QTL detection power of multi-parental RIL populations in Arabidopsis thaliana

A major goal of today's biology is to understand the genetic basis of quantitative traits. This can be achieved by statistical methods that evaluate the association between molecular marker variation and phenotypic variation in different types of mapping populations. The objective of this work was to evaluate the statistical power of quantitative trait loci (QTL) detection of various multi-parental mating designs, as well as to assess the reasons for the observed differences. Our study was based on an empirical data of 20 Arabidopsis thaliana accessions, which have been selected to capture the maximum genetic diversity. The examined mating designs differed strongly with respect to the statistical power to detect QTL. We observed the highest power to detect QTL for the diallel cross with random mating design. The results of our study suggested that performing sibling mating within subpopulations of joint-linkage mapping populations has the potential to considerably increase the power for QTL detection. Our results, however, revealed that using designs in which more than two parental alleles segregate in each subpopulation increases the power even more.     

Gene duplication and divergence produce divergent MHC genotypes without disassortative mating

Genes of the major histocompatibility complex (MHC) exhibit heterozygote advantage in immune defence, which in turn can select for MHC‐disassortative mate choice. However, many species lack this expected pattern of MHC‐disassortative mating. A possible explanation lies in evolutionary processes following gene duplication: if two duplicated MHC genes become functionally diverged from each other, offspring will inherit diverse multilocus genotypes even under random mating. We used locus‐specific primers for high‐throughput sequencing of two expressed MHC Class II B genes in Leach's storm‐petrels, Oceanodroma leucorhoa, and found that exon 2 alleles fall into two gene‐specific monophyletic clades. We tested for disassortative vs. random mating at these two functionally diverged Class II B genes, using multiple metrics and different subsets of exon 2 sequence data. With good statistical power, we consistently found random assortment of mates at MHC. Despite random mating, birds had MHC genotypes with functionally diverged alleles, averaging 13 amino acid differences in pairwise comparisons of exon 2 alleles within individuals. To test whether this high MHC diversity in individuals is driven by evolutionary divergence of the two duplicated genes, we built a phylogenetic permutation model. The model showed that genotypic diversity was strongly impacted by sequence divergence between the most common allele of each gene, with a smaller additional impact of monophyly of the two genes. Divergence of allele sequences between genes may have reduced the benefits of actively seeking MHC‐dissimilar mates, in which case the evolutionary history of duplicated genes is shaping the adaptive landscape of sexual selection.     

DISRUPTIVE SELECTION ON BODY WEIGHT IN DROSOPHILA MELANOGASTER

Disruptive selection can have two consequences in a population: the rise of polymorphism or the divergence of the population. Divergence creates subpopulations which can be sexually isolated. Previous studies have shown that these consequences depend on the pattern of mate choices by the individuals. We have studied the effects of different patterns of mating (free mating, enforced random mating and enforced assortative mating) in a population of Drosophila melanogaster subjected to disruptive selection on body weight. Disruptive selection increased the weight dispersion in all mating patterns but brought about divergence within the population only when it occurred in association with enforced assortative mating (without complete sexual isolation between the subpopulations). When mating was free, the dispersion, measured by change in the coefficient of variation, was only somewhat larger than with enforced random mating: thus the principal consequence of disruptive selection was the rise of polymorphism in the population.     

Sampling strategy optimization to increase statistical power in landscape genomics: A simulation‐based approach

