Polygenic score accuracy in ancient samples: Quantifying the effects of allelic turnover

Polygenic scores link the genotypes of ancient individuals to their phenotypes, which are often unobservable, offering a tantalizing opportunity to reconstruct complex trait evolution. In practice, however, interpretation of ancient polygenic scores is subject to numerous assumptions. For one, the genome-wide association (GWA) studies from which polygenic scores are derived, can only estimate effect sizes for loci segregating in contemporary populations. Therefore, a GWA study may not correctly identify all loci relevant to trait variation in the ancient population. In addition, the frequencies of trait-associated loci may have changed in the intervening years. Here, we devise a theoretical framework to quantify the effect of this allelic turnover on the statistical properties of polygenic scores as functions of population genetic dynamics, trait architecture, power to detect significant loci, and the age of the ancient sample. We model the allele frequencies of loci underlying trait variation using the Wright-Fisher diffusion, and employ the spectral representation of its transition density to find analytical expressions for several error metrics, including the expected sample correlation between the polygenic scores of ancient individuals and their true phenotypes, referred to as polygenic score accuracy. Our theory also applies to a two-population scenario and demonstrates that allelic turnover alone may explain a substantial percentage of the reduced accuracy observed in cross-population predictions, akin to those performed in human genetics. Finally, we use simulations to explore the effects of recent directional selection, a bias-inducing process, on the statistics of interest. We find that even in the presence of bias, weak selection induces minimal deviations from our neutral expectations for the decay of polygenic score accuracy. By quantifying the limitations of polygenic scores in an explicit evolutionary context, our work lays the foundation for the development of more sophisticated statistical procedures to analyze both temporally and geographically resolved polygenic scores.     

Spatially and temporally varying selection on intrapopulation quantitative trait loci for a life history trade-off in Mimulus guttatus

Why do populations remain genetically variable despite strong continuous natural selection? Mutation reconstitutes variation eliminated by selection and genetic drift, but theoretical and experimental studies each suggest that mutation‐selection balance insufficient to explain extant genetic variation in most complex traits. The alternative hypothesis of balancing selection, wherein selection maintains genetic variation, is an aggregate of multiple mechanisms (spatial and temporal heterogeneity in selection, frequency‐dependent selection, antagonistic pleiotropy, etc.). Most of these mechanisms have been demonstrated for Mendelian traits, but there is little comparable data for loci affecting quantitative characters. Here, we report a 3‐year field study of selection on intrapopulation quantitative trait loci (QTL) of flower size, a highly polygenic trait in Mimulus guttatus. The QTL exhibit antagonistic pleiotropy: alleles that increase flower size, reduce viability, but increase fecundity. The magnitude and direction of selection fluctuates yearly and on a spatial scale of metres. This study provides direct evidence of balancing selection mechanisms on QTL of an ecologically relevant trait.     

Signs of selective pressure on genetic variants affecting human height

Many decades of scientific investigation have proved the role of selective pressure in Homo Sapiens at least at the level of individual genes or loci. Nevertheless, there are examples of polygenic traits that are bound to be under selection, but studies devoted to apply population genetics methods to unveil such occurrence are still lacking. Stature provides a relevant example of well-studied polygenic trait for which is now available a genome-wide association study which has identified the genes involved in this trait, and which is known to be under selection. We studied the behavior of F_ST in a simulated toy model to detect population differentiation on a generic polygenic phenotype under selection. The simulations showed that the set of alleles involved in the trait has a higher mean F_ST value than those undergoing genetic drift only. In view of this we looked for an increase in the mean F_ST value of the 180 variants associated to human height. For this set of alleles we found F_ST to be significantly higher than the genomic background (p = 0.0356). On the basis of a statistical analysis we excluded that the increase was just due to the presence of outliers. We also proved as marginal the role played by local adaptation phenomena, even on different phenotypes in linkage disequilibrium with genetic variants involved in height. The increase of F_ST for the set of alleles involved in a polygenic trait seems to provide an example of symmetry breaking phenomenon concerning the population differentiation. The splitting in the allele frequencies would be driven by the initial conditions in the population dynamics which are stochastically modified by events like drift, bottlenecks, etc, and other stochastic events like the born of new mutations.     

