Estimating population structure in diploids with multilocus dominant DNA markers

Multilocus DNA markers [random amplified polymorphic DNA (RAPDs), amplified fragment length polymorphism (AFLPs)] are important for population studies because they reveal many polymorphic loci distributed over the genome. The markers are dominant, that is two phenotypes are distinguished at each locus, with a band and with no band. The latter one represents null-homozygotes with unamplified, recessive null-alleles. The frequency of a null-allele can be estimated by taking the square root of the fraction of individuals with no band. Lynch and Milligan (1994) have suggested a modified procedure that reduces bias introduced by the square-root transform. However, the procedure recommends to ignore those samples in which fewer than four null-homozygotes are observed. This may lead to significant bias in estimates of genetic diversity. In this study, I introduce a Bayesian approach to estimation of null-allele frequencies for dominant DNA markers. It follows from computer simulations and data on two conifer species that the Bayesian method gives nearly unbiased estimates of heterozygosity, genetic distances and F-statistics. The influence of a prior distribution and departure from Hardy-Weinberg proportions on the estimates is also considered.     

Genetic Diversity and Differentiation in Hedychium spicatum, a Valuable Medicinal Plant of Indian Himalaya

Hedychium spicatum, a perennial rhizomatous medicinal plant distributed in subtropical and temperate parts, is considered nearly endemic to the Himalayan region.In this study allozyme markers were utilized to assess genetic variations and relationships among 12 distinct populations of this species from the West Himalaya of India. A high level of genetic diversity was found among the populations. Of the 13 loci generated using eight enzymes, 12 (92%) were polymorphic. F-statistics suggested a prevalence of a high heterozygote excess among populations (F(IS) = -0.51). Gene flow estimates and geographic distances between populations did not correlate significantly (r = -0.0258, P < 0.3550). The excess heterozygosity may be attributed to high pollinator mobility and inbreeding coefficient within the subpopulation, relative to the total F(IS) value. High frequencies of several alleles at different loci probably reflect the breeding pattern, as the species propagates clonally as well as through seeds. We also discuss conservation implications for the target species.     

An approximate Bayesian computation approach to overcome biases that arise when using amplified fragment length polymorphism markers to study population structure

There is great interest in using amplified fragment length polymorphism (AFLP) markers because they are inexpensive and easy to produce. It is, therefore, possible to generate a large number of markers that have a wide coverage of species genomes. Several statistical methods have been proposed to study the genetic structure using AFLPs but they assume Hardy-Weinberg equilibrium and do not estimate the inbreeding coefficient, F(IS). A Bayesian method has been proposed by Holsinger and colleagues that relaxes these simplifying assumptions but we have identified two sources of bias that can influence estimates based on these markers: (i) the use of a uniform prior on ancestral allele frequencies and (ii) the ascertainment bias of AFLP markers. We present a new Bayesian method that avoids these biases by using an implementation based on the approximate Bayesian computation (ABC) algorithm. This new method estimates population-specific F(IS) and F(ST) values and offers users the possibility of taking into account the criteria for selecting the markers that are used in the analyses. The software is available at our web site (http://www-leca.ujf-grenoble.fr/logiciels.htm). Finally, we provide advice on how to avoid the effects of ascertainment bias.     

Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.     

A Bayesian approach to inferring population structure from dominant markers

Molecular markers derived from polymerase chain reaction (PCR) amplification of genomic DNA are an important part of the toolkit of evolutionary geneticists. Random amplified polymorphic DNA markers (RAPDs), amplified fragment length polymorphisms (AFLPs) and intersimple sequence repeat (ISSR) polymorphisms allow analysis of species for which previous DNA sequence information is lacking, but dominance makes it impossible to apply standard techniques to calculate F-statistics. We describe a Bayesian method that allows direct estimates of FST from dominant markers. In contrast to existing alternatives, we do not assume previous knowledge of the degree of within-population inbreeding. In particular, we do not assume that genotypes within populations are in Hardy-Weinberg proportions. Our estimate of FST incorporates uncertainty about the magnitude of within-population inbreeding. Simulations show that samples from even a relatively small number of loci and populations produce reliable estimates of FST. Moreover, some information about the degree of within-population inbreeding (FIS) is available from data sets with a large number of loci and populations. We illustrate the method with a reanalysis of RAPD data from 14 populations of a North American orchid, Platanthera leucophaea.     