An increasing number of studies are using landscape genomics to investigate local adaptation in wild and domestic populations. Implementation of this approach requires the sampling phase to consider the complexity of environmental settings and the burden of logistical constraints. These important aspects are often underestimated in the literature dedicated to sampling strategies. In this study, we computed simulated genomic data sets to run against actual environmental data in order to trial landscape genomics experiments under distinct sampling strategies. These strategies differed by design approach (to enhance environmental and/or geographical representativeness at study sites), number of sampling locations and sample sizes. We then evaluated how these elements affected statistical performances (power and false discoveries) under two antithetical demographic scenarios. Our results highlight the importance of selecting an appropriate sample size, which should be modified based on the demographic characteristics of the studied population. For species with limited dispersal, sample sizes above 200 units are generally sufficient to detect most adaptive signals, while in random mating populations this threshold should be increased to 400 units. Furthermore, we describe a design approach that maximizes both environmental and geographical representativeness of sampling sites and show how it systematically outperforms random or regular sampling schemes. Finally, we show that although having more sampling locations (between 40 and 50 sites) increase statistical power and reduce false discovery rate, similar results can be achieved with a moderate number of sites (20 sites). Overall, this study provides valuable guidelines for optimizing sampling strategies for landscape genomics experiments.     

Stable linkage disequilibrium without epistasis in subdivided populations

In a large random mating population stable linkage disequilibrium occurs only when there is epistasis. However if a population is divided into a number of subpopulations among which migration occurs, stable linkage disequilibrium in each subpopulation may be produced without epistasis. In the case of two subpopulations a necessary condition for linkage equilibrium in the absence of epistasis is that at least at one of the two loci under consideration the gene frequency must be the same for the two populations. This condition is rather severe and any violation of this will lead to stable linkage disequilibrium. A similar conclusion can be made with more than two populations. In general the presence of linkage disequilibrium does not necessarily imply the existence of epistasis even in equilibrium populations.     

Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.     

gesp: A computer program for modelling genetic effective population size,inbreeding and divergence in substructured populations

The genetically effective population size (N_e) is of key importance for quantifying rates of inbreeding and genetic drift and is often used in conservation management to set targets for genetic viability. The concept was developed for single, isolated populations and the mathematical means for analysing the expected N_e in complex, subdivided populations have previously not been available. We recently developed such analytical theory and central parts of that work have now been incorporated into a freely available software tool presented here. gesp (Genetic Effective population size, inbreeding and divergence in Substructured Populations) is R‐based and designed to model short‐ and long‐term patterns of genetic differentiation and effective population size of subdivided populations. The algorithms performed by gesp allow exact computation of global and local inbreeding and eigenvalue effective population size, predictions of genetic divergence among populations (G_ST) as well as departures from random mating (F_IS, F_IT) while varying (i) subpopulation census and effective size, separately or including trend of the global population size, (ii) rate and direction of migration between all pairs of subpopulations, (iii) degree of relatedness and divergence among subpopulations, (iv) ploidy (haploid or diploid) and (v) degree of selfing. Here, we describe gesp and exemplify its use in conservation genetics modelling.     

EVIDENCE FOR CLIMATE‐DRIVEN DIVERSIFICATION? A CAUTION FOR INTERPRETING ABC INFERENCES OF SIMULTANEOUS HISTORICAL EVENTS

Approximate Bayesian computation (ABC) is rapidly gaining popularity in population genetics. One example, msBayes , infers the distribution of divergence times among pairs of taxa, allowing phylogeographers to test hypotheses about historical causes of diversification in co‐distributed groups of organisms. Using msBayes , we infer the distribution of divergence times among 22 pairs of populations of vertebrates distributed across the Philippine Archipelago. Our objective was to test whether sea‐level oscillations during the Pleistocene caused diversification across the islands. To guide interpretation of our results, we perform a suite of simulation‐based power analyses. Our empirical results strongly support a recent simultaneous divergence event for all 22 taxon pairs, consistent with the prediction of the Pleistocene‐driven diversification hypothesis. However, our empirical estimates are sensitive to changes in prior distributions, and our simulations reveal low power of the method to detect random variation in divergence times and bias toward supporting clustered divergences. Our results demonstrate that analyses exploring power and prior sensitivity should accompany ABC model selection inferences. The problems we identify are potentially mitigable with uniform priors over divergence models (rather than classes of models) and more flexible prior distributions on demographic and divergence‐time parameters.     

