Microsatellite behavior with range constraints: parameter estimation and improved distances for use in phylogenetic reconstruction

The complex Y-chromosomal history of gorillas

Studies of the evolutionary relationships among gorilla populations using autosomal and mitochondrial sequences suggest that male-mediated gene flow may have been important in the past, but data on the Y-chromosomal relationships among the gorilla subspecies are limited. Here, we genotyped blood and noninvasively collected fecal samples from 12 captives and 257 wild male gorillas of known origin representing all four subspecies (Gorilla gorilla gorilla, G. g. diehli, G. beringei beringei, and G. b. graueri) at 10 Y-linked microsatellite loci resulting in 102 unique Y-haplotypes for 224 individuals. We found that western lowland gorilla (G. g. gorilla) haplotypes were consistently more diverse than any other subspecies for all measures of diversity and comprised several genetically distinct groups. However, these did not correspond to geographical proximity and some closely related haplotypes were found several hundred kilometers apart. Similarly, our broad sampling of eastern gorillas revealed that mountain (G. b. beringei) and Grauer's (G. b. graueri) gorilla Y-chromosomal haplotypes did not form distinct clusters. These observations suggest structure in the ancestral population with subsequent mixing of differentiated haplotypes by male dispersal for western lowland gorillas, and postisolation migration or incomplete lineage sorting due to short divergence times for eastern gorillas.

Stabilizing selection on microsatellite allele length at arginine vasopressin 1a receptor and oxytocin receptor loci

The loci arginine vasopressin receptor 1a (avpr1a) and oxytocin receptor (oxtr) have evolutionarily conserