Microsatellite allele sizes: a simple test to assess their significance on genetic differentiation

The mutation process at microsatellite loci typically occurs at high rates and with stepwise changes in allele sizes, features that may introduce bias when using classical measures of population differentiation based on allele identity (e.g., F(ST), Nei's Ds genetic distance). Allele size-based measures of differentiation, assuming a stepwise mutation process [e.g., Slatkin's R(ST), Goldstein et al.'s (deltamu)(2)], may better reflect differentiation at microsatellite loci, but they suffer high sampling variance. The relative efficiency of allele size- vs. allele identity-based statistics depends on the relative contributions of mutations vs. drift to population differentiation. We present a simple test based on a randomization procedure of allele sizes to determine whether stepwise-like mutations contributed to genetic differentiation. This test can be applied to any microsatellite data set designed to assess population differentiation and can be interpreted as testing whether F(ST) = R(ST). Computer simulations show that the test efficiently identifies which of F(ST) or R(ST) estimates has the lowest mean square error. A significant test, implying that R(ST) performs better than F(ST), is obtained when the mutation rate, mu, for a stepwise mutation process is (a) >/= m in an island model (m being the migration rate among populations) or (b) >/= 1/t in the case of isolated populations (t being the number of generations since population divergence). The test also informs on the efficiency of other statistics used in phylogenetical reconstruction [e.g., Ds and (deltamu)(2)], a nonsignificant test meaning that allele identity-based statistics perform better than allele size-based ones. This test can also provide insights into the evolutionary history of populations, revealing, for example, phylogeographic patterns, as illustrated by applying it on three published data sets.     

Population genetic structure of the endangered tropical tree species Caryocar brasiliense, based on variability at microsatellite loci

We report the population genetic structure of the endangered tropical tree species Caryocar brasiliense, based on variability at 10 microsatellite loci. Additionally, we compare heterozygosity and inbreeding estimates for continuous and fragmented populations and discuss the consequences for conservation. For a total of 314 individuals over 10 populations, the number of alleles per locus ranged from 20 to 27 and expected and observed heterozygosity varied from 0.129 to 0.924 and 0.067 to 1.000, respectively. Significant values of theta and R(ST) showed important genetic differentiation among populations. theta was much lower than R(ST), suggesting that identity by state and identity by descent have diverged in these populations. Although a significant amount of inbreeding was found under the identity by descent model (f = 0.11), an estimate of inbreeding for microsatellite markers based on a more adequate stepwise mutation model showed no evidence of nonrandom mating (R(IS) = 0.04). Differentiation (pairwise F(ST)) was positively correlated with geographical distance, as expected under the isolation by distance model. No effect of fragmentation on heterozygosity or inbreeding could be detected. This is most likely due to the fact that Cerrado fragmentation is a relatively recent event (approximately 60 years) compared to the species life cycle. Also, the populations surveyed from both fragmented and disturbed areas were composed mainly of adult individuals, already present prior to ecosystem fragmentation. Adequate hypothesis testing of the effect of habitat fragmentation will require the recurrent analysis of juveniles across generations in both fragmented and nonfragmented areas.     

A comparison of two indirect methods for estimating average levels of gene flow using microsatellite data

We compare the performance of Nm estimates based on FST and RST obtained from microsatellite data using simulations of the stepwise mutation model with range constraints in allele size classes. The results of the simulations suggest that the use of microsatellite loci can lead to serious overestimations of Nm, particularly when population sizes are large (N > 5000) and range constraints are high (K < 20). The simulations also indicate that, when population sizes are small (N /= 50) and many loci (nl >/= 20), RST performs better than FST for most of the parameter space. However, FST-based estimates are always better than RST when sample sizes are moderate or small (ns 相似文献   

Equilibrium Values of Measures of Population Subdivision for Stepwise Mutation Processes

Expected values of WRIGHT's F-statistics are functions of probabilities of identity in state. These values may be quite different under an infinite allele model and under stepwise mutation processes such as those occurring at microsatellite loci. However, a relationship between the probability of identity in state in stepwise mutation models and the distribution of coalescence times can be deduced from the relationship between probabilities of identity by descent and the distribution of coalescence times. The values of F(IS) and F(ST) can be computed using this property. Examination of the conditional probability of identity in state given some coalescence time and of the distribution of coalescence times are also useful for explaining the properties of F(IS) and F(ST) at high mutation rate loci, as shown here in an island model of population structure.     