All sheeps and sizes: a genetic investigation of mature body size across sheep breeds reveals a polygenic nature

Mature body size is genetically correlated with growth rate, an important economic trait in the sheep industry. Mature body size has been studied extensively in humans as well as cattle and other domestic animal populations but not in sheep. Six‐hundred and sixteen ewes, across 22 breeds, were measured for 28 linear measurements representing various skeletal parts. PCA from these measures generated principal components 1 and 2 which represented 66 and 7% of the phenotypic variation respectively. Two‐hundred and twenty sheep were genotyped on the Illumina Ovine HD beadchip for a GWAS investigating mature body size and linear body measurements. Forty‐six (Bonferroni P < 0.05) SNP associations across 14 chromosomes were identified utilizing principal component 1, representing overall body size, revealing mature body size to have fewer loci of large effect than other domestic species such as dogs and horses. Genome‐wide associations for individual linear measures identified major quantitative trait loci for withers height and ear length. Withers height was associated (Bonferroni P < 0.05) with 12 SNPs across six chromosomes whereas ear length was associated with a single locus on chromosome 3, containing MSRB3. This analysis identified several loci known to be associated with mature body size in other species such as NCAPG, LCORL, and HMGA2. Mature body size is more polygenic in sheep than other domesticated species, making the development of genomic selection for the trait the most efficient option for maintaining or reducing mature body size in sheep.     

Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and G x E interactions

We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.     

Parallel selection mapping using artificially selected mice reveals body weight control loci

Understanding how polygenic traits evolve under selection is an unsolved problem, because challenges exist for identifying genes underlying a complex trait and understanding how multilocus selection operates in the genome. Here we study polygenic response to selection using artificial selection experiments. Inbred strains from seven independent long-term selection experiments for extreme mouse body weight ("high" lines weigh 42-77 g versus 16-40 g in "control" lines) were genotyped at 527,572 SNPs to identify loci controlling body weight. We identified 67 parallel selected regions (PSRs) where high lines share variants rarely found among the controls. By comparing allele frequencies in one selection experiment against its unselected control, we found classical selective sweeps centered on the PSRs. We present evidence supporting two G protein-coupled receptors GPR133 and Prlhr as positional candidates controlling body weight. Artificial selection may mimic natural selection in the wild: compared to control loci, we detected reduced heterozygosity in PSRs in unusually large wild mice on islands. Many PSRs overlap loci associated with human height variation, possibly through evolutionary conserved functional pathways. Our data suggest that parallel selection on complex traits may evoke parallel responses at many genes involved in diverse but relevant pathways.     

An Approximate Model of Polygenic Inheritance

The finite polygenic model approximates polygenic inheritance by postulating that a quantitative trait is determined by n independent, additive loci. The 3(n) possible genotypes for each person in this model limit its applicability. CANNINGS, THOMPSON, and SKOLNICK suggested a simplified, nongenetic version of the model involving only 2n + 1 genotypes per person. This article shows that this hypergeometric polygenic model also approximates polygenic inheritance well. In particular, for noninbred pedigrees, trait means, variances, covariances, and marginal distributions match those of the ordinary finite polygenic model. Furthermore as n -> &, the trait values within a pedigree collectively tend toward multivariate normality. The implications of these results for likelihood evaluation under the polygenic threshold and mixed models of inheritance are discussed. Finally, a simple numerical example illustrates the application of the hypergeometric polygenic model to risk prediction under the polygenic threshold model.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Identification of QTL for UV-protective eye area pigmentation in cattle by progeny phenotyping and genome-wide association analysis