Nei's to Bayes': comparing computational methods and genetic markers to estimate patterns of genetic variation in Tolpis (Asteraceae)

Accurate determination of patterns of genetic variation provides a powerful inferential tool for studies of evolution and conservation. For more than 30 years, enzyme electrophoresis was the preferred method for elucidating these patterns. As a result, evolutionary geneticists have acquired considerable understanding of the relationship between patterns of allozyme variation and aspects of evolutionary process. Myriad molecular markers and statistical analyses have since emerged, enabling improved estimates of patterns of genetic diversity. With these advances, there is a need to evaluate results obtained with different markers and analytical methods. We present a comparative study of gene statistic estimates (F(ST), G(ST), F(IS), H(S), and H(T)) calculated from an intersimple sequence repeat (ISSR) and an allozyme data set derived from the same populations using both standard and Bayesian statistical approaches. Significant differences were found between estimates, owing to the effects of marker and analysis type. Most notably, F(ST) estimates for codominant data differ between Bayesian and standard approaches. Levels of statistical significance are greatly affected by methodology and, in some cases, are not associated with similar levels of biological significance. Our results suggest that caution should be used in equating or comparing results obtained using different markers and/or methods of analysis.     

The effective founder effect in a spatially expanding population

The gradual loss of diversity and the establishment of clines in allele frequencies associated with range expansions are patterns observed in many species, including humans. These patterns can result from a series of founder events occurring as populations colonize previously unoccupied areas. We develop a model of an expanding population and, using a branching process approximation, show that spatial gradients reflect different amounts of genetic drift experienced by different subpopulations. We then use this model to measure the net average strength of the founder effect, and we demonstrate that the predictions from the branching process model fit simulation results well. We further show that estimates of the effective founder size are robust to potential confounding factors such as migration between subpopulations. We apply our method to data from Arabidopsis thaliana. We find that the average founder effect is approximately three times larger in the Americas than in Europe, possibly indicating that a more recent, rapid expansion occurred.     

Random amplified polymorphic DNA diversity of marginal and central populations in Pinus contorta subsp. latifolia.

Fifteen populations of lodgepole pine (Pinus contorta subsp. latifolia) were surveyed for diversity across 52 random amplified polymorphic DNAs (RAPDs). The objective was to compare single-locus and multilocus structures in four marginal, three intermediate, and eight central populations. Single-locus estimates indicated average observed and expected heterozygosity to be 0.19 and 0.17, respectively. When these estimates were split into population categories, a clear trend of increasing diversity was detected in the direction of marginal to central populations. F-statistics indicated an excess of heterozygotes, with F(IS) ranging from -0.08 for marginal populations to -0.15 for central populations and averaging -0.12 over 15 populations. The estimates of F(ST) decreased towards the margins of the species range, indicating increased population differentiation. Forty-nine of 52 RAPDs tested neutral in the Ewens-Watterson analysis. Multilocus analysis showed significant two-locus and high-order gametic disequilibria in all 15 populations. The most prominent components of the two-locus analysis were the variance of disequilibrium (VD, 46.2%) and the multilocus Wahlund effect (31.9%). This high value for VD indicated that founder effects could explain much of the observed multilocus associations. When analyzed by population categories, the VD showed a decreasing trend indicating that variation due to founder effects was more prominent in marginal populations. The two-locus Wahlund effect (WC) that is characteristic of strong population subdivision was highest in the central populations. This indicated significant levels of gene flow between populations with different allelic combinations.     

Population structure, effective population size and adverse effects of stocking in the endangered Australian eastern freshwater cod Maccullochella ikei

Microsatellite markers were used to examine spatio-temporal genetic variation in the endangered eastern freshwater cod Maccullochella ikei in the Clarence River system, eastern Australia. High levels of population structure were detected. A model-based clustering analysis of multilocus genotypes identified four populations that were highly differentiated by F-statistics (F(ST) = 0·09 - 0·49; P < 0·05), suggesting fragmentation and restricted dispersal particularly among upstream sites. Hatchery breeding programmes were used to re-establish locally extirpated populations and to supplement remnant populations. Bayesian and frequency-based analyses of hatchery fingerling samples provided evidence for population admixture in the hatchery, with the majority of parental stock sourced from distinct upstream sites. Comparison between historical and contemporary wild-caught samples showed a significant loss of heterozygosity (21%) and allelic richness (24%) in the Mann and Nymboida Rivers since the commencement of stocking. Fragmentation may have been a causative factor; however, temporal shifts in allele frequencies suggest swamping with hatchery-produced M. ikei has contributed to the genetic decline in the largest wild population. This study demonstrates the importance of using information on genetic variation and population structure in the management of breeding and stocking programmes, particularly for threatened species.     

