Statistical properties of population differentiation estimators under stepwise mutation in a finite island model

Microsatellite loci mutate at an extremely high rate and are generally thought to evolve through a stepwise mutation model. Several differentiation statistics taking into account the particular mutation scheme of the microsatellite have been proposed. The most commonly used is R(ST) which is independent of the mutation rate under a generalized stepwise mutation model. F(ST) and R(ST) are commonly reported in the literature, but often differ widely. Here we compare their statistical performances using individual-based simulations of a finite island model. The simulations were run under different levels of gene flow, mutation rates, population number and sizes. In addition to the per locus statistical properties, we compare two ways of combining R(ST) over loci. Our simulations show that even under a strict stepwise mutation model, no statistic is best overall. All estimators suffer to different extents from large bias and variance. While R(ST) better reflects population differentiation in populations characterized by very low gene-exchange, F(ST) gives better estimates in cases of high levels of gene flow. The number of loci sampled (12, 24, or 96) has only a minor effect on the relative performance of the estimators under study. For all estimators there is a striking effect of the number of samples, with the differentiation estimates showing very odd distributions for two samples.     

Phylogeography of chamois (Rupicapra spp.) inferred from microsatellites

Evolutionary relationships among populations of chamois (Rupicapra spp.) across their current range from the Caucasus to the Cantabrian Mountains were investigated. The allelic variation in 23 microsatellite loci was assessed in eight geographical populations, recognised as subspecies of the two closely related species R. pyrenaica and R. rupicapra. Analysis of variance in allele frequencies (Fst, statistics) and in repeat numbers (Rst, statistics) showed these data to be highly structured. Two genetic distances between pairs of populations, Ds and (deltamu)(2), were computed and phylogenetic trees were constructed. Similar patterns were produced by the different statistics. All trees indicate a deep divergence between the two recognised species, which is compatible with archaeological data that place their split in the Riss-Würm interglacial period. Genetic distances between pairs of populations are highly correlated with geographical distance. This suggests that the history of the genus during Pleistocene glacial-interglacial periods was dominated by expansions and contractions within limited geographic regions, leading to alternate contact and isolation of contiguous populations. In addition, the alpine barrier has played a substantial role in West-East differentiation.     

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.     

Genetic structure in the coral-reef-associated Banggai cardinalfish, Pterapogon kauderni

In this study, we used 11 polymorphic microsatellite loci to show that oceanic distances as small as 2-5 km are sufficient to produce high levels of population genetic structure (multilocus F(ST) as high as 0.22) in the Banggai cardinalfish (Pterapogon kauderni), a heavily exploited reef fish lacking a pelagic larval dispersal phase. Global F(ST) among all populations, separated by a maximum distance of 203 km, was 0.18 (R(ST) = 0.35). Moreover, two lines of evidence suggest that estimates of F(ST) may actually underestimate the true level of genetic structure. First, within-locus F(ST) values were consistently close to the theoretical maximum set by the average within-population heterozygosity. Second, the allele size permutation test showed that R(ST) values were significantly larger than F(ST) values, indicating that populations have been isolated long enough for mutation to have played a role in generating allelic variation among populations. The high level of microspatial structure observed in this marine fish indicates that life history traits such as lack of pelagic larval phase and a good homing ability do indeed play a role in shaping population genetic structure in the marine realm.     

POLYSAT: an R package for polyploid microsatellite analysis

We present an R package to help remedy the lack of software for manipulating and analysing autopolyploid and allopolyploid microsatellite data. POLYSAT can handle genotype data of any ploidy, including populations of mixed ploidy, and assumes that allele copy number is always ambiguous in partial heterozygotes. It can import and export genotype data in eight different formats, calculate pairwise distances between individuals using a stepwise mutation and infinite alleles model, estimate ploidy based on allele counts and estimate allele frequencies and pairwise F(ST) values. This software is freely available through the Comprehensive R Archive Network (http://cran.r-project.org/) and includes a thorough tutorial.     

Deriving evolutionary relationships among populations using microsatellites and (deltamu)(2): all loci are equal,but some are more equal than others..