Comparing relative rates of pollen and seed gene flow in the island model using nuclear and organelle measures of population structure

We describe a method for comparing nuclear and organelle population differentiation (F(ST)) in seed plants to test the hypothesis that pollen and seed gene flow rates are equal. Wright's infinite island model is used, with arbitrary levels of self-fertilization and biparental organelle inheritance. The comparison can also be applied to gene flow in animals. Since effective population sizes are smaller for organelle genomes than for nuclear genomes and organelles are often uniparentally inherited, organelle F(ST) is expected to be higher at equilibrium than nuclear F(ST) even if pollen and seed gene flow rates are equal. To reject the null hypothesis of equal seed and pollen gene flow rates, nuclear and organelle F(ST)'s must differ significantly from their expected values under this hypothesis. Finite island model simulations indicate that infinite island model expectations are not greatly biased by finite numbers of populations (>/=100 subpopulations). The power to distinguish dissimilar rates of pollen and seed gene flow depends on confidence intervals for fixation index estimates, which shrink as more subpopulations and loci are sampled. Using data from the tropical tree Corythophora alta, we rejected the null hypothesis that seed and pollen gene flow rates are equal but cannot reject the alternative hypothesis that pollen gene flow is 200 times greater than seed gene flow.     

Comparisons of likelihood and machine learning methods of individual classification

Classification methods used in machine learning (e.g., artificial neural networks, decision trees, and k-nearest neighbor clustering) are rarely used with population genetic data. We compare different nonparametric machine learning techniques with parametric likelihood estimations commonly employed in population genetics for purposes of assigning individuals to their population of origin ("assignment tests"). Classifier accuracy was compared across simulated data sets representing different levels of population differentiation (low and high F(ST)), number of loci surveyed (5 and 10), and allelic diversity (average of three or eight alleles per locus). Empirical data for the lake trout (Salvelinus namaycush) exhibiting levels of population differentiation comparable to those used in simulations were examined to further evaluate and compare classification methods. Classification error rates associated with artificial neural networks and likelihood estimators were lower for simulated data sets compared to k-nearest neighbor and decision tree classifiers over the entire range of parameters considered. Artificial neural networks only marginally outperformed the likelihood method for simulated data (0-2.8% lower error rates). The relative performance of each machine learning classifier improved relative likelihood estimators for empirical data sets, suggesting an ability to "learn" and utilize properties of empirical genotypic arrays intrinsic to each population. Likelihood-based estimation methods provide a more accessible option for reliable assignment of individuals to the population of origin due to the intricacies in development and evaluation of artificial neural networks.     

Microsatellite genetic variation in small and isolated populations of Magnolia sieboldii ssp. japonica

Magnolia sieboldii ssp. japonica, distributed mainly in western Japan, is restricted to high elevation areas (1000-2000 m above sea level) and usually forms small isolated populations. Four microsatellite loci were assayed for 19 populations from six regions spanning the range of distribution, and the levels and distribution of genetic variation were estimated. All four loci were variable, with a total of 39 alleles, but the overall level of microsatellite genetic variation was low, especially compared with a related species, M. obovata. Genetic structure in M. sieboldii was characterised by low intrapopulational genetic variation (A = 3.74 and H(o) = 0.366 on average) and high genetic differentiation even among regional populations. Highly significant isolation-by-distance (IBD) models at the short distance were detected. Genetic drift and limited gene flow was considered to be important in determining the genetic structure within regions. Total genetic differentiation was remarkably high (F(ST) = 0.488 and R(ST) = 0.538), suggesting genetic barriers among regions. Neighbour-joining dendrograms relating the 19 populations, and further analysis on the IBD models, revealed that a stepwise mutation model was more suited than an infinite allele model to explain the genetic differentiation among regions. It is suggested that mutation at microsatellite loci might be influential in generating the genetic differentiation among regions. These results showed the potential of hypervariable microsatellite loci to evaluate the effects of genetic drift and population isolation within regions, and to detect genetic distinctiveness, in spite of the loss of overall genetic variation in M. sieboldii.     

Allele Frequencies at Microsatellite Loci: The Stepwise Mutation Model Revisited

We summarize available data on the frequencies of alleles at microsatellite loci in human populations and compare observed distributions of allele frequencies to those generated by a simulation of the stepwise mutation model. We show that observed frequency distributions at 108 loci are consistent with the results of the model under the assumption that mutations cause an increase or decrease in repeat number by one and under the condition that the product Nu, where N is the effective population size and u is the mutation rate, is larger than one. We show that the variance of the distribution of allele sizes is a useful estimator of Nu and performs much better than previously suggested estimators for the stepwise mutation model. In the data, there is no correlation between the mean and variance in allele size at a locus or between the number of alleles and mean allele size, which suggests that the mutation rate at these loci is independent of allele size.     

