Interpreting population- and family-based genome-wide association studies in the presence of confounding.

A central aim of genome-wide association studies (GWASs) is to estimate direct genetic effects: the causal effects on an individual's phenotype of the alleles that they carry. However, estimates of direct effects can be subject to genetic and environmental confounding and can also absorb the "indirect" genetic effects of relatives' genotypes. Recently, an important development in controlling for these confounds has been the use of within-family GWASs, which, because of the randomness of mendelian segregation within pedigrees, are often interpreted as producing unbiased estimates of direct effects. Here, we present a general theoretical analysis of the influence of confounding in standard population-based and within-family GWASs. We show that, contrary to common interpretation, family-based estimates of direct effects can be biased by genetic confounding. In humans, such biases will often be small per-locus, but can be compounded when effect-size estimates are used in polygenic scores (PGSs). We illustrate the influence of genetic confounding on population- and family-based estimates of direct effects using models of assortative mating, population stratification, and stabilizing selection on GWAS traits. We further show how family-based estimates of indirect genetic effects, based on comparisons of parentally transmitted and untransmitted alleles, can suffer substantial genetic confounding. We conclude that, while family-based studies have placed GWAS estimation on a more rigorous footing, they carry subtle issues of interpretation that arise from confounding.

Demographic inference for spatially heterogeneous populations using long shared haplotypes.

We introduce a modified spatial Λ-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective population density. We derive an analytical formula for the expected number of shared haplotype segments between two individuals depending on their sampling locations. This formula involves the transition density of a skew diffusion which appears as a scaling limit of the ancestral lineages of individuals in this model. We then show that this formula can be used to infer the dispersal parameters and the effective population density of both regions, using a composite likelihood approach, and we demonstrate the efficiency of this method on a range of simulated data sets.

The temporal and genomic scale of selection following hybridization.

Genomic evidence supports an important role for selection in shaping patterns of introgression along the genome, but frameworks for understanding the evolutionary dynamics within hybrid populations that underlie these patterns have been lacking. Due to the clock-like effect of recombination in hybrids breaking up parental haplotypes, drift and selection produce predictable patterns of ancestry variation at varying spatial genomic scales through time. Here, we develop methods based on the Discrete Wavelet Transform to study the genomic scale of local ancestry variation and its association with recombination rates and show that these methods capture temporal dynamics of drift and genome-wide selection after hybridization. We apply these methods to published datasets from hybrid populations of swordtail fish (Xiphophorus) and baboons (Papio) and to inferred Neanderthal introgression in modern humans. Across systems, upward of 20% of variation in local ancestry at the broadest genomic scales can be attributed to systematic selection against introgressed alleles, consistent with strong selection acting on early-generation hybrids. Signatures of selection at fine genomic scales suggest selection over longer time scales; however, we suggest that our ability to confidently infer selection at fine scales is likely limited by inherent biases in current methods for estimating local ancestry from contiguous segments of genomic similarity. Wavelet approaches will become widely applicable as genomic data from systems with introgression become increasingly available and can help shed light on generalities of the genomic consequences of interspecific hybridization.

The contribution of gene flow, selection, and genetic drift to five thousand years of human allele frequency change.

Genomic time series from experimental evolution studies and ancient DNA datasets offer us a chance to directly observe the interplay of various evolutionary forces. We show how the genome-wide variance in allele frequency change between two time points can be decomposed into the contributions of gene flow, genetic drift, and linked selection. In closed populations, the contribution of linked selection is identifiable because it creates covariances between time intervals, and genetic drift does not. However, repeated gene flow between populations can also produce directionality in allele frequency change, creating covariances. We show how to accurately separate the fraction of variance in allele frequency change due to admixture and linked selection in a population receiving gene flow. We use two human ancient DNA datasets, spanning around 5,000 y, as time transects to quantify the contributions to the genome-wide variance in allele frequency change. We find that a large fraction of genome-wide change is due to gene flow. In both cases, after correcting for known major gene flow events, we do not observe a signal of genome-wide linked selection. Thus despite the known role of selection in shaping long-term polymorphism levels, and an increasing number of examples of strong selection on single loci and polygenic scores from ancient DNA, it appears to be gene flow and drift, and not selection, that are the main determinants of recent genome-wide allele frequency change. Our approach should be applicable to the growing number of contemporary and ancient temporal population genomics datasets.

