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.     

Enhanced AFLP genome scans detect local adaptation in high-altitude populations of a small rodent (Microtus arvalis)

Adaptation to adverse environmental conditions such as high altitude requires physiological and/or morphological changes. Genome scans provide a means to identify the genetic basis of such adaptations without previous knowledge about the particular genetic variants or traits under selection. In this study, we scanned 3027 amplified fragment length polymorphisms (AFLP) in four populations of the common vole Microtus arvalis for loci associated with local adaptation and high altitude. We investigated voles from two populations at high elevation (~2000 m a.s.l.) representing the upper limit of the altitudinal distribution of the species and two geographically close low-altitude populations (<600 m a.s.l.). Statistical analysis incorporated a new Bayesian F(ST) outlier approach specifically developed for AFLP markers, which considers the intensity of AFLP bands instead of mere presence/absence and allows to derive population-based estimates of allele frequencies and F(IS) values. Computer simulations showed that this approach increases the statistical power of the detection of AFLP markers under selection almost to the power of single nucleotide polymorphism (SNP) data without compromising specificity. Our enhanced genome scan resulted in 20 prime candidate markers for positive selection, which show mostly extremely high allele frequency differences between the low- and high-altitude populations. The comparison of global- and pairwise-enhanced genome scans demonstrated further that very strong selective signatures may also be associated with single populations suggesting the importance of local adaptation in alpine populations of common voles.     

Genetic diversity analysis using lowly polymorphic dominant markers: the example of AFLP in pigs

DNA markers are commonly used for large-scale evaluation of genetic diversity in farm animals, as a component of the management of animal genetic resources. AFLP markers are useful for such studies as they can be generated relatively simply; however, challenges in analysis arise from their dominant scoring and the low level of polymorphism of some markers. This paper describes the results obtained with a set of AFLP markers in a study of 59 pig breeds. AFLP fingerprints were generated using four primer combinations (PC), yielding a total of 148 marker loci, and average harmonic mean of breed sample size was 37.3. The average proportion of monomorphic populations was 63% (range across loci: 3%-98%). The moment-based method of Hill and Weir (2004, Mol Ecol 13:895-908) was applied to estimate gene frequencies, gene diversity (F(ST)), and Reynolds genetic distances. A highly significant average F(ST) of 0.11 was estimated, together with highly significant PC effects on gene diversity. The variance of F(ST) across loci also significantly exceeded the variance expected under the hypothesis of AFLP neutrality, strongly suggesting the sensitivity of AFLP to selection or other forces. Moment estimates were compared to estimates derived from the square root estimation of gene frequency, as currently applied for dominant markers, and the biases incurred in the latter method were evaluated. The paper discusses the hypotheses underlying the moment estimations and various issues relating to the biallelic, dominant, and lowly polymorphic nature of this set of AFLP markers and to their use as compared to microsatellites for measuring genetic diversity.     

Effects of ascertainment bias on recovering human demographic history.

In recent years multilocus data sets have been used to study the demographic history of human populations. In this paper (1) analyses previously done on 60 short tandem repeat (STR) loci are repeated on 30 restriction site polymorphism (RSP) markers; (2) relative population weights are estimated from the RSP data set and compared to previously published estimates from STR and craniometric data sets; and (3) computer simulations are performed to show the effects of ascertainment bias on relative population weight estimates. Not surprisingly, given that the RSP markers were originally identified in a small panel of Caucasians, estimates of relative population weights are biased and the European population weight is artificially inflated. However, the effects of ascertainment bias are not apparent in a principal components plot or estimates of FST. Ascertainment bias can have a large effect in other genetic systems with inherently low heterozygosity such as Alus or single nucleotide polymorphisms (SNPs), and care must be taken to have prior knowledge of how polymorphic markers in a given data set were originally identified. Otherwise, results can be skewed and interpretations faulty.     

Maximum-likelihood and markov chain monte carlo approaches to estimate inbreeding and effective size from allele frequency changes

Maximum-likelihood and Bayesian (MCMC algorithm) estimates of the increase of the Wright-Malécot inbreeding coefficient, F(t), between two temporally spaced samples, were developed from the Dirichlet approximation of allelic frequency distribution (model MD) and from the admixture of the Dirichlet approximation and the probabilities of fixation and loss of alleles (model MDL). Their accuracy was tested using computer simulations in which F(t) = 10% or less. The maximum-likelihood method based on the model MDL was found to be the best estimate of F(t) provided that initial frequencies are known exactly. When founder frequencies are estimated from a limited set of founder animals, only the estimates based on the model MD can be used for the moment. In this case no method was found to be the best in all situations investigated. The likelihood and Bayesian approaches give better results than the classical F-statistics when markers exhibiting a low polymorphism (such as the SNP markers) are used. Concerning the estimations of the effective population size all the new estimates presented here were found to be better than the F-statistics classically used.     