Measuring population differentiation using GST or D? A simulation study with microsatellite DNA markers under a finite island model and nonequilibrium conditions

The genetic differentiation of populations is a key parameter in population genetic investigations. Wright's F(ST) (and its relatives such as G(ST) ) has been a standard measure of differentiation. However, the deficiencies of these indexes have been increasingly realized in recent years, leading to some new measures being proposed, such as Jost's D (Molecular Ecology, 2008; 17, 4015). The existence of these new metrics has stimulated considerable debate and induced some confusion on which statistics should be used for estimating population differentiation. Here, we report a simulation study with neutral microsatellite DNA loci under a finite island model to compare the performance of G(ST) and D, particularly under nonequilibrium conditions. Our results suggest that there exist fundamental differences between the two statistics, and neither G(ST) nor D operates satisfactorily in all situations for quantifying differentiation. D is very sensitive to mutation models but G(ST) noticeably less so, which limits D's utility in population parameter estimation and comparisons across genetic markers. Also, the initial heterozygosity of the starting populations has some important effects on both the individual behaviours of G(ST) and D and their relative behaviours in early differentiation, and this effect is much greater for D than G(ST) . In the early stages of differentiation, when initial heterozygosity is relatively low (<0.5, if the number of subpopulations is large), G(ST) increases faster than D; the opposite is true when initial heterozygosity is high. Therefore, the state of the ancestral population appears to have some lasting impacts on population differentiation. In general, G(ST) can measure differentiation fairly well when heterozygosity is low whatever the causes; however, when heterozygosity is high (e.g. as a result of either high mutation rate or high initial heterozygosity) and gene flow is moderate to strong, G(ST) fails to measure differentiation. Interestingly, when population size is not very small (e.g. N ≥ 1000), G(ST) measures differentiation quite linearly with time over a long duration when gene flow is absent or very weak even if mutation rate is not low (e.g. μ = 0.001). In contrast, D, as a differentiation measure, performs rather robustly in all these situations. In practice, both indexes should be calculated and the relative levels of heterozygosities (especially H(S) ) and gene flow taken into account. We suggest that a comparison of the two indexes can generate useful insights into the evolutionary processes that influence population differentiation.     

Joint estimation of contemporary seed and pollen dispersal rates among plant populations

There are few statistical methods for estimating contemporary dispersal among plant populations. A maximum-likelihood procedure is introduced here that uses pre- and post-dispersal population samples of biparentally inherited genetic markers to jointly estimate contemporary seed and pollen immigration rates from a set of discrete external sources into a target population. Monte Carlo simulations indicate that accurate estimates and reliable confidence intervals can be obtained using this method for both pollen and seed migration rates at modest sample sizes (100 parents/population and 100 offspring) when population differentiation is moderate (F(ST) ≥ 0.1), or by increasing pre-dispersal samples (to about 500 parents/population) when genetic divergence is weak (F(ST) = 0.01). The method exhibited low sensitivity to the number of source populations and achieved good accuracy at affordable genetic resolution (10 loci with 10 equifrequent alleles each). Unsampled source populations introduced positive biases in migration rate estimates from sampled sources, although they were minor when the proportion of immigration from the latter was comparatively low. A practical application of the method to a metapopulation of the Australian resprouter shrub Banksia attenuata revealed comparable levels of directional seed and pollen migration among dune groups, and the estimate of seed dispersal was higher than a previous estimate based on conservative assignment tests. The method should be of interest to researchers and managers assessing broad-scale nonequilibrium seed and pollen gene flow dynamics in plants.     

A maximum-likelihood method for the estimation of pairwise relatedness in structured populations

A maximum-likelihood estimator for pairwise relatedness is presented for the situation in which the individuals under consideration come from a large outbred subpopulation of the population for which allele frequencies are known. We demonstrate via simulations that a variety of commonly used estimators that do not take this kind of misspecification of allele frequencies into account will systematically overestimate the degree of relatedness between two individuals from a subpopulation. A maximum-likelihood estimator that includes F(ST) as a parameter is introduced with the goal of producing the relatedness estimates that would have been obtained if the subpopulation allele frequencies had been known. This estimator is shown to work quite well, even when the value of F(ST) is misspecified. Bootstrap confidence intervals are also examined and shown to exhibit close to nominal coverage when F(ST) is correctly specified.     