Distinct ancient structural polymorphisms control heterodichogamy in walnuts and hickories.

The maintenance of stable mating type polymorphisms is a classic example of balancing selection, underlying the nearly ubiquitous 50/50 sex ratio in species with separate sexes. One lesser known but intriguing example of a balanced mating polymorphism in angiosperms is heterodichogamy - polymorphism for opposing directions of dichogamy (temporal separation of male and female function in hermaphrodites) within a flowering season. This mating system is common throughout Juglandaceae, the family that includes globally important and iconic nut and timber crops - walnuts (Juglans), as well as pecan and other hickories (Carya). In both genera, heterodichogamy is controlled by a single dominant allele. We fine-map the locus in each genus, and find two ancient (>50 Mya) structural variants involving different genes that both segregate as genus-wide trans-species polymorphisms. The Juglans locus maps to a ca. 20 kb structural variant adjacent to a probable trehalose phosphate phosphatase (TPPD-1), homologs of which regulate floral development in model systems. TPPD-1 is differentially expressed between morphs in developing male flowers, with increased allele-specific expression of the dominant haplotype copy. Across species, the dominant haplotype contains a tandem array of duplicated sequence motifs, part of which is an inverted copy of the TPPD-1 3' UTR. These repeats generate various distinct small RNAs matching sequences within the 3' UTR and further downstream. In contrast to the single-gene Juglans locus, the Carya heterodichogamy locus maps to a ca. 200-450 kb cluster of tightly linked polymorphisms across 20 genes, some of which have known roles in flowering and are differentially expressed between morphs in developing flowers. The dominant haplotype in pecan, which is nearly always heterozygous and appears to rarely recombine, shows markedly reduced genetic diversity and is over twice as long as its recessive counterpart due to accumulation of various types of transposable elements. We did not detect either genetic system in other heterodichogamous genera within Juglandaceae, suggesting that additional genetic systems for heterodichogamy may yet remain undiscovered.

The contribution of gene flow, selection, and genetic drift to five thousand years of human allele frequency change.

Genomic time series from experimental evolution studies and ancient DNA datasets offer us a chance to directly observe the interplay of various evolutionary forces. We show how the genome-wide variance in allele frequency change between two time points can be decomposed into the contributions of gene flow, genetic drift, and linked selection. In closed populations, the contribution of linked selection is identifiable because it creates covariances between time intervals, and genetic drift does not. However, repeated gene flow between populations can also produce directionality in allele frequency change, creating covariances. We show how to accurately separate the fraction of variance in allele frequency change due to admixture and linked selection in a population receiving gene flow. We use two human ancient DNA datasets, spanning around 5,000 years, as time transects to quantify the contributions to the genome-wide variance in allele frequency change. We find that a large fraction of genome-wide change is due to gene flow. In both cases, after correcting for known major gene flow events, we do not observe a signal of genome-wide linked selection. Thus despite the known role of selection in shaping long-term polymorphism levels, and an increasing number of examples of strong selection on single loci and polygenic scores from ancient DNA, it appears to be gene flow and drift, and not selection, that are the main determinants of recent genome-wide allele frequency change. Our approach should be applicable to the growing number of contemporary and ancient temporal population genomics datasets.

Polygenic response of sex chromosomes to sexual antagonism.

Sexual antagonism occurs when males and females differ in their phenotypic fitness optima but are constrained in their evolution to these optima because of their shared genome. The sex chromosomes, which have distinct evolutionary "interests" relative to the autosomes, are theorized to play an important role in sexually antagonistic conflict. However, the evolutionary responses of sex chromosomes and autosomes have usually been considered independently, that is, via contrasting the response of a gene located on either an X chromosome or an autosome. Here, we study the coevolutionary response of the X chromosome and autosomes to sexually antagonistic selection acting on a polygenic phenotype. We model a phenotype initially under stabilizing selection around a single optimum, followed by a sudden divergence of the male and female optima. We find that, in the absence of dosage compensation, the X chromosome promotes evolution toward the female optimum, inducing coevolutionary male-biased responses on the autosomes. Dosage compensation obscures the female-biased interests of the X, causing it to contribute equally to male and female phenotypic change. We further demonstrate that fluctuations in an adaptive landscape can generate prolonged intragenomic conflict and accentuate the differential responses of the X and autosomes to this conflict.