Estimating levels of inbreeding using AFLP markers

In the absence of detailed pedigree records, researchers have attempted to estimate individuals' levels of inbreeding using molecular markers, generally making use of heterozygosity measures based on microsatellite markers. Here we report and validate a method for estimating an individual's inbreeding coefficient, f, using amplified fragment length polymorphism (AFLP) markers. We use simulations to confirm that our measure scales appropriately with f when allele frequencies can be estimated from a subset of outbred individuals. We also present an approach for obtaining satisfactory estimates even in the absence of an independent set of known outbred individuals from which to estimate allele frequencies. We then test our method against empirical data from 179 wild and captive-bred old-field mice, Peromyscus polionotus subgriseus, comprising pedigree-based estimates of f, along with genetic data from 94 AFLP markers and 12 microsatellites. Inbreeding estimates based on both AFLP and microsatellite markers were found to correlate strongly with pedigree-based inbreeding coefficients. Owing to their ease of amplification in any species, AFLP markers may prove to be a valuable new tool for estimating f in natural populations and for examining correlations between heterozygosity and fitness.     

Bayesian statistical treatment of the fluorescence of AFLP bands leads to accurate genetic structure inference

Ever since the introduction of allozymes in the 1960s, evolutionary biologists and ecologists have continued to search for more powerful molecular markers to estimate important parameters such as effective population size and migration rates and to make inferences about the demographic history of populations, the relationships between individuals and the genetic architecture of phenotypic variation (Bensch & Akesson 2005; Bonin et al. 2007). Choosing a marker requires a thorough consideration of the trade-offs associated with the different techniques and the type of data obtained from them. Some markers can be very informative but require substantial amounts of start-up time (e.g. microsatellites), while others require very little time but are much less polymorphic. Amplified fragment length polymorphism (AFLP) is a firmly established molecular marker technique that falls in this latter category. AFLPs are widely distributed throughout the genome and can be used on organisms for which there is no a priori sequence information (Meudt & Clarke 2007). These properties together with their moderate cost and short start-up time have made them the method of choice for many molecular ecology studies of wild species (Bensch & Akesson 2005). However, they have a major disadvantage, they are dominant. This represents a very important limitation because many statistical genetics methods appropriate for molecular ecology studies require the use of codominant markers. In this issue, Foll et al. (2010) present an innovative hierarchical Bayesian method that overcomes this limitation. The proposed approach represents a comprehensive statistical treatment of the fluorescence of AFLP bands and leads to accurate inferences about the genetic structure of natural populations. Besides allowing a quasi-codominant treatment of AFLPs, this new method also solves the difficult problems posed by subjectivity in the scoring of AFLP bands.     

An evaluation of the methods to estimate effective population size from measures of linkage disequilibrium

In 1971, John Sved derived an approximate relationship between linkage disequilibrium (LD) and effective population size for an ideal finite population. This seminal work was extended by Sved and Feldman (Theor Pop Biol 4, 129, 1973) and Weir and Hill (Genetics 95, 477, 1980) who derived additional equations with the same purpose. These equations yield useful estimates of effective population size, as they require a single sample in time. As these estimates of effective population size are now commonly used on a variety of genomic data, from arrays of single nucleotide polymorphisms to whole genome data, some authors have investigated their bias through simulation studies and proposed corrections for different mating systems. However, the cause of the bias remains elusive. Here, we show the problems of using LD as a statistical measure and, analogously, the problems in estimating effective population size from such measure. For that purpose, we compare three commonly used approaches with a transition probability‐based method that we develop here. It provides an exact computation of LD. We show here that the bias in the estimates of LD and effective population size are partly due to low‐frequency markers, tightly linked markers or to a small total number of crossovers per generation. These biases, however, do not decrease when increasing sample size or using unlinked markers. Our results show the issues of such measures of effective population based on LD and suggest which of the method here studied should be used in empirical studies as well as the optimal distance between markers for such estimates.     

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.     