Microsatellite null alleles and estimation of population differentiation

Microsatellite null alleles are commonly encountered in population genetics studies, yet little is known about their impact on the estimation of population differentiation. Computer simulations based on the coalescent were used to investigate the evolutionary dynamics of null alleles, their impact on F(ST) and genetic distances, and the efficiency of estimators of null allele frequency. Further, we explored how the existing method for correcting genotype data for null alleles performed in estimating F(ST) and genetic distances, and we compared this method with a new method proposed here (for F(ST) only). Null alleles were likely to be encountered in populations with a large effective size, with an unusually high mutation rate in the flanking regions, and that have diverged from the population from which the cloned allele state was drawn and the primers designed. When populations were significantly differentiated, F(ST) and genetic distances were overestimated in the presence of null alleles. Frequency of null alleles was estimated precisely with the algorithm presented in Dempster et al. (1977). The conventional method for correcting genotype data for null alleles did not provide an accurate estimate of F(ST) and genetic distances. However, the use of the genetic distance of Cavalli-Sforza and Edwards (1967) corrected by the conventional method gave better estimates than those obtained without correction. F(ST) estimation from corrected genotype frequencies performed well when restricted to visible allele sizes. Both the proposed method and the traditional correction method have been implemented in a program that is available free of charge at http://www.montpellier.inra.fr/URLB/. We used 2 published microsatellite data sets based on original and redesigned pairs of primers to empirically confirm our simulation results.     

G'ST and D do not replace FST

The genetic differentiation among populations is affected by mutation as well as by migration, drift and selection. For loci with high mutation rates, such as microsatellites, the amount of mutation can influence the values of indices of differentiation such as G(ST) and F(ST). For many purposes, this effect is undesirable, and as a result, new indices such as G'(ST) and D have been proposed to measure population differentiation. This paper shows that these new indices are not effective measures of the causes or consequences of population structure. Both G'(ST) and D depend heavily on mutation rate, but both are insensitive to any population genetic process when the mutation rate is high relative to the migration rate. Furthermore, D is specific to the locus being measured, and so little can be inferred about the population demography from D. However, at equilibrium, D may provide an index of whether a particular marker is more strongly affected by mutation than by migration. I argue that F(ST) is a more important summary of the effects of population structure than D and that R(ST) or other measures that explicitly account for the mutation process are much better than G(ST), G'(ST), or D for highly mutable markers. Markers with lower mutation rates will often be easier to interpret.     

Power for detecting genetic divergence: differences between statistical methods and marker loci

Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G-test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general.     

Molecular and quantitative genetic differentiation across Europe in yellow dung flies

Relating geographic variation in quantitative traits to underlying population structure is crucial for understanding processes driving population differentiation, isolation and ultimately speciation. Our study represents a comprehensive population genetic survey of the yellow dung fly Scathophaga stercoraria, an important model organism for evolutionary and ecological studies, over a broad geographic scale across Europe (10 populations from the Swiss Alps to Iceland). We simultaneously assessed differentiation in five quantitative traits (body size, development time, growth rate, proportion of diapausing individuals and duration of diapause), to compare differentiation in neutral marker loci (F(ST)) to that of quantitative traits (Q(ST)). Despite long distances and uninhabitable areas between sampled populations, population structuring was very low but significant (F(ST) = 0.007, 13 microsatellite markers; F(ST) = 0.012, three allozyme markers; F(ST) = 0.007, markers combined). However, only two populations (Iceland and Sweden) showed significant allelic differentiation to all other populations. We estimated high levels of gene flow [effective number of migrants (Nm) = 6.2], there was no isolation by distance, and no indication of past genetic bottlenecks (i.e. founder events) and associated loss of genetic diversity in any northern or island population. In contrast to the low population structure, quantitative traits were strongly genetically differentiated among populations, following latitudinal clines, suggesting that selection is responsible for life history differentiation in yellow dung flies across Europe.     

Microsatellites can be misleading: an empirical and simulation study

Abstract. It has been long recognized that highly polymorphic genetic markers can lead to underestimation of divergence between populations when migration is low. Microsatellite loci, which are characterized by extremely high mutation rates, are particularly likely to be affected. Here, we report genetic differentiation estimates in a contact zone between two chromosome races of the common shrew ( Sorex araneus ), based on 10 autosomal microsatellites, a newly developed Y-chromosome microsatellite, and mitochondrial DNA. These results are compared to previous data on proteins and karyotypes. Estimates of genetic differentiation based on F - and R -statistics are much lower for autosomal microsatellites than for all other genetic markers. We show by simulations that this discrepancy stems mainly from the high mutation rate of microsatellite markers for F -statististics and from deviations from a single-step mutation model for R -statistics. The sex-linked genetic markers show that all gene exchange between races is mediated by females. The absence of male-mediated gene flow most likely results from male hybrid sterility.     