Pigmentation patterns allow for the differentiation of cattle breeds. A dominantly inherited white head is characteristic for animals of the Fleckvieh (FV) breed. However, a minority of the FV animals exhibits peculiar pigmentation surrounding the eyes (ambilateral circumocular pigmentation, ACOP). In areas where animals are exposed to increased solar ultraviolet radiation, ACOP is associated with a reduced susceptibility to bovine ocular squamous cell carcinoma (BOSCC, eye cancer). Eye cancer is the most prevalent malignant tumour affecting cattle. Selection for animals with ACOP rapidly reduces the incidence of BOSCC. To identify quantitative trait loci (QTL) underlying ACOP, we performed a genome-wide association study using 658,385 single nucleotide polymorphisms (SNPs). The study population consisted of 3579 bulls of the FV breed with a total of 320,186 progeny with phenotypes for ACOP. The proportion of progeny with ACOP was used as a quantitative trait with high heritability (h(2)?=?0.79). A variance component based approach to account for population stratification uncovered twelve QTL regions on seven chromosomes. The identified QTL point to MCM6, PAX3, ERBB3, KITLG, LEF1, DKK2, KIT, CRIM1, ATRN, GSDMC, MITF and NBEAL2 as underlying genes for eye area pigmentation in cattle. The twelve QTL regions explain 44.96% of the phenotypic variance of the proportion of daughters with ACOP. The chromosomes harbouring significantly associated SNPs account for 54.13% of the phenotypic variance, while another 19.51% of the phenotypic variance is attributable to chromosomes without identified QTL. Thus, the missing heritability amounts to 7% only. Our results support a polygenic inheritance pattern of ACOP in cattle and provide the basis for efficient genomic selection of animals that are less susceptible to serious eye diseases.     

Moving from QTL experimental results to the utilization of QTL in breeding programmes

Results from quantitative trait loci studies cannot be readily implemented into breeding schemes through marker assisted selection because of uncertainty about whether the quantitative trait loci identified are real and whether the identified quantitative trait loci are segregating in the breeding population. The present paper outlines and discusses strategies to reduce uncertainty in the results from quantitative trait loci studies. One strategy to confirm results from quantitative trait loci studies is to combine P -values from many quantitative trait loci experiments, while another is to establish a confirmation study. The power of a confirmation study must be high to ensure that the postulated quantitative trait loci can be verified. In the calculation of the experimental power, there are many issues that have to be addressed: size of the quantitative trait loci to be detected, significance level required, experimental design and expected heterozygosity for the design. To ensure marker assisted selection can be quickly implemented once quantitative trait loci are confirmed, DNA samples should be retained from daughters, and the sires and dams of elite sires.     

Evidence for a new major gene influencing meat quality in pigs

The present investigation primarily deals with the inheritance of a pigmeat quality trait, the Napole technological yield (RTN), a measure of cooked weight to fresh weight. This trait as well as lean percentage at 100 kg liveweight and fattening length from 20 to 100 kg liveweight were recorded on 3459 offspring from 67 sires and 433 dams, and 3052 offspring from 64 sires and 405 dams in Penshire (P66) and Pen Ar Lan (P77) composite lines respectively. The hypothesis of a major 2-allele locus contributing to RTN was tested by use of a segregation analysis method. Highly significant likelihood ratios (mixed vs. polygenic transmission models) lead us to conclude that a major gene RN- exerting an unfavourable effect on RTN is segregating in both lines. Maximum likelihood estimates of the parameters under the hypothesis of mixed (monogenic + polygenic) inheritance show that the difference between the means of the 2 homozygotes amounts to about 3 phenotypic standard deviations of the trait, whereas the complete dominance of RN- cannot be rejected. The frequency of RN- is about 0.6 in both lines. These results are discussed in connection with the previously reported 'Hampshire effect' on pigmeat quality, as the Hampshire breed is a common component of the foundation stock of the 2 composite lines under study.     

Advances in QTL mapping in pigs

Over the past 15 years advances in the porcine genetic linkage map and discovery of useful candidate genes have led to valuable gene and trait information being discovered. Early use of exotic breed crosses and now commercial breed crosses for quantitative trait loci (QTL) scans and candidate gene analyses have led to 110 publications which have identified 1,675 QTL. Additionally, these studies continue to identify genes associated with economically important traits such as growth rate, leanness, feed intake, meat quality, litter size, and disease resistance. A well developed QTL database called PigQTLdb is now as a valuable tool for summarizing and pinpointing in silico regions of interest to researchers. The commercial pig industry is actively incorporating these markers in marker-assisted selection along with traditional performance information to improve traits of economic performance. The long awaited sequencing efforts are also now beginning to provide sequence available for both comparative genomics and large scale single nucleotide polymorphism (SNP) association studies. While these advances are all positive, development of useful new trait families and measurement of new or underlying traits still limits future discoveries. A review of these developments is presented.     