Estimating genetic drift and effective population size from temporal shifts in dominant gene marker frequencies

Measurement of temporal change in allele frequencies represents an indirect method for estimating the genetically effective size of populations. When allele frequencies are estimated for gene markers that display dominant gene expression, such as, e.g. random amplified polymorphic DNA (RAPD) and amplified fragment length polymorphism (AFLP) markers, the estimates can be seriously biased. We quantify bias for previous allele frequency estimators and present a new expression that is generally less biased and provides a more precise assessment of temporal allele frequency change. We further develop an estimator for effective population size that is appropriate when dealing with dominant gene markers. Comparison with estimates based on codominantly expressed genes, such as allozymes or microsatellites, indicates that about twice as many loci or sampled individuals are required when using dominant markers to achieve the same precision.     

Statistical analysis of binary data generated from multilocus dominant DNA markers

The use of methodologies such as RAPD and AFLP for studying genetic variation in natural populations is widespread in the ecology community. Because data generated using these methods exhibit dominance, their statistical treatment is less straightforward. Several estimators have been proposed for estimating population genetic parameters, assuming simple random sampling and the Hardy-Weinberg (HW) law. The merits of these estimators remain unclear because no comparative studies of their theoretical properties have been carried out. Furthermore, ascertainment bias has not been explicitly modelled. Here, we present a comparison of a set of candidate estimators of null allele frequency (q), locus-specific heterozygosity (h) and average heterozygosity () in terms of their bias, standard error, and root mean square error (RMSE). For estimating q and h, we show that none of the estimators considered has the least RMSE over the parameter space. Our proposed zero-correction procedure, however, generally leads to estimators with improved RMSE. Assuming a beta model for the distribution of null homozygote proportions, we show how correction for ascertainment bias can be carried out using a linear transform of the sample average of h and the truncated beta-binomial likelihood. Simulation results indicate that the maximum likelihood and empirical Bayes estimator of have negligible bias and similar RMSE. Ascertainment bias in estimators of is most pronounced when the beta distribution is J-shaped and negligible when the latter is inverse J-shaped. The validity of the current findings depends importantly on the HW assumption-a point that we illustrate using data from two published studies.     

Distribution of Simple Sequence Repeat and AFLP Markers in Molecular Linkage Map of Rice

SSR (simple sequence repeat) and AFLP (amplified fragment length polymorphism) are PCR-based molecular markers developed in recent years. In this study, the authors analyzed the polymorphisms, inheritance and distribution of SSR and AFLP markers using an F2 population from a cross between cultivar "Aijiao Nante" ( Oryza sativa L. ssp. indica) and an accession of the common wild rice ( O. rufipogon Griff). A total of 200 new markers were obtained including 28 SSR and 172 AFLP markers. Six of the 28 SSR markers were developed by National Key Laboratory of Crop Genetic Improvement (NKLCGI) using DNA sequences from GenBank and the other 22 were from data published previously. The 172 AFLP markers were from a total 228 polymorphic bands amplified using 25 selected primer combinations. Mapping of the 200 new markers using NKLCGI' S previously developed RFLP map based on the same F2 population resolved these markers to all 12 rice chromosomes. Integration of the SSR and AFLP markers into the RFLP map resulted in a high density molecular linkage map containing 612 polymorphic loci.     

A resolution of the ascertainment sampling problem. II. Generalizations and numerical results

The ascertainment problem arises when families are sampled by a nonrandom process and some assumption about this sampling process must be made in order to estimate genetic parameters. Under classical ascertainment assumptions, estimation of genetic parameters cannot be separated from estimation of the parameters of the ascertainment process, so that any misspecification of the ascertainment process causes biases in estimation of the genetic parameters. Ewens and Shute proposed a resolution to this problem, involving conditioning the likelihood of the sample on the part of the data which is "relevant to ascertainment." The usefulness of this approach can only be assessed by examining the properties (in particular, bias and standard error) of the estimates which arise by using it for a wide range of parameter values and family size distributions and then comparing these biases and standard errors with those arising under classical ascertainment procedures. These comparisons are carried out in the present paper, and we also compare the proposed method with procedures which condition on, or ignore, parts of the data.     