INVITED REVIEW: What is a population? An empirical evaluation of some genetic methods for identifying the number of gene pools and their degree of connectivity

We review commonly used population definitions under both the ecological paradigm (which emphasizes demographic cohesion) and the evolutionary paradigm (which emphasizes reproductive cohesion) and find that none are truly operational. We suggest several quantitative criteria that might be used to determine when groups of individuals are different enough to be considered 'populations'. Units for these criteria are migration rate (m) for the ecological paradigm and migrants per generation (Nm) for the evolutionary paradigm. These criteria are then evaluated by applying analytical methods to simulated genetic data for a finite island model. Under the standard parameter set that includes L = 20 High mutation (microsatellite-like) loci and samples of S = 50 individuals from each of n = 4 subpopulations, power to detect departures from panmixia was very high ( approximately 100%; P < 0.001) even with high gene flow (Nm = 25). A new method, comparing the number of correct population assignments with the random expectation, performed as well as a multilocus contingency test and warrants further consideration. Use of Low mutation (allozyme-like) markers reduced power more than did halving S or L. Under the standard parameter set, power to detect restricted gene flow below a certain level X (H(0): Nm < X) can also be high, provided that true Nm < or = 0.5X. Developing the appropriate test criterion, however, requires assumptions about several key parameters that are difficult to estimate in most natural populations. Methods that cluster individuals without using a priori sampling information detected the true number of populations only under conditions of moderate or low gene flow (Nm < or = 5), and power dropped sharply with smaller samples of loci and individuals. A simple algorithm based on a multilocus contingency test of allele frequencies in pairs of samples has high power to detect the true number of populations even with Nm = 25 but requires more rigorous statistical evaluation. The ecological paradigm remains challenging for evaluations using genetic markers, because the transition from demographic dependence to independence occurs in a region of high migration where genetic methods have relatively little power. Some recent theoretical developments and continued advances in computational power provide hope that this situation may change in the future.     

Naive application of permutation testing leads to inflated type I error rates

Failure to account for family structure within populations or in complex mating designs via uninformed applications of permutation testing will lead to inflated type I error rates. Careful consideration of the design factors is essential since some situations allow several valid permutation strategies, and the choice that maximizes statistical power will not always be intuitive.     

EVOLUTION OF DIVERGENT FEMALE MATING PREFERENCE IN RESPONSE TO EXPERIMENTAL SEXUAL SELECTION

Sexual selection is predicted to drive the coevolution of mating signals and preferences (mating traits) within populations, and could play a role in speciation if sexual isolation arises due to mating trait divergence between populations. However, few studies have demonstrated that differences in mating traits between populations result from sexual selection alone. Experimental evolution is a promising approach to directly examine the action of sexual selection on mating trait divergence among populations. We manipulated the opportunity for sexual selection (low vs. high) in populations of Drosophila pseudoobscura. Previous studies on these experimental populations have shown that sexual selection manipulation resulted in the divergence between sexual selection treatments of several courtship song parameters, including interpulse interval (IPI) which markedly influences male mating success. Here, we measure female preference for IPI using a playback design to test for preference divergence between the sexual selection treatments after 130 generations of experimental sexual selection. The results suggest that female preference has coevolved with male signal, in opposite directions between the sexual selection treatments, providing direct evidence of the ability of sexual selection to drive the divergent coevolution of mating traits between populations. We discuss the implications in the context sexual selection and speciation.     

Cytonuclear disequilibria in a spatially structured hybrid zone

A hybrid zone model was developed that uses a stepping-stone model of population structure along with both nuclear and cytoplasmic genotypes to evaluate the effect that migration has on random mating organisms when no selection is present. Numerical simulations indicate that a number of different allele frequency and cytonuclear disequilibrium patterns can be found across the hybrid zone when it has reached equilibrium, and these results are discussed in the context of relative migration rates of the two sexes and the two source populations. The importance of numbers of subpopulations sampled, census time, and the persistence of pure species individuals into the hybrid zone are also discussed. Although this model does not consider selection or assortative mating in the hybrid zone, it should provide a useful baseline for evaluating joint cytonuclear genetic data from a structurally complex hybrid zone.     