Joint estimation of migration rate and effective population size using the island model

Using the island model of population demography, I report that the demographic parameters migration rate and effective population size can be jointly estimated with equilibrium probabilities of identity in state calculated using a sample of genotypes collected at a single point in time from a single generation. The method, which uses moment-type estimators, applies to dioecious populations in which females and males have identical demography and monoecious populations with no selfing and requires that offspring genotypes are sampled following reproduction and prior to migration. I illustrate the estimation procedure using the infinite-island model with no mutation and the finite-island model with three kinds of mutation models. In the infinite-island model with no mutation, the estimators can be expressed as simple functions of estimates of the F-statistic parameters F(IT) and F(ST). In the finite-island model with mutation among k alleles, mutation rate, migration rate, and effective population size can be simultaneously estimated. The estimates of migration rate and effective population size are somewhat robust to violations in assumptions that may arise in empirical applications such as different kinds of mutation models and deviations from temporal equilibrium.     

The effects of dominance, regular inbreeding and sampling design on Q(ST), an estimator of population differentiation for quantitative traits

To test whether quantitative traits are under directional or homogenizing selection, it is common practice to compare population differentiation estimates at molecular markers (F(ST)) and quantitative traits (Q(ST)). If the trait is neutral and its determinism is additive, then theory predicts that Q(ST) = F(ST), while Q(ST) > F(ST) is predicted under directional selection for different local optima, and Q(ST) < F(ST) is predicted under homogenizing selection. However, nonadditive effects can alter these predictions. Here, we investigate the influence of dominance on the relation between Q(ST) and F(ST) for neutral traits. Using analytical results and computer simulations, we show that dominance generally deflates Q(ST) relative to F(ST). Under inbreeding, the effect of dominance vanishes, and we show that for selfing species, a better estimate of Q(ST) is obtained from selfed families than from half-sib families. We also compare several sampling designs and find that it is always best to sample many populations (>20) with few families (five) rather than few populations with many families. Provided that estimates of Q(ST) are derived from individuals originating from many populations, we conclude that the pattern Q(ST) > F(ST), and hence the inference of directional selection for different local optima, is robust to the effect of nonadditive gene actions.     

Evidence for fine-scale genetic structure and estuarine colonisation in a potential high gene flow marine goby (Pomatoschistus minutus)

Marine fish seem to experience evolutionary processes that are expected to produce genetically homogeneous populations. We have assessed genetic diversity and differentiation in 15 samples of the sand goby Pomatoschistus minutus (Pallas, 1770) (Gobiidae, Teleostei) from four major habitats within the Southern Bight of the North Sea, using seven microsatellite and 13 allozyme loci. Despite its high dispersal potential, microsatellite loci revealed a moderate level of differentiation (overall F(ST)=0.026; overall R(ST)=0.058). Both hierarchical analysis of molecular variance and multivariate analysis revealed significant differentiation (P<0.01) between estuarine, coastal and marine samples with microsatellites, but not with allozymes. Comparison among the different estimators of differentiation (F(ST) and R(ST)) pointed to possible historical events and contemporary habitat fragmentation. Samples were assigned to two breeding units in the estuary and coastal region. Despite this classification, there were indications of a complex and dynamic spatiotemporal structure, which is, most likely, determined by historical events and local oceanic currents.     

Equilibrium between genetic drift and migration at various mutation rates: simulation analysis

Rates of approach to equilibrium values of F(ST)/R(ST) at various mutation rates and using different mutation models (K-allele model KAM and stepwise model SMM) were analyzed numerically for the finite island model and the one-dimensional stepping stone models of migration, using simulation. In the island model of migration and the KAM mutation model, the rate of approach to the equilibrium F(ST) value was appreciably higher and the equilibrium value was almost twofold lower at micro (mutation rate) = m (migration rate) than at micro < m. In the one-dimensional stepping stone model of migration and the KAM model of mutation, the mutation rate significantly affected both the rate of approaching F(ST) equilibrium and the equilibrium value. In both island and one-dimensional stepping stone models and SMM, R(ST) was not influenced by various mutation rates. The rate of approach to the equilibrium values of both F(ST) and R(ST) was lower for the stepping stone model than to the island model. RST was rather resistant to deviations from the SMM mutation model.