A model-based method for identifying species hybrids using multilocus genetic data

We present a statistical method for identifying species hybrids using data on multiple, unlinked markers. The method does not require that allele frequencies be known in the parental species nor that separate, pure samples of the parental species be available. The method is suitable for both markers with fixed allelic differences between the species and markers without fixed differences. The probability model used is one in which parentals and various classes of hybrids (F(1)'s, F(2)'s, and various backcrosses) form a mixture from which the sample is drawn. Using the framework of Bayesian model-based clustering allows us to compute, by Markov chain Monte Carlo, the posterior probability that each individual belongs to each of the distinct hybrid classes. We demonstrate the method on allozyme data from two species of hybridizing trout, as well as on two simulated data sets.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. II. Combining prior knowledge with experimental evidence

Summary A Bayesian method was developed for identifying genetic markers linked to quantitative trait loci (QTL) by analyzing data from daughter or granddaughter designs and single markers or marker pairs. Traditional methods may yield unrealistic results because linkage tests depend on number of markers and QTL gene effects associated with selected markers are overestimated. The Bayesian or posterior probability of linkage combines information from a daughter or granddaughter design with the prior probability of linkage between a marker locus and a QTL. If the posterior probability exceeds a certain quantity, linkage is declared. Upon linkage acceptance, Bayesian estimates of marker-QTL recombination rate and QTL gene effects and frequencies are obtained. The Bayesian estimates of QTL gene effects account for different amounts of information by shrinking information from data toward the mean or mode of a prior exponential distribution of gene effects. Computation of the Bayesian analysis is feasible. Exact results are given for biallelic QTL, and extensions to multiallelic QTL are suggested.     

Patterns of differentiation in a colour polymorphism and in neutral markers reveal rapid genetic changes in natural damselfly populations

The existence and mode of selection operating on heritable adaptive traits can be inferred by comparing population differentiation in neutral genetic variation between populations (often using F(ST) values) with the corresponding estimates for adaptive traits. Such comparisons indicate if selection acts in a diversifying way between populations, in which case differentiation in selected traits is expected to exceed differentiation in neutral markers [F(ST )(selected) > F(ST )(neutral)], or if negative frequency-dependent selection maintains genetic polymorphisms and pulls populations towards a common stable equilibrium [F(ST) (selected) < F(ST) (neutral)]. Here, we compared F(ST) values for putatively neutral data (obtained using amplified fragment length polymorphism) with estimates of differentiation in morph frequencies in the colour-polymorphic damselfly Ischnura elegans. We found that in the first year (2000), population differentiation in morph frequencies was significantly greater than differentiation in neutral loci, while in 2002 (only 2 years and 2 generations later), population differentiation in morph frequencies had decreased to a level significantly lower than differentiation in neutral loci. Genetic drift as an explanation for population differentiation in morph frequencies could thus be rejected in both years. These results indicate that the type and/or strength of selection on morph frequencies in this system can change substantially between years. We suggest that an approach to a common equilibrium morph frequency across all populations, driven by negative frequency-dependent selection, is the cause of these temporal changes. We conclude that inferences about selection obtained by comparing F(ST) values from neutral and adaptive genetic variation are most useful when spatial and temporal data are available from several populations and time points and when such information is combined with other ecological sources of data.     