GENES WITH SOCIAL EFFECTS ARE EXPECTED TO HARBOR MORE SEQUENCE VARIATION WITHIN AND BETWEEN SPECIES

The equilibrium sequence diversity of genes within a population and the rate of sequence divergence between populations or species depends on a variety of factors, including expression pattern, mutation rate, nature of selection, random drift, and mating system. Here, we extend population genetic theory developed for maternal-effect genes to predict the equilibrium polymorphism within species and sequence divergence among species for genes with social effects on fitness. We show how the fitness effects of genes, mating system, and genetic system affect predicted gene polymorphism. We find that, because genes with indirect social effects on fitness effectively experience weaker selection, they are expected to harbor higher levels of polymorphism relative to genes with direct fitness effects. The relative increase in polymorphism is proportional to the inverse of the genetic relatedness between individuals expressing the gene and their social partners that experience the fitness effects of the gene. We find a similar pattern of more rapid divergence between populations or species for genes with indirect social effects relative to genes with direct effects. We focus our discussion on the social insects, organisms with diverse indirect genetic effects, mating and genetic systems, and we suggest specific examples for testing our predictions with emerging sociogenomic tools.     

Effective population size,genetic diversity,and coalescence time in subdivided populations

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.     

A comparison of four methods for detecting weak genetic structure from marker data

Genetic structure is ubiquitous in wild populations and is the result of the processes of natural selection, genetic drift, mutation, and gene flow. Genetic drift and divergent selection promotes the generation of genetic structure, while gene flow homogenizes the subpopulations. The ability to detect genetic structure from marker data diminishes rapidly with a decreasing level of differentiation among subpopulations. Weak genetic structure may be unimportant over evolutionary time scales but could have important implications in ecology and conservation biology. In this paper we examine methods for detecting and quantifying weak genetic structures using simulated data. We simulated populations consisting of two putative subpopulations evolving for up to 50 generations with varying degrees of gene flow (migration), and varying amounts of information (allelic diversity). There are a number of techniques available to detect and quantify genetic structure but here we concentrate on four methods: F(ST), population assignment, relatedness, and sibship assignment. Under the simple mating system simulated here, the four methods produce qualitatively similar results. However, the assignment method performed relatively poorly when genetic structure was weak and we therefore caution against using this method when the analytical aim is to detect fine-scale patterns. Further work should examine situations with different mating systems, for example where a few individuals dominate reproductive output of the population. This study will help workers to design their experiments (e.g., sample sizes of markers and individuals), and to decide which methods are likely to be most appropriate for their particular data.     

Multilocus population structure of Tapesia yallundae in Washington State

Population genetic structure of the fungal wheat pathogen Tapesia yallundae in Washington State was determined using genetically characterized amplified fragment length polymorphic (AFLP) markers and mating-type (MAT1-1 or MAT1-2). Segregation and linkage relationships among 164 AFLP markers and MAT were analysed using 59 progeny derived from an in vitro cross. Alleles at 158 AFLP loci and the mating-type locus segregated in a 1:1 ratio. Ten unlinked markers were chosen to determine genetic and genotypic diversity and to test the hypothesis of random mating and population differentiation among five subpopulations of T. yallundae representative of the geographical distribution of wheat production in eastern Washington. Among 228 isolates collected, overall gene diversity was high (h = 0.425) and a total of 91 unique multilocus genotypes (MLG) were identified, with 32 MLG occurring at least twice. The overall population genetic structure was consistent with random mating based on the segregation of mating-type, index of association (IA), parsimony tree length permutation test (PTLPT) and genotypic diversity analyses. However, clonal genotypes were found within each subpopulation and were also distributed among the five subpopulations. No significant differences in allele frequencies were found among the five subpopulations for all 10 loci based on contingency table analysis (G2) and Wier & Cockerham's population differentiation statistic theta (theta = -0.008, P = 0.722). T. yallundae appears to consist of a large homogeneous population throughout eastern Washington with both sexual and asexual reproduction contributing to the observed population genetic structure despite no report of sexual fruiting bodies of T. yallundae occurring under natural field conditions.     

