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.

Two teosintes made modern maize.

The origins of maize were the topic of vigorous debate for nearly a century, but neither the current genetic model nor earlier archaeological models account for the totality of available data, and recent work has highlighted the potential contribution of a wild relative, Zea mays ssp. mexicana. Our population genetic analysis reveals that the origin of modern maize can be traced to an admixture between ancient maize and Zea mays ssp. mexicana in the highlands of Mexico some 4000 years after domestication began. We show that variation in admixture is a key component of maize diversity, both at individual loci and for additive genetic variation underlying agronomic traits. Our results clarify the origin of modern maize and raise new questions about the anthropogenic mechanisms underlying dispersal throughout the Americas.

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.

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.

Recombination and selection against introgressed DNA.

Introgressed DNA is often deleterious at many loci in the recipient species' genome, and is therefore purged by selection. Here, we use mathematical modeling and whole-genome simulations to study the influence of recombination on this process. We find that aggregate recombination controls the genome-wide rate of purging in the early generations after admixture, when purging is most rapid. Aggregate recombination is influenced by the number of chromosomes and heterogeneity in their size, and by the number of crossovers and their locations along chromosomes. A comparative prediction is that species with fewer chromosomes should purge introgressed ancestry more profoundly, and should therefore exhibit weaker genomic signals of historical introgression. Turning to within-genome patterns, we show that, in species with autosomal recombination in both sexes, more purging is expected on sex chromosomes than autosomes, all else equal. The opposite prediction holds for species without autosomal recombination in the heterogametic sex. Finally, positive correlations between recombination rate and introgressed ancestry have recently been observed within the genomes of several species. We show that these correlations are likely driven not by recombination's effect in unlinking neutral from deleterious introgressed alleles, but by recombination's effect on the rate of purging of deleterious introgressed alleles themselves.

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.

Mendel's First Law: partisan interests and the parliament of genes.

Mendel's First Law requires explanation because of the possibility of 'meiotic drivers', genes that distort fair segregation for selfish gain. The suppression of drive, and the restoration of fair segregation, is often attributed to genes at loci unlinked to the drive locus-such genes cannot benefit from drive but do suffer its associated fitness costs. However, selection can also favour suppressors at loci linked to the drive locus, raising the question of whether suppression of drive usually comes from linked or unlinked loci. Here, I study linked and unlinked suppression in a two-locus model with initial stable polymorphism at the drive locus. I find that the invasion rate of suppressors is a decreasing function of the recombination fraction between the drive and suppressor loci. Surprisingly, the relative likelihood of unlinked vs. linked suppression increases with the strength of drive and is insensitive to the fitness costs of the driver allele. I find that the chromosomal position of the driver influences how rapidly it is suppressed, with a driver in the middle of a chromosome suppressed more rapidly than a driver near the tip. When drive is strong, only a small number of chromosomes are required for suppression usually to derive from unlinked loci. In contrast, when drive is weak, and especially when suppressor alleles are associated with fitness costs, suppression will usually come from linked loci unless the genome comprises many chromosomes.

Dominance shifts increase the likelihood of soft selective sweeps.

Genetic models of adaptation to a new environment have typically assumed that the alleles involved maintain a constant fitness dominance across the old and new environments. However, theories of dominance suggest that this should often not be the case. Instead, the alleles involved should frequently shift from recessive deleterious in the old environment to dominant beneficial in the new environment. Here, we study the consequences of these expected dominance shifts for the genetics of adaptation to a new environment. We find that dominance shifts increase the likelihood that adaptation occurs from standing variation, and that multiple alleles from the standing variation are involved (a soft selective sweep). Furthermore, we find that expected dominance shifts increase the haplotypic diversity of selective sweeps, rendering soft sweeps more detectable in small genomic samples. In cases where an environmental change threatens the viability of the population, we show that expected dominance shifts of newly beneficial alleles increase the likelihood of evolutionary rescue and the number of alleles involved. Finally, we apply our results to a well-studied case of adaptation to a new environment: the evolution of pesticide resistance at the Ace locus in Drosophila melanogaster. We show that, under reasonable demographic assumptions, the expected dominance shift of resistant alleles causes soft sweeps to be the most frequent outcome in this case, with the primary source of these soft sweeps being the standing variation at the onset of pesticide use, rather than recurrent mutation thereafter.

A new model of sex chromosome evolution.

A new model, based on the evolution of gene regulation, challenges the classical theory.

Invasion and maintenance of meiotic drivers in populations of ascomycete fungi.