Causal interpretations of family GWAS in the presence of heterogeneous effects.

Family-based genome-wide association studies (GWAS) have emerged as a gold standard for assessing causal effects of alleles and polygenic scores. Notably, family studies are often claimed to provide an unbiased estimate of the average causal effect (or average treatment effect; ATE) of an allele, on the basis of an analogy between the random transmission of alleles from parents to children and a randomized controlled trial. Here, we show that this interpretation does not hold in general. Because Mendelian segregation only randomizes alleles among children of heterozygotes, the effects of alleles in the children of homozygotes are not observable. Consequently, if an allele has different average effects in the children of homozygotes and heterozygotes, as can arise in the presence of gene-by-environment interactions, gene-by-gene interactions, or differences in LD patterns, family studies provide a biased estimate of the average effect in the sample. At a single locus, family-based association studies can be thought of as providing an unbiased estimate of the average effect in the children of heterozygotes (i.e., a local average treatment effect; LATE). This interpretation does not extend to polygenic scores, however, because different sets of SNPs are heterozygous in each family. Therefore, other than under specific conditions, the within-family regression slope of a PGS cannot be assumed to provide an unbiased estimate for any subset or weighted average of families. Instead, family-based studies can be reinterpreted as enabling an unbiased estimate of the extent to which Mendelian segregation at loci in the PGS contributes to the population-level variance in the trait. Because this estimate does not include the between-family variance, however, this interpretation applies to only (roughly) half of the sample PGS variance. In practice, the potential biases of a family-based GWAS are likely smaller than those arising from confounding in a standard, population-based GWAS, and so family studies remain important for the dissection of genetic contributions to phenotypic variation. Nonetheless, the causal interpretation of family-based GWAS estimates is less straightforward than has been widely appreciated.

Demographic inference for spatially heterogeneous populations using long shared haplotypes.

We introduce a modified spatial Λ-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective population density. We derive an analytical formula for the expected number of shared haplotype segments between two individuals depending on their sampling locations. This formula involves the transition density of a skew diffusion which appears as a scaling limit of the ancestral lineages of individuals in this model. We then show that this formula can be used to infer the dispersal parameters and the effective population density of both regions, using a composite likelihood approach, and we demonstrate the efficiency of this method on a range of simulated data sets.

The temporal and genomic scale of selection following hybridization.

Genomic evidence supports an important role for selection in shaping patterns of introgression along the genome, but frameworks for understanding the dynamics underlying these patterns within hybrid populations have been lacking. Here, we develop methods based on the Wavelet Transform to understand the spatial genomic scale of local ancestry variation and its association with recombination rates. We present theory and use simulations to show how wavelet-based decompositions of ancestry variance along the genome and the correlation between ancestry and recombination reflect the joint effects of recombination, genetic drift, and genome-wide selection against introgressed alleles. Due to the clock-like effect of recombination in hybrids breaking up parental haplotypes, drift and selection produce predictable patterns of local ancestry variation at varying spatial genomic scales through time. Using wavelet approaches to identify the genomic scale of variance in ancestry and its correlates, we show that these methods can detect temporally localized effects of drift and selection. We apply these methods to previously published datasets from hybrid populations of swordtail fish (Xiphophorus) and baboons (Papio), and to inferred Neanderthal introgression in modern humans. Across systems, we find that upwards of 20% of the variation in local ancestry at the broadest genomic scales can be attributed to systematic selection against introgressed alleles, consistent with strong selection acting on early-generation hybrids. We also see signals of selection at fine genomic scales and much longer time scales. However, we show that our ability to confidently infer selection at fine scales is likely limited by inherent biases in current methods for estimating local ancestry from genomic similarity. Wavelet approaches will become widely applicable as genomic data from systems with introgression become increasingly available, and can help shed light on generalities of the genomic consequences of interspecific hybridization.