Identification of a threshold level to assess essential derivation in durum wheat

Essentially derived varieties (EDV) are considered to be those that are obtained from an original variety by means of methods that do not substantially modify its genetic structure, and whose characteristics are therefore derived from the original. The identification of EDV requires the definition of a threshold value of genetic similarity between the new and the original variety that if exceeded would suggest derivation. Although protocols for estimating genetic similarities based on molecular markers have been proposed for EDV identification in some species, no information was available for durum wheat (Triticum durum). A set of 60 genotypes (F8 or F9 lines and their parents) representing different levels of relatedness were profiled using 14 (later reduced to 13 by excluding the most deviant one) amplified fragment length polymorphism (AFLP) primer combinations and 109 simple sequence repeat (SSR) loci evenly distributed in the genome. For both marker types, an EDV threshold was calculated according to the “tail principle” on the distributions of Jaccard similarities among the subset of 39 independent genotypes. For all pairs of closely related lines branched in advanced generations (F7–F8), or for all but one pairs of lines deriving from the same F4 family, similarities exceeded the thresholds for both marker types, indicating a very good agreement in showing cases of suspected derivation. Compared to SSR markers, AFLP markers appear more suitable for assessing essential derivation because of their superior cost-efficiency. Based on 13 AFLP primer combinations, a threshold of 0.96 Jaccard similarity is proposed, below which a variety should be considered to be independently derived.     

The effects of conditioning on probands to correct for multiple ascertainment.

Cannings and Thompson suggested conditioning on the phenotypes of the probands to correct for ascertainment in the analysis of pedigree data. The method assumes single ascertainment and can be expected to yield asymptotically biased parameter estimates except in this specific case. However, because the method is easy to apply, we investigated the degree of bias in the more typical situation of multiple ascertainment, in the hope that the bias might be small and that the method could be applied more generally. To explore the utility of conditioning on probands to correct for multiple ascertainment, we calculated the asymptotic value of the segregation ratio for two versions of the simple Mendelian segregation model on sibship data. For both versions, we found that this asymptotic value decreased approximately linearly as the ascertainment probability increased. When ascertainment was complete, the segregation-ratio estimates were zero, not just asymptotically but for finite sample size as well. In some cases, conditioning on probands actually resulted in greater parameter bias than no ascertainment correction at all. These results hold for a variety of sibship-size distributions, several modes of inheritance, and a wide range of population prevalences of affected individuals.     

Increased inbreeding and strong kinship structure in Taxus baccata estimated from both AFLP and SSR data

Habitat fragmentation can have severe genetic consequences for trees, such as increased inbreeding and decreased effective population size. In effect, local populations suffer from reduction of genetic variation, and thus loss of adaptive capacity, which consequently increases their risk of extinction. In Europe, Taxus baccata is among a number of tree species experiencing strong habitat fragmentation. However, there is little empirical data on the population genetic consequences of fragmentation for this species. This study aimed to characterize local genetic structure in two natural remnants of English yew in Poland based on both amplified fragment length polymorphism (AFLP) and microsatellite (SSR) markers. We introduced a Bayesian approach that estimates the average inbreeding coefficient using AFLP (dominant) markers. Results showed that, in spite of high dispersal potential (bird-mediated seed dispersal and wind-mediated pollen dispersal), English yew populations show strong kinship structure, with a spatial extent of 50–100 m, depending on the population. The estimated inbreeding levels ranged from 0.016 to 0.063, depending on the population and marker used. Several patterns were evident: (1) AFLP markers showed stronger kinship structure than SSRs; (2) AFLP markers provided higher inbreeding estimates than SSRs; and (3) kinship structure and inbreeding were more pronounced in denser populations regardless of the marker used. Our results suggest that, because both kinship structure and (bi-parental) inbreeding exist in populations of English yew, gene dispersal can be fairly limited in this species. Furthermore, at a local scale, gene dispersal intensity can be more limited in a dense population.     

Improving AFLP analysis of large‐scale patterns of genetic variation – a case study with the Central African lianas Haumania spp (Marantaceae) showing interspecific gene flow

AFLP markers are often used to study patterns of population genetic variation and gene flow because they offer a good coverage of the nuclear genome, but the reliability of AFLP scoring is critical. To assess interspecific gene flow in two African rainforest liana species (Haumania danckelmaniana, H. liebrechtsiana) where previous evidence of chloroplast captures questioned the importance of hybridization and species boundaries, we developed new AFLP markers and a novel approach to select reliable bands from their degree of reproducibility. The latter is based on the estimation of the broad‐sense heritability of AFLP phenotypes, an improvement over classical scoring error rates, which showed that the polymorphism of most AFLP bands was affected by a substantial nongenetic component. Therefore, using a quantitative genetics framework, we also modified an existing estimator of pairwise kinship coefficient between individuals correcting for the limited heritability of markers. Bayesian clustering confirms the recognition of the two Haumania species. Nevertheless, the decay of the relatedness between individuals of distinct species with geographic distance demonstrates that hybridization affects the nuclear genome. In conclusion, although we showed that AFLP markers might be substantially affected by nongenetic factors, their analysis using the new methods developed considerably advanced our understanding of the pattern of gene flow in our model species.     