Meiotic drivers (MDs) are selfish genetic elements that are able to become overrepresented among the products of meiosis. This transmission advantage makes it possible for them to spread in a population even when they impose fitness costs on their host organisms. Whether an MD can invade a population, and subsequently reach fixation or coexist in a stable polymorphism, depends on the one hand on the biology of the host organism, including its life cycle, mating system, and population structure, and on the other hand on the specific fitness effects of the driving allele on the host. Here, we present a population genetic model for spore killing, a type of drive specific to fungi. We show how ploidy level, rate of selfing, and efficiency of spore killing affect the invasion probability of a driving allele and the conditions for its stable coexistence with a nondriving allele. Our model can be adapted to different fungal life cycles, and is applied here to two well-studied genera of filamentous ascomycetes known to harbor spore-killing elements, Neurospora and Podospora. We discuss our results in the light of recent empirical findings for these two systems.

Variation in Genetic Relatedness Is Determined by the Aggregate Recombination Process.

The genomic proportion that two relatives share identically by descent-their genetic relatedness-can vary depending on the history of recombination and segregation in their pedigree. Previous calculations of the variance of genetic relatedness have defined genetic relatedness as the proportion of total genetic map length (cM) shared by relatives, and have neglected crossover interference and sex differences in recombination. Here, we consider genetic relatedness as the proportion of the total physical genome (bp) shared by relatives, and calculate its variance for general pedigree relationships, making no assumptions about the recombination process. For the relationships of grandparent-grandoffspring and siblings, the variance of genetic relatedness is a simple decreasing function of [Formula: see text], the average proportion of locus pairs that recombine in meiosis. For general pedigree relationships, the variance of genetic relatedness is a function of metrics analogous to [Formula: see text] Therefore, features of the aggregate recombination process that affect [Formula: see text] and analogs also affect variance in genetic relatedness. Such features include the number of chromosomes and heterogeneity in their size, the number of crossovers and their spatial organization along chromosomes, and sex differences in recombination. Our calculations help to explain several recent observations about variance in genetic relatedness, including that it is reduced by crossover interference (which is known to increase [Formula: see text]). Our methods further allow us to calculate the neutral variance of ancestry among F2s in a hybrid cross, enabling precise statistical inference in F2-based tests for various kinds of selection.

On the logic of Fisherian sexual selection.

In Fisher's model of sexual selection, a female preference for a male trait spreads together with the trait because their genetic bases become correlated. This can be interpreted as a "greenbeard" system: a preference gene, by inducing a female to mate with a trait-bearing male, favors itself because the male is disproportionately likely also to carry the preference gene. Here, we use this logic to argue that Fisherian sexual selection in diploids proceeds via two channels: (i) trait-bearing males are disproportionately the product of matings between preference-bearing mothers and trait-bearing fathers, and thus trait and preference genes are correlated "in trans"; (ii) trait and preference genes come into gametic phase disequilibrium, and thus are correlated "in cis." Gametic phase disequilibrium is generated by three distinct mechanisms that we identify. The trans channel does not operate when sexual selection is restricted to the haploid phase, and therefore represents a fundamental difference between haploid and diploid models of sexual selection. We show that the cis and trans channels contribute equally to the spread of the preference when recombination between the preference and trait loci is free, but that the trans channel is substantially more important when linkage is tight.

Per-Nucleus Crossover Covariation and Implications for Evolution.

Crossing over is a nearly universal feature of sexual reproduction. Here, analysis of crossover numbers on a per-chromosome and per-nucleus basis reveals a fundamental, evolutionarily conserved feature of meiosis: within individual nuclei, crossover frequencies covary across different chromosomes. This effect results from per-nucleus covariation of chromosome axis lengths. Crossovers can promote evolutionary adaptation. However, the benefit of creating favorable new allelic combinations must outweigh the cost of disrupting existing favorable combinations. Covariation concomitantly increases the frequencies of gametes with especially high, or especially low, numbers of crossovers, and thus might concomitantly enhance the benefits of crossing over while reducing its costs. A four-locus population genetic model suggests that such an effect can pertain in situations where the environment fluctuates: hyper-crossover gametes are advantageous when the environment changes while hypo-crossover gametes are advantageous in periods of environmental stasis. These findings reveal a new feature of the basic meiotic program and suggest a possible adaptive advantage.

A rigorous measure of genome-wide genetic shuffling that takes into account crossover positions and Mendel's second law.

Comparative studies in evolutionary genetics rely critically on evaluation of the total amount of genetic shuffling that occurs during gamete production. Such studies have been hampered by the absence of a direct measure of this quantity. Existing measures consider crossing-over by simply counting the average number of crossovers per meiosis. This is qualitatively inadequate, because the positions of crossovers along a chromosome are also critical: a crossover toward the middle of a chromosome causes more shuffling than a crossover toward the tip. Moreover, traditional measures fail to consider shuffling from independent assortment of homologous chromosomes (Mendel's second law). Here, we present a rigorous measure of genome-wide shuffling that does not suffer from these limitations. We define the parameter [Formula: see text] as the probability that the alleles at two randomly chosen loci are shuffled during gamete production. This measure can be decomposed into separate contributions from crossover number and position and from independent assortment. Intrinsic implications of this metric include the fact that [Formula: see text] is larger when crossovers are more evenly spaced, which suggests a selective advantage of crossover interference. Utilization of [Formula: see text] is enabled by powerful emergent methods for determining crossover positions either cytologically or by DNA sequencing. Application of our analysis to such data from human male and female reveals that (i) [Formula: see text] in humans is close to its maximum possible value of 1/2 and that (ii) this high level of shuffling is due almost entirely to independent assortment, the contribution of which is ∼30 times greater than that of crossovers.