An evaluation of prior influence on the predictive ability of Bayesian model averaging

Model averaging is gaining popularity among ecologists for making inference and predictions. Methods for combining models include Bayesian model averaging (BMA) and Akaike’s Information Criterion (AIC) model averaging. BMA can be implemented with different prior model weights, including the Kullback–Leibler prior associated with AIC model averaging, but it is unclear how the prior model weight affects model results in a predictive context. Here, we implemented BMA using the Bayesian Information Criterion (BIC) approximation to Bayes factors for building predictive models of bird abundance and occurrence in the Chihuahuan Desert of New Mexico. We examined how model predictive ability differed across four prior model weights, and how averaged coefficient estimates, standard errors and coefficients’ posterior probabilities varied for 16 bird species. We also compared the predictive ability of BMA models to a best single-model approach. Overall, Occam’s prior of parsimony provided the best predictive models. In general, the Kullback–Leibler prior, however, favored complex models of lower predictive ability. BMA performed better than a best single-model approach independently of the prior model weight for 6 out of 16 species. For 6 other species, the choice of the prior model weight affected whether BMA was better than the best single-model approach. Our results demonstrate that parsimonious priors may be favorable over priors that favor complexity for making predictions. The approach we present has direct applications in ecology for better predicting patterns of species’ abundance and occurrence.     

Estimating polygenic effects using markers of the entire genome

Molecular markers have been used to map quantitative trait loci. However, they are rarely used to evaluate effects of chromosome segments of the entire genome. The original interval-mapping approach and various modified versions of it may have limited use in evaluating the genetic effects of the entire genome because they require evaluation of multiple models and model selection. Here we present a Bayesian regression method to simultaneously estimate genetic effects associated with markers of the entire genome. With the Bayesian method, we were able to handle situations in which the number of effects is even larger than the number of observations. The key to the success is that we allow each marker effect to have its own variance parameter, which in turn has its own prior distribution so that the variance can be estimated from the data. Under this hierarchical model, we were able to handle a large number of markers and most of the markers may have negligible effects. As a result, it is possible to evaluate the distribution of the marker effects. Using data from the North American Barley Genome Mapping Project in double-haploid barley, we found that the distribution of gene effects follows closely an L-shaped Gamma distribution, which is in contrast to the bell-shaped Gamma distribution when the gene effects were estimated from interval mapping. In addition, we show that the Bayesian method serves as an alternative or even better QTL mapping method because it produces clearer signals for QTL. Similar results were found from simulated data sets of F(2) and backcross (BC) families.     

Genetic diversity and multilocus structure in sexual Otiorhynchus alpicola populations (Goleoptera: Gurculionidae)

Otiorhynchus alpicola Boh. (Coleoptera: Curculionidae) is distributed on high mountains of central, southern and south-eastern Europe. On the Balkan peninsula, this species is patchily distributed on mountain peaks at heights over 1800 m. To examine the organization of isoenzyme variation of the ten sexual (diploid) populations, starch gel electrophoresis of enzymes was used. The average heterozygosity over 14 gene loci was 0.11. For diploid O. alpicola, F-statistics were used to assess population heterogeneity and substructuring. The data indicate that, compared with other insects, this high-altitude weevil species is genetically very differentiated (the average F _ST= 0.35). In addition, gene-flow among populations was extremely low (the estimates of N_em from Wright's F _ST and Slatkin private-allele methods were 0.47 and 0.83, respectively). Pairwise linkage disequilibrium (LD) parameters were estimated from zygotic frequencies using Burrows' method. The average rate of significant LD in analysed populations of O. alpicola was about 27%. The pattern of LD over the diploid populations indicates that stochastic factors might be a primary cause of the observed multilocus associations.     

Genetic variability and founder effect in the pitcher plant Sarracenia purpurea (Sarraceniaceae) in populations introduced into Switzerland: from inbreeding to invasion

BACKGROUND AND AIMS: The long-lived and mainly outcrossing species Sarracenia purpurea has been introduced into Switzerland and become invasive. This creates the opportunity to study reactions to founder effect and how a species can circumvent deleterious effects of bottlenecks such as reduced genetic diversity, inbreeding and extinction through mutational meltdown, to emerge as a highly invasive plant. METHODS: A population genetic survey by random amplified polymorphism DNA markers (RAPD) together with historical insights and a field pollination experiment were carried out. KEY RESULTS: At the regional scale, S. purpurea shows low structure (thetast=0.072) due to a recent founder event and important subsequent growth. Nevertheless, multivariate statistical analyses reveal that, because of a bottleneck that shifted allele frequencies, most of the variability is independent among populations. In one population (Tenasses) the species has become invasive and genetic analysis reveals restricted gene flow and family structure (thetast=0.287). Although inbreeding appears to be high (Fis >0.410 from a Bayesian estimation), a field pollination experiment failed to detect significant inbreeding depression upon F1 seed number and seed weight fitness-traits. Furthermore, crosses between unrelated individuals produced F1 seeds with significantly reduced fitness, thus showing local outbreeding depression. CONCLUSIONS: The results suggest that, under restricted gene flow among families, the species may not only have rapidly purged deleterious alleles, but also have undergone some form of selection for inbreeding due to co-adaptation between loci.     

