects on multiple, selected complex traits with the genetic architecture of a given trait
we can ask, e.g., how cis-acting mutational effects on gene expression translate into contributions to trait heritability
doing so may help to explain why the heritability of many complex traits is widely distributed across the genome, rather than being concentrated around specific genes and pathways that are important to those traits
low-frequency, large-effect associations are more indicative of genes that directly affect a trait
common, smaller-effect ones are indicative of more general attributes of gene regulatory networks
the integration of evolutionary models and GWAS data may also turn out to be key to learning about biology from GWASs