Selection for synchronized cell division in simple multicellular organisms.

The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular organism requires multiple rounds of cell division, a natural question is whether these cell divisions should be synchronous or not. We study a population model in which there compete simple multicellular organisms that grow by either synchronous or asynchronous cell divisions. We demonstrate that natural selection can act differently on synchronous and asynchronous cell division, and we offer intuition for why these phenotypes are generally not neutral variants of each other.

Sexual antagonism and the instability of environmental sex determination.

The sex of an organism can be determined by its genetics or its early environment. Across the animal kingdom, genetic sex determination (GSD) is far more common than environmental sex determination (ESD). Here, we propose an explanation for this pattern: the coupling of genes that bias offspring sex ratios towards one sex with genes that are beneficial in that sex but costly in the other. Gradual strengthening of the sex-specific tendency of this association eventuates in a neo-sex chromosome; that is, GSD. Our model predicts to which system of heterogamety ESD will evolve when nesting behaviour is an important determinant of brood sex ratios. It explains the puzzling observation in some GSD species of sex reversal induced by extreme environments. The model also suggests an approach to discovering sex-determining genes in ESD species.

The evolution of queen control over worker reproduction in the social Hymenoptera.

A trademark of eusocial insect species is reproductive division of labor, in which workers forego their own reproduction while the queen produces almost all offspring. The presence of the queen is key for maintaining social harmony, but the specific role of the queen in the evolution of eusociality remains unclear. A long-discussed scenario is that a queen either behaviorally or chemically sterilizes her workers. However, the demographic and ecological conditions that enable such manipulation are still debated. We study a simple model of evolutionary dynamics based on haplodiploid genetics. Our model is set in the commonly observed case where workers have lost the ability to lay female (diploid) eggs by mating, but retain the ability to lay male (haploid) eggs. We consider a mutation that acts in a queen, causing her to control the reproductive behavior of her workers. Our mathematical analysis yields precise conditions for the evolutionary emergence and stability of queen-induced worker sterility. These conditions do not depend on the queen's mating frequency. We find that queen control is always established if it increases colony reproductive efficiency, but can evolve even if it decreases colony efficiency. We further derive the conditions under which queen control is evolutionarily stable against invasion by mutant workers who have recovered the ability to lay male eggs.

Drift-Induced Selection Between Male and Female Heterogamety.

Evolutionary transitions between male and female heterogamety are common in both vertebrates and invertebrates. Theoretical studies of these transitions have found that, when all genotypes are equally fit, continuous paths of intermediate equilibria link the two sex chromosome systems. This observation has led to a belief that neutral evolution along these paths can drive transitions, and that arbitrarily small fitness differences among sex chromosome genotypes can determine the system to which evolution leads. Here, we study stochastic evolutionary dynamics along these equilibrium paths. We find non-neutrality, both in transitions retaining the ancestral pair of sex chromosomes, and in those creating a new pair. In fact, substitution rates are biased in favor of dominant sex determining chromosomes, which fix with higher probabilities than mutations of no effect. Using diffusion approximations, we show that this non-neutrality is a result of "drift-induced selection" operating at every point along the equilibrium paths: stochastic jumps off the paths return with, on average, a directional bias in favor of the dominant segregating sex chromosome. Our results offer a novel explanation for the observed preponderance of dominant sex determining genes, and hint that drift-induced selection may be a common force in standard population genetic systems.

The Red Queen and King in finite populations.

In antagonistic symbioses, such as host-parasite interactions, one population's success is the other's loss. In mutualistic symbioses, such as division of labor, both parties can gain, but they might have different preferences over the possible mutualistic arrangements. The rates of evolution of the two populations in a symbiosis are important determinants of which population will be more successful: Faster evolution is thought to be favored in antagonistic symbioses (the "Red Queen effect"), but disfavored in certain mutualistic symbioses (the "Red King effect"). However, it remains unclear which biological parameters drive these effects. Here, we analyze the effects of the various determinants of evolutionary rate: generation time, mutation rate, population size, and the intensity of natural selection. Our main results hold for the case where mutation is infrequent. Slower evolution causes a long-term advantage in an important class of mutualistic interactions. Surprisingly, less intense selection is the strongest driver of this Red King effect, whereas relative mutation rates and generation times have little effect. In antagonistic interactions, faster evolution by any means is beneficial. Our results provide insight into the demographic evolution of symbionts.