Interpreting population and family-based genome-wide association studies in the presence of confounding.

A central aim of genome-wide association studies (GWASs) is to estimate direct genetic effects: the causal effects on an individual's phenotype of the alleles that they carry. However, estimates of direct effects can be subject to genetic and environmental confounding, and can also absorb the 'indirect' genetic effects of relatives' genotypes. Recently, an important development in controlling for these confounds has been the use of within-family GWASs, which, because of the randomness of Mendelian segregation within pedigrees, are often interpreted as producing unbiased estimates of direct effects. Here, we present a general theoretical analysis of the influence of confounding in standard population-based and within-family GWASs. We show that, contrary to common interpretation, family-based estimates of direct effects can be biased by genetic confounding. In humans, such biases will often be small per-locus, but can be compounded when effect size estimates are used in polygenic scores. We illustrate the influence of genetic confounding on population- and family-based estimates of direct effects using models of assortative mating, population stratification, and stabilizing selection on GWAS traits. We further show how family-based estimates of indirect genetic effects, based on comparisons of parentally transmitted and untransmitted alleles, can suffer substantial genetic confounding. In addition to known biases that can arise in family-based GWASs when interactions between family members are ignored, we show that biases can also arise from gene-by-environment (G×E) interactions when parental genotypes are not distributed identically across interacting environmental and genetic backgrounds. We conclude that, while family-based studies have placed GWAS estimation on a more rigorous footing, they carry subtle issues of interpretation that arise from confounding and interactions.

Luck, lottery, or legacy? The problem of confounding. A reply to Harden.

A reply to Harden's response to Coop and Przeworski (2022).

Assortative mating enhances postzygotic barriers to gene flow via ancestry bundling.

Hybridization and subsequent genetic introgression are now known to be common features of the histories of many species, including our own. Following hybridization, selection often purges introgressed DNA genome-wide. While assortative mating can limit hybridization in the first place, it is also known to play an important role in postzygotic selection against hybrids and, thus, the purging of introgressed DNA. However, this role is usually thought of as a direct one: a tendency for mates to be conspecific reduces the sexual fitness of hybrids, reducing the transmission of introgressed ancestry. Here, we explore a second, indirect role of assortative mating as a postzygotic barrier to gene flow. Under assortative mating, parents covary in their ancestry, causing ancestry to be "bundled" in their offspring and later generations. This bundling effect increases ancestry variance in the population, enhancing the efficiency with which postzygotic selection purges introgressed DNA. Using whole-genome simulations, we show that the bundling effect can comprise a substantial portion of mate choice's overall effect as a postzygotic barrier to gene flow. We then derive a simple method for estimating the impact of the bundling effect from standard metrics of assortative mating. Applying this method to data from a diverse set of hybrid zones, we find that the bundling effect increases the purging of introgressed DNA by between 1.2-fold (in a baboon system with weak assortative mating) and 14-fold (in a swordtail system with strong assortative mating). Thus, assortative mating's bundling effect contributes substantially to the genetic isolation of species.

Population differentiation of polygenic score predictions under stabilizing selection.

Given the many small-effect loci uncovered by genome-wide association studies (GWAS), polygenic scores have become central to genomic medicine, and have found application in diverse settings including evolutionary studies of adaptation. Despite their promise, polygenic scores have been found to suffer from limited portability across human populations. This at first seems in conflict with the observation that most common genetic variation is shared among populations. We investigate one potential cause of this discrepancy: stabilizing selection on complex traits. Counterintuitively, while stabilizing selection constrains phenotypic evolution, it accelerates the loss and fixation of alleles underlying trait variation within populations (GWAS loci). Thus even when populations share an optimum phenotype, stabilizing selection erodes the variance contributed by their shared GWAS loci, such that predictions from GWAS in one population explain less of the phenotypic variation in another. We develop theory to quantify how stabilizing selection is expected to reduce the prediction accuracy of polygenic scores in populations not represented in GWAS samples. In addition, we find that polygenic scores can substantially overstate average genetic differences of phenotypes among populations. We emphasize stabilizing selection around a common optimum as a useful null model to connect patterns of allele frequency and polygenic score differentiation. This article is part of the theme issue 'Celebrating 50 years since Lewontin's apportionment of human diversity'.