Robustness of compound Dirichlet priors for Bayesian inference of branch lengths

We modified the phylogenetic program MrBayes 3.1.2 to incorporate the compound Dirichlet priors for branch lengths proposed recently by Rannala, Zhu, and Yang (2012. Tail paradox, partial identifiability and influential priors in Bayesian branch length inference. Mol. Biol. Evol. 29:325-335.) as a solution to the problem of branch-length overestimation in Bayesian phylogenetic inference. The compound Dirichlet prior specifies a fairly diffuse prior on the tree length (the sum of branch lengths) and uses a Dirichlet distribution to partition the tree length into branch lengths. Six problematic data sets originally analyzed by Brown, Hedtke, Lemmon, and Lemmon (2010. When trees grow too long: investigating the causes of highly inaccurate Bayesian branch-length estimates. Syst. Biol. 59:145-161) are reanalyzed using the modified version of MrBayes to investigate properties of Bayesian branch-length estimation using the new priors. While the default exponential priors for branch lengths produced extremely long trees, the compound Dirichlet priors produced posterior estimates that are much closer to the maximum likelihood estimates. Furthermore, the posterior tree lengths were quite robust to changes in the parameter values in the compound Dirichlet priors, for example, when the prior mean of tree length changed over several orders of magnitude. Our results suggest that the compound Dirichlet priors may be useful for correcting branch-length overestimation in phylogenetic analyses of empirical data sets.     

Genetic Differentiation and Estimation of Gene Flow from F-Statistics under Isolation by Distance

I reexamine the use of isolation by distance models as a basis for the estimation of demographic parameters from measures of population subdivision. To that aim, I first provide results for values of F-statistics in one-dimensional models and coalescence times in two-dimensional models, and make more precise earlier results for F-statistics in two-dimensional models and coalescence times in one-dimensional models. Based on these results, I propose a method of data analysis involving the regression of F(ST)/(1 - F(ST)) estimates for pairs of subpopulations on geographic distance for populations along linear habitats or logarithm of distance for populations in two-dimensional habitats. This regression provides in principle an estimate of the product of population density and second moment of parental axial distance. In two cases where comparison to direct estimates is possible, the method proposed here is more satisfactory than previous indirect methods.     

Exact moment calculations for genetic models with migration,mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. In addition, we provide closed-form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.     

Bayesian inference of genetic parameters for ultrasound scanning traits of Kivircik lambs

Ultrasound scanning traits have been adapted in selection programs in many countries to improve carcass traits for lean meat production. As the genetic parameters of the traits interested are important for breeding programs, the estimation of these parameters was aimed at the present investigation. The estimated parameters were direct and maternal heritability as well as genetic correlations between the studied traits. The traits were backfat thickness (BFT), skin+backfat thickness (SBFT), eye muscle depth (MD) and live weights at the day of scanning (LW). The breed investigated was Kivircik, which has a high quality of meat. Six different multi-trait animal models were fitted to determine the most suitable model for the data using Bayesian approach. Based on deviance information criterion, a model that includes direct additive genetic effects, maternal additive genetic effects, direct maternal genetic covariance and maternal permanent environmental effects revealed to be the most appropriate for the data, and therefore, inferences were built on the results of that model. The direct heritability estimates for BFT, SBFT, MD and LW were 0.26, 0.26, 0.23 and 0.09, whereas the maternal heritability estimates were 0.27, 0.27, 0.24 and 0.20, respectively. Negative genetic correlations were obtained between direct and maternal effects for BFT, SBFT and MD. Both direct and maternal genetic correlations between traits were favorable, whereas BFT–MD and SBFT–MD had negligible direct genetic correlation. The highest direct and maternal genetic correlations were between BFT and SBFT (0.39) and between MD and LW (0.48), respectively. Our results, in general, indicated that maternal effects should be accounted for in estimation of genetic parameters of ultrasound scanning traits in Kivircik lambs, and SBFT can be used as a selection criterion to improve BFT.