Population-based resequencing of experimentally evolved populations reveals the genetic basis of body size variation in Drosophila melanogaster

Body size is a classic quantitative trait with evolutionarily significant variation within many species. Locating the alleles responsible for this variation would help understand the maintenance of variation in body size in particular, as well as quantitative traits in general. However, successful genome-wide association of genotype and phenotype may require very large sample sizes if alleles have low population frequencies or modest effects. As a complementary approach, we propose that population-based resequencing of experimentally evolved populations allows for considerable power to map functional variation. Here, we use this technique to investigate the genetic basis of natural variation in body size in Drosophila melanogaster. Significant differentiation of hundreds of loci in replicate selection populations supports the hypothesis that the genetic basis of body size variation is very polygenic in D. melanogaster. Significantly differentiated variants are limited to single genes at some loci, allowing precise hypotheses to be formed regarding causal polymorphisms, while other significant regions are large and contain many genes. By using significantly associated polymorphisms as a priori candidates in follow-up studies, these data are expected to provide considerable power to determine the genetic basis of natural variation in body size.     

Integration of Random Forest with population‐based outlier analyses provides insight on the genomic basis and evolution of run timing in Chinook salmon (Oncorhynchus tshawytscha)

Anadromous Chinook salmon populations vary in the period of river entry at the initiation of adult freshwater migration, facilitating optimal arrival at natal spawning. Run timing is a polygenic trait that shows evidence of rapid parallel evolution in some lineages, signifying a key role for this phenotype in the ecological divergence between populations. Studying the genetic basis of local adaptation in quantitative traits is often impractical in wild populations. Therefore, we used a novel approach, Random Forest, to detect markers linked to run timing across 14 populations from contrasting environments in the Columbia River and Puget Sound, USA. The approach permits detection of loci of small effect on the phenotype. Divergence between populations at these loci was then examined using both principle component analysis and F_ST outlier analyses, to determine whether shared genetic changes resulted in similar phenotypes across different lineages. Sequencing of 9107 RAD markers in 414 individuals identified 33 predictor loci explaining 79.2% of trait variance. Discriminant analysis of principal components of the predictors revealed both shared and unique evolutionary pathways in the trait across different lineages, characterized by minor allele frequency changes. However, genome mapping of predictor loci also identified positional overlap with two genomic outlier regions, consistent with selection on loci of large effect. Therefore, the results suggest selective sweeps on few loci and minor changes in loci that were detected by this study. Use of a polygenic framework has provided initial insight into how divergence in a trait has occurred in the wild.     

Genetic response from marker assisted selection in an outbred population for differing marker bracket sizes and with two identified quantitative trait loci.

Effect of flanking quantitative trait loci (QTL)-marker bracket size on genetic response to marker assisted selection in an outbred population was studied by simulation of a nucleus breeding scheme. In addition, genetic response with marker assisted selection (MAS) from two quantitative trait loci on the same and different chromosome(s) was investigated. QTL that explained either 5% or 10% of phenotypic variance were simulated. A polygenic component was simulated in addition to the quantitative trait loci. In total, 35% of the phenotypic variance was due to genetic factors. The trait was measured on females only. Having smaller marker brackets flanking the QTL increased the genetic response from MAS selection. This was due to the greater ability to trace the QTL transmission from one generation to the next with the smaller flanking QTL-marker bracket, which increased the accuracy of estimation of the QTL allelic effects. Greater negative covariance between effects at both QTL was observed when two QTL were located on the same chromosome compared to different chromosomes. Genetic response with MAS was greater when the QTL were on the same chromosome in the early generations and greater when they were on different chromosomes in the later generations of MAS.     