Numerous studies have relied on microsatellite DNA data to assess the relationships among populations in a phylogenetic framework, converting microsatellite allelic composition of populations into evolutionary distances. Among other coefficients, (deltamu)(2) and R(st) are often employed because they make use of the differences in allele sizes on the basis of the stepwise mutation model. While it has been recognized that some microsatellites can yield disproportionate interpopulation distance estimates, no formal investigation has been conducted to evaluate to what extent such loci could affect the topology of the corresponding dendrograms. Here we show that single loci, displaying extremely large among-population variance, can greatly bias the topology of the phylogenetic tree, using data from European grayling (Thymallus thymallus, Salmonidae) populations. Importantly, we also demonstrate that the inclusion of a single disproportionate locus will lead to an overestimation of the stability of trees assessed using bootstrapping. To avoid this bias, we introduce a simple statistical test for detecting loci with significantly disproportionate variance prior to phylogenetic analyses and further show that exclusion of offending loci eliminates the false increase in phylogram stability.     

Microsatellite variation in colonizing and palearctic populations of Drosophila subobscura

The recent colonization of North America by Drosophila subobscura has provided a great opportunity to analyze a colonization process from the beginning. A comparative study using 10 microsatellite loci was conducted for five European and two North American populations. No genetic differentiation between European populations was detected, indicating that gene flow is high among them and that the microsatellites used in the present work represent neutral markers not subject to differentiation due to selection. Extensive reduction in the number of alleles and a significant decrease in heterozygosity in colonizing populations were detected that could be explained by the founder effect and a subsequent quick but not infinite expansion. Assuming that all alleles present in the colonized area were carried by the sample of colonizers, we estimated that most probably 4-11 individuals expanded in the new area. F(ST) and the chord distance measures reflect the colonization process more accurately, since drift has been the major force in differentiating the Old and New World populations, and thus other measures considering allele size differences, such as Rho(ST) and deltamu2, are less reliable for studying nonequilibrium populations. Finally, our results were consistent with the two-phase microsatellite mutational model, indicating that most alleles are generated by gain or loss of a repeat unit, while some alleles originate by more complex mutations.     

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.     

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.     

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.     

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.     

If FST does not measure neutral genetic differentiation,then comparing it with QST is misleading. Or is it?

The comparison between neutral genetic differentiation (F(ST) ) and quantitative genetic differentiation (Q(ST) ) is commonly used to test for signatures of selection in population divergence. However, there is an ongoing discussion about what F(ST) actually measures, even resulting in some alternative metrics to express neutral genetic differentiation. If there is a problem with F(ST) , this could have repercussions for its comparison with Q(ST) as well. We show that as the mutation rate of the neutral marker increases, F(ST) decreases: a higher within-population heterozygosity (He) yields a lower F(ST) value. However, the same is true for Q(ST) : a higher mutation rate for the underlying QTL also results in a lower Q(ST) estimate. The effect of mutation rate is equivalent in Q(ST) and F(ST) . Hence, the comparison between Q(ST) and F(ST) remains valid, if one uses neutral markers whose mutation rates are not too high compared to those of quantitative traits. Usage of highly variable neutral markers such as hypervariable microsatellites can lead to serious biases and the incorrect inference that divergent selection has acted on populations. Much of the discussion on F(ST) seems to stem from the misunderstanding that it measures the differentiation of populations, whereas it actually measures the fixation of alleles. In their capacity as measures of population differentiation, Hedrick's G'(ST) and Jost's D reach their maximum value of 1 when populations do not share alleles even when there remains variation within populations, which invalidates them for comparisons with Q(ST) .     