Lottery, luck, or legacy. A review of "The Genetic Lottery: Why DNA matters for social equality".

A book review of "The genetic lottery: why DNA matters for social equality." (Princeton University Press, 2021) by Kathryn Paige Harden.

Selective sorting of ancestral introgression in maize and teosinte along an elevational cline.

While often deleterious, hybridization can also be a key source of genetic variation and pre-adapted haplotypes, enabling rapid evolution and niche expansion. Here we evaluate these opposing selection forces on introgressed ancestry between maize (Zea mays ssp. mays) and its wild teosinte relative, mexicana (Zea mays ssp. mexicana). Introgression from ecologically diverse teosinte may have facilitated maize's global range expansion, in particular to challenging high elevation regions (> 1500 m). We generated low-coverage genome sequencing data for 348 maize and mexicana individuals to evaluate patterns of introgression in 14 sympatric population pairs, spanning the elevational range of mexicana, a teosinte endemic to the mountains of Mexico. While recent hybrids are commonly observed in sympatric populations and mexicana demonstrates fine-scale local adaptation, we find that the majority of mexicana ancestry tracts introgressed into maize over 1000 generations ago. This mexicana ancestry seems to have maintained much of its diversity and likely came from a common ancestral source, rather than contemporary sympatric populations, resulting in relatively low FST between mexicana ancestry tracts sampled from geographically distant maize populations. Introgressed mexicana ancestry in maize is reduced in lower-recombination rate quintiles of the genome and around domestication genes, consistent with pervasive selection against introgression. However, we also find mexicana ancestry increases across the sampled elevational gradient and that high introgression peaks are most commonly shared among high-elevation maize populations, consistent with introgression from mexicana facilitating adaptation to the highland environment. In the other direction, we find patterns consistent with adaptive and clinal introgression of maize ancestry into sympatric mexicana at many loci across the genome, suggesting that maize also contributes to adaptation in mexicana, especially at the lower end of its elevational range. In sympatric maize, in addition to high introgression regions we find many genomic regions where selection for local adaptation maintains steep gradients in introgressed mexicana ancestry across elevation, including at least two inversions: the well-characterized 14 Mb Inv4m on chromosome 4 and a novel 3 Mb inversion Inv9f surrounding the macrohairless1 locus on chromosome 9. Most outlier loci with high mexicana introgression show no signals of sweeps or local sourcing from sympatric populations and so likely represent ancestral introgression sorted by selection, resulting in correlated but distinct outcomes of introgression in different contemporary maize populations.

The timing of human adaptation from Neanderthal introgression.

Admixture has the potential to facilitate adaptation by providing alleles that are immediately adaptive in a new environment or by simply increasing the long-term reservoir of genetic diversity for future adaptation. A growing number of cases of adaptive introgression are being identified in species across the tree of life, however the timing of selection, and therefore the importance of the different evolutionary roles of admixture, is typically unknown. Here, we investigate the spatio-temporal history of selection favoring Neanderthal-introgressed alleles in modern human populations. Using both ancient and present-day samples of modern humans, we integrate the known demographic history of populations, namely population divergence and migration, with tests for selection. We model how a sweep placed along different branches of an admixture graph acts to modify the variance and covariance in neutral allele frequencies among populations at linked loci. Using a method based on this model of allele frequencies, we study previously identified cases of adaptive Neanderthal introgression. From these, we identify cases in which Neanderthal-introgressed alleles were quickly beneficial and other cases in which they persisted at low frequency for some time. For some of the alleles that persisted at low frequency, we show that selection likely independently favored them later on in geographically separated populations. Our work highlights how admixture with ancient hominins has contributed to modern human adaptation and contextualizes observed levels of Neanderthal ancestry in present-day and ancient samples.

Selection and hybridization shaped the rapid spread of African honey bee ancestry in the Americas.