The evolution of reproductive isolation in spatially structured populations

Abstract.— Recent models of speciation have incorporated population structure and migration into the classic model of speciation in which reproductive isolation arises as a by-product of divergence. In this paper, we expanded these models to explore the joint effects of migration and population subdivision on speciation in a spatially explicit context. The results of our simulation support previous results concerning the influence of population subdivision on the accumulation of reproductive isolation. The simulation also shows that speciation in subdivided populations occurs most rapidly when subpopulations are not strictly allopatric. These results counter the widespread notion that speciation is most likely to occur in allopatric populations and suggest that there are useful insights to be gained by incorporating increasingly realistic types of population structure into models of speciation.     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Combined next‐generation sequencing and morphology reveal fine‐scale speciation in Crocodile Skinks (Squamata: Scincidae: Tribolonotus)

Next‐generation sequencing has vast potential to revolutionize the fields of phylogenetics and population genetics through its ability to collect genomic scale data sets of thousands of orthologous loci. Despite this potential, other types of data (e.g. morphology, ecology) remain important, particularly for studies endeavouring to delimit species. Here, we integrate next‐generation sequencing with morphology to examine divergence between populations of Tribolonotus pseudoponceleti on the islands of Buka and Bougainville in the Solomon Archipelago. We used the Ion Torrent PGM to collect over 648 Mbp of sequence data for 12 samples, representing 1526 loci recovered from all samples, and 3342 were recovered from at least six samples. Genetic structure analyses strongly support the distinctiveness of these two populations, and Bayes factor delimitations decisively select speciation between Buka and Bougainville. Principal components and discriminant function analyses reveal concordant morphological divergence. Finally, demographic analyses via diffusion approximation and approximate Bayesian computation prefer a complex model of mid‐Pleistocene divergence with migration, and a later decrease or cessation of migration and population size shift, suggesting a scenario in which migration was enabled by Pleistocene merging of these two islands, and limited when isolated by higher sea levels. Further analysis of four Sanger sequenced loci in IMa2 had limited power to distinguish among models including and excluding migration, but resulted in similar population size and divergence time estimates, although with much broader confidence intervals. This study represents a framework for how next‐generation sequencing and morphological data can be combined and leveraged towards validating putative species and testing demographic scenarios for speciation.     

Improved eigenanalysis of discrete subpopulations and admixture using the minimum average partial test

Principal components analysis of genetic data has benefited from advances in random matrix theory. The Tracy-Widom distribution has been identified as the limiting distribution of the lead eigenvalue, enabling formal hypothesis testing of population structure. Additionally, a phase change exists between small and large eigenvalues, such that population divergence below a threshold of F(ST) is impossible to detect and above which it is always detectable. I show that the plug-in estimate of the effective number of markers in the EIGENSOFT software often exceeds the rank of the sample covariance matrix, leading to a systematic overestimation of the number of significant principal components. I describe an alternative plug-in estimate that eliminates the problem. This improvement is not just an asymptotic result but is directly applicable to finite samples. The minimum average partial test, based on minimizing the average squared partial correlation between individuals, can detect population structure at smaller F(ST) values than the corrected test. The minimum average partial test is applicable to both unadmixed and admixed samples, with arbitrary numbers of discrete subpopulations or parental populations, respectively. Application of the minimum average partial test to the 11 HapMap Phase III samples, comprising 8 unadmixed samples and 3 admixed samples, revealed 13 significant principal components.