On the genetic architecture of rapidly adapting and convergent life history traits in guppies

The genetic basis of traits shapes and constrains how adaptation proceeds in nature; rapid adaptation can proceed using stores of polygenic standing genetic variation or hard selective sweeps, and increasing polygenicity fuels genetic redundancy, reducing gene re-use (genetic convergence). Guppy life history traits evolve rapidly and convergently among natural high- and low-predation environments in northern Trinidad. This system has been studied extensively at the phenotypic level, but little is known about the underlying genetic architecture. Here, we use four independent F2 QTL crosses to examine the genetic basis of seven (five female, two male) guppy life history phenotypes and discuss how these genetic architectures may facilitate or constrain rapid adaptation and convergence. We use RAD-sequencing data (16,539 SNPs) from 370 male and 267 female F2 individuals. We perform linkage mapping, estimates of genome-wide and per-chromosome heritability (multi-locus associations), and QTL mapping (single-locus associations). Our results are consistent with architectures of many loci of small-effect for male age and size at maturity and female interbrood period. Male trait associations are clustered on specific chromosomes, but female interbrood period exhibits a weak genome-wide signal suggesting a potentially highly polygenic component. Offspring weight and female size at maturity are also associated with a single significant QTL each. These results suggest rapid, repeatable phenotypic evolution of guppies may be facilitated by polygenic trait architectures, but subsequent genetic redundancy may limit gene re-use across populations, in agreement with an absence of strong signatures of genetic convergence from recent analyses of wild guppies.Subject terms: Evolutionary genetics, Quantitative trait     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

Powerful detection of polygenic selection and evidence of environmental adaptation in US beef cattle

Selection on complex traits can rapidly drive evolution, especially in stressful environments. This polygenic selection does not leave intense sweep signatures on the genome, rather many loci experience small allele frequency shifts, resulting in large cumulative phenotypic changes. Directional selection and local adaptation are changing populations; but, identifying loci underlying polygenic or environmental selection has been difficult. We use genomic data on tens of thousands of cattle from three populations, distributed over time and landscapes, in linear mixed models with novel dependent variables to map signatures of selection on complex traits and local adaptation. We identify 207 genomic loci associated with an animal’s birth date, representing ongoing selection for monogenic and polygenic traits. Additionally, hundreds of additional loci are associated with continuous and discrete environments, providing evidence for historical local adaptation. These candidate loci highlight the nervous system’s possible role in local adaptation. While advanced technologies have increased the rate of directional selection in cattle, it has likely been at the expense of historically generated local adaptation, which is especially problematic in changing climates. When applied to large, diverse cattle datasets, these selection mapping methods provide an insight into how selection on complex traits continually shapes the genome. Further, understanding the genomic loci implicated in adaptation may help us breed more adapted and efficient cattle, and begin to understand the basis for mammalian adaptation, especially in changing climates. These selection mapping approaches help clarify selective forces and loci in evolutionary, model, and agricultural contexts.     

Sensitivity to dietary obesity linked to a locus on Chromosome 15 in a CAST/Ei × C57BL/6J F2 intercross

Details of a new model of diet-dependent polygenic obesity are presented. CAST/Ei (Mus m. castaneus) mice remain lean after 12 weeks on a high-fat (32 kcal% fat) diet, while C57BL/6J mice become obese. The genes responsible for the obesity segregate in an F₂ population derived from an intercross between CAST/Ei and C57BL/6J mice. Quantitative trait analysis, with simple sequence length polymorphisms (SSLPs) at loci previously linked to rodent obesities, identified a quantitative trait locus (QTL) on Chromosome (Chr) 15, accounting for approximately 9% of the variance in adiposity and 14% of the variance in mesenteric depot size. This locus appears to be at the same location as the dietary obesity-3 (Do3) locus controlling body fat content, which was previously identified in an F₂ population derived from an SWR/J × AKR/J cross. This is also at the same location as the multigenic obesity-4 (Mob4) locus found in BSB mice, which display spontaneous polygenic obesity. Suggestive linkage also was found at loci close to the single gene mutations A ^y on Chr 2 and tub on Chr 7. Received 15 January 1996 / Accepted 12 May 1996     

Reaching new heights: insights into the genetics of human stature

Human height is a highly heritable, classic polygenic trait. Until recently, there had been limited success in identifying the specific genetic variants that explain normal variation of human height. The advent of large-scale genome-wide association studies, however, has led to dramatic progress. In the past 18 months, the first robust common variant associations were identified and there are now 44 loci known to influence normal variation of height. In this review, we summarize this exciting recent progress, discuss implicated biological pathways, the overlap with monogenic growth and skeletal dysplasia syndromes, links to disease and insights into the genetic architecture of this model polygenic trait. We also discuss the strong probability of finding several hundred more such loci in the near future.