Recent biological invasions offer 'natural' laboratories to understand the genetics and ecology of adaptation, hybridization, and range limits. One of the most impressive and well-documented biological invasions of the 20th century began in 1957 when Apis mellifera scutellata honey bees swarmed out of managed experimental colonies in Brazil. This newly-imported subspecies, native to southern and eastern Africa, both hybridized with and out-competed previously-introduced European honey bee subspecies. Populations of scutellata-European hybrid honey bees rapidly expanded and spread across much of the Americas in less than 50 years. We use broad geographic sampling and whole genome sequencing of over 300 bees to map the distribution of scutellata ancestry where the northern and southern invasions have presently stalled, forming replicated hybrid zones with European bee populations in California and Argentina. California is much farther from Brazil, yet these hybrid zones occur at very similar latitudes, consistent with the invasion having reached a climate barrier. At these range limits, we observe genome-wide clines for scutellata ancestry, and parallel clines for wing length that span hundreds of kilometers, supporting a smooth transition from climates favoring scutellata-European hybrid bees to climates where they cannot survive winter. We find no large effect loci maintaining exceptionally steep ancestry transitions. Instead, we find most individual loci have concordant ancestry clines across South America, with a build-up of somewhat steeper clines in regions of the genome with low recombination rates, consistent with many loci of small effect contributing to climate-associated fitness trade-offs. Additionally, we find no substantial reductions in genetic diversity associated with rapid expansions nor complete dropout of scutellata ancestry at any individual loci on either continent, which suggests that the competitive fitness advantage of scutellata ancestry at lower latitudes has a polygenic basis and that scutellata-European hybrid bees maintained large population sizes during their invasion. To test for parallel selection across continents, we develop a null model that accounts for drift in ancestry frequencies during the rapid expansion. We identify several peaks within a larger genomic region where selection has pushed scutellata ancestry to high frequency hundreds of kilometers past the present cline centers in both North and South America and that may underlie high-fitness traits driving the invasion.

Estimating the genome-wide contribution of selection to temporal allele frequency change.

Rapid phenotypic adaptation is often observed in natural populations and selection experiments. However, detecting the genome-wide impact of this selection is difficult since adaptation often proceeds from standing variation and selection on polygenic traits, both of which may leave faint genomic signals indistinguishable from a noisy background of genetic drift. One promising signal comes from the genome-wide covariance between allele frequency changes observable from temporal genomic data (e.g., evolve-and-resequence studies). These temporal covariances reflect how heritable fitness variation in the population leads changes in allele frequencies at one time point to be predictive of the changes at later time points, as alleles are indirectly selected due to remaining associations with selected alleles. Since genetic drift does not lead to temporal covariance, we can use these covariances to estimate what fraction of the variation in allele frequency change through time is driven by linked selection. Here, we reanalyze three selection experiments to quantify the effects of linked selection over short timescales using covariance among time points and across replicates. We estimate that at least 17 to 37% of allele frequency change is driven by selection in these experiments. Against this background of positive genome-wide temporal covariances, we also identify signals of negative temporal covariance corresponding to reversals in the direction of selection for a reasonable proportion of loci over the time course of a selection experiment. Overall, we find that in the three studies we analyzed, linked selection has a large impact on short-term allele frequency dynamics that is readily distinguishable from genetic drift.

Genetic Signatures of Evolutionary Rescue by a Selective Sweep.

One of the most useful models in population genetics is that of a selective sweep and the consequent hitch-hiking of linked neutral alleles. While variations on this model typically assume constant population size, many instances of strong selection and rapid adaptation in nature may co-occur with complex demography. Here, we extend the hitch-hiking model to evolutionary rescue, where adaptation and demography not only co-occur but are intimately entwined. Our results show how this feedback between demography and evolution determines-and restricts-the genetic signatures of evolutionary rescue, and how these differ from the signatures of sweeps in populations of constant size. In particular, we find rescue to harden sweeps from standing variance or new mutation (but not from migration), reduce genetic diversity both at the selected site and genome-wide, and increase the range of observed Tajima's D values. For a given initial rate of population decline, the feedback between demography and evolution makes all of these differences more dramatic under weaker selection, where bottlenecks are prolonged. Nevertheless, it is likely difficult to infer the co-incident timing of the sweep and bottleneck from these simple signatures, never mind a feedback between them. Temporal samples spanning contemporary rescue events may offer one way forward.