Genetic diversity analysis of elite European maize (Zea mays L.) inbred lines using AFLP, SSR, and SNP markers reveals ascertainment bias for a subset of SNPs

Recent advances in high-throughput sequencing technologies have triggered a shift toward single-nucleotide polymorphism (SNP) markers. A systematic bias can be introduced if SNPs are ascertained in a small panel of genotypes and then used for characterizing a larger population (ascertainment bias). With the objective of evaluating a potential ascertainment bias of the Illumina MaizeSNP50 array with respect to elite European maize dent and flint inbred lines, we compared the genetic diversity among these materials based on 731 amplified fragment length polymorphisms (AFLPs), 186 simple sequence repeats (SSRs), 41,434 SNPs of the MaizeSNP50 array (SNP-A), and two subsets of it, i.e., 30,068 Panzea (SNP-P) and 11,366 Syngenta markers (SNP-S). We evaluated the bias effects on major allele frequency, allele number, gene diversity, modified Roger’s distance (MRD), and on molecular variance (AMOVA). We revealed ascertainment bias in SNP-A, compared to AFLPs and SSRs. It affected especially European flint lines analyzed with markers (SNP-S) specifically developed to maximize differences among North American dent germplasm. The bias affected all genetic parameters, but did not substantially alter the relative distances between inbred lines within groups. For these reasons, we conclude that the SNP markers of the MaizeSNP50 array can be employed for breeding purposes in the investigated material. However, attention should be paid in case of comparisons between genotypes belonging to different heterotic groups. In this case, it is advisable to prefer a marker subset with potentially low ascertainment bias, like in our case the SNP-P marker set.     

Estimating population structure from AFLP amplification intensity

In the last decade, amplified fragment length polymorphisms (AFLPs) have become one of the most widely used molecular markers to study the genetic structure of natural populations. Most of the statistical methods available to study the genetic structure of populations using AFLPs consider these markers as dominant and are thus unable to distinguish between individuals being heterozygous or homozygous for the dominant allele. Some attempts have been made to treat AFLPs as codominant markers by using AFLP band intensities to infer the most likely genotype of each individual. These two approaches have some drawbacks, the former discarding potentially valuable information and the latter being sometimes unable to correctly assign genotypes to individuals. In this study, we propose an alternative likelihood‐based approach, which does not attempt at inferring the genotype of each individual, but rather incorporate the uncertainty about genotypes into a Bayesian framework leading to the estimation of population‐specific F_IS and F_ST coefficients. We show with simulations that the accuracy of our method is much higher than one using AFLP as dominant markers and is generally close to what would be obtained by using the same number of Single‐Nucleotide Polymorphism (SNP) markers. The method is applied to a data set of four populations of the common vole (Microtus arvalis) from Grisons in Switzerland, for which we obtained 562 polymorphic AFLP markers. Our approach is very general and has the potential to make AFLP markers as useful as SNP data for nonmodel species.     

Evaluating the performance of a multilocus Bayesian method for the estimation of migration rates

Bayesian methods have become extremely popular in molecular ecology studies because they allow us to estimate demographic parameters of complex demographic scenarios using genetic data. Articles presenting new methods generally include sensitivity studies that evaluate their performance, but they tend to be limited and need to be followed by a more thorough evaluation. Here we evaluate the performance of a recent method, bayesass , which allows the estimation of recent migration rates among populations, as well as the inbreeding coefficient of each local population. We expand the simulation study of the original publication by considering multi-allelic markers and scenarios with varying number of populations. We also investigate the effect of varying migration rates and F _ST more thoroughly in order to identify the region of parameter space where the method is and is not able to provide accurate estimates of migration rate. Results indicate that if the demographic history of the species being studied fits the assumptions of the inference model, and if genetic differentiation is not too low ( F _ST ≥ 0.05), then the method can give fairly accurate estimates of migration rates even when they are fairly high (about 0.1). However, when the assumptions of the inference model are violated, accurate estimates are obtained only if migration rates are very low ( m  = 0.01) and genetic differentiation is high ( F _ST ≥ 0.10). Our results also show that using posterior assignment probabilities as an indication of how much confidence we can place on the assignments is problematical since the posterior probability of assignment can be very high even when the individual assignments are very inaccurate.