New methods employing multilocus genotypes to select or exclude populations as origins of individuals

A new method for assigning individuals of unknown origin to populations, based on the genetic distance between individuals and populations, was compared to two existing methods based on the likelihood of multilocus genotypes. The distribution of the assignment criterion (genetic distance or genotype likelihood) for individuals of a given population was used to define the probability that an individual belongs to the population. Using this definition, it becomes possible to exclude a population as the origin of an individual, a useful extension of the currently available assignment methods. Using simulated data based on the coalescent process, the different methods were evaluated, varying the time of divergence of populations, the mutation model, the sample size, and the number of loci. Likelihood-based methods (especially the Bayesian method) always performed better than distance methods. Other things being equal, genetic markers were always more efficient when evolving under the infinite allele model than under the stepwise mutation model, even for equal values of the differentiation parameter F(st). Using the Bayesian method, a 100% correct assignment rate can be achieved by scoring ca. 10 microsatellite loci (H approximately 0.6) on 30-50 individuals from each of 10 populations when the F(st) is near 0.1.     

Contrasting microsatellite variation between subalpine and western larch, two closely related species with different distribution patterns

Subalpine larch (Larix lyallii Parl.) and western larch (Larix occidentalis Nutt.) represent two closely related species with contrasting abundance and distribution patterns in Western North America. Genetic diversity at seven informative microsatellite loci was determined for 19 populations of subalpine larch and nine populations of western larch. Contrasting genetic diversity and patterns of population differentiation were observed between the two species. The overall within-population genetic diversity parameters were lower in subalpine larch (A = 3.2; A(P) = 3.6; H(E) = 0.418) than in western larch (A(P) = 5.51; H(E) = 0.580), a pattern that is likely related to historical or demographic factors. No evidence of interspecific hybridization was observed. Significantly more population differentiation (theta = 0.15; R(ST) = 0.07), consistent with more restricted gene flow, was observed for subalpine larch as compared to western larch (theta = 0.05; R(ST) = 0.04). Under the assumption of an infinite allele mutation model, 12 of the 19 subalpine larch populations showed signs of deviation from the mutation-drift equilibrium, which suggests Holocene population bottlenecks and fluctuations in effective population size for this species. None of the western larch populations deviated significantly from the mutation-drift equilibrium. For both species, Mantel's test revealed a significant positive relationship between geographical and genetic distances indicative of isolation by distance. A similar geographical structure was detected in both species, suggesting at least two genetically distinct glacial populations in each species. The various implications for gene conservation are discussed.     

The complex biogeographic history of a widespread tropical tree species

Many tropical forest tree species have broad geographic ranges, and fossil records indicate that population disjunctions in some species were established millions of years ago. Here we relate biogeographic history to patterns of population differentiation, mutational and demographic processes in the widespread rainforest tree Symphonia globulifera using ribosomal (ITS) and chloroplast DNA sequences and nuclear microsatellite (nSSR) loci. Fossil records document sweepstakes dispersal origins of Neotropical S. globulifera populations from Africa during the Miocene. Despite historical long-distance gene flow, nSSR differentiation across 13 populations from Costa Rica, Panama, Ecuador (east and west of Andes) and French Guiana was pronounced (F(ST)= 0.14, R(ST)= 0.39, P < 0.001) and allele-size mutations contributed significantly (R(ST) > F(ST)) to the divergences between cis- and trans-Andean populations. Both DNA sequence and nSSR data reflect contrasting demographic histories in lower Mesoamerica and Amazonia. Amazon populations show weak phylogeographic structure and deviation from drift-mutation equilibrium indicating recent population expansion. In Mesoamerica, genetic drift was strong and contributed to marked differentiation among populations. The genetic structure of S. globulifera contains fingerprints of drift-dispersal processes and phylogeographic footprints of geological uplifts and sweepstakes dispersal.     

Microsatellite size homoplasy, SSCP, and population structure: a case study in the freshwater snail Bulinus truncatus

The extent of microsatellite size homoplasy, as well as its effect on several population genetics statistics, was investigated in natural populations using the single-strand conformation polymorphism (SSCP) method. The analysis was conducted using 240 individuals from 13 populations of the freshwater snail Bulinus truncatus at a GT(n)CT(m) compound microsatellite locus. We showed that SSCP can be used to uncover, at least partly, size homoplasy in the core sequence of this category of loci. Eight conformers (SSCP variants) were detected among the three size variants (electromorphs). Sequencing revealed that each conformer corresponded to a different combination of repeats in the GT(n) and CT(m) arrays. Part of this additional variability was detected within populations, resulting in a substantial increase in gene diversity in four populations. Additional variability also changed the values of parameters used to analyze population differentiation among populations: pairwise tests of differentiation were significant much more often with conformers than with electromorphs. On the other hand, pairwise estimates of F(st) were either smaller or larger with conformers than with electromorphs, depending on whether or not electromorphs were shared among populations. However, estimates of F(st) (or analogs) over all populations were very similar, ranging between 0.66 and 0.75. Our results were consistent with the theoretical prediction that homoplasy should not always lead to stronger population structure. Finally, conformer sequences and electromorph size distribution suggested that single-point and/or stepwise mutations occurring simultaneously in the different repeated arrays of compound microsatellites produce sequence variation without size variation and hence generate more size homoplasy than expected under a simple stepwise mutation model.     

Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance

In numerous species, individual dispersal is restricted in space so that "continuous" populations evolve under isolation by distance. A method based on individual genotypes assuming a lattice population model was recently developed to estimate the product Dsigma2, where D is the population density and sigma2 is the average squared parent-offspring distance. We evaluated the influence on this method of both mutation rate and mutation model, with a particular reference to microsatellite markers, as well as that of the spatial scale of sampling. Moreover, we developed and tested a nonparametric bootstrap procedure allowing the construction of confidence intervals for the estimation of Dsigma2. These two objectives prompted us to develop a computer simulation algorithm based on the coalescent theory giving individual genotypes for a continuous population under isolation by distance. Our results show that the characteristics of mutational processes at microsatellite loci, namely the allele size homoplasy generated by stepwise mutations, constraints on allele size, and change of slippage rate with repeat number, have little influence on the estimation of Dsigma2. In contrast, a high genetic diversity (approximately 0.7-0.8), as is commonly observed for microsatellite markers, substantially increases the precision of the estimation. However, very high levels of genetic diversity (>0.85) were found to bias the estimation. We also show that statistics taking into account allele size differences give unreliable estimations (i.e., high variance of Dsigma2 estimation) even under a strict stepwise mutation model. Finally, although we show that this method is reasonably robust with respect to the sampling scale, sampling individuals at a local geographical scale gives more precise estimations of Dsigma2.     

A program to compare genetic differentiation statistics across loci using resampling of individuals and loci

Comparisons of genetic differentiation across populations based on different loci can provide insight into the evolutionary patterns acting on various regions of genomes. Here, we develop a program to statistically compare population genetic differentiation statistics (F(ST) or G'(ST) ) calculated from different loci. The program employs a routine that resamples either or both of individuals and loci and calculates a bootstrap confidence interval in the statistics. Resampling individuals is important when fewer than 25 individuals are sampled per population and when confidence intervals are required for individual loci. Resampling loci provides confidence intervals for sets of loci, such as a set presumed to be neutral, but can be anticonservative if fewer than 20 loci are analysed. We demonstrate the program using previously published data on the genetic differentiation at a major histocompatibility complex locus and at microsatellite loci across 10 populations of the guppy (Poecilia reticulata).     

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.     

On the size distribution of private microsatellite alleles

Private microsatellite alleles tend to be found in the tails rather than in the interior of the allele size distribution. To explain this phenomenon, we have investigated the size distribution of private alleles in a coalescent model of two populations, assuming the symmetric stepwise mutation model as the mode of microsatellite mutation. For the case in which four alleles are sampled, two from each population, we condition on the configuration in which three distinct allele sizes are present, one of which is common to both populations, one of which is private to one population, and the third of which is private to the other population. Conditional on this configuration, we calculate the probability that the two private alleles occupy the two tails of the size distribution. This probability, which increases as a function of mutation rate and divergence time between the two populations, is seen to be greater than the value that would be predicted if there was no relationship between privacy and location in the allele size distribution. In accordance with the prediction of the model, we find that in pairs of human populations, the frequency with which private microsatellite alleles occur in the tails of the allele size distribution increases as a function of genetic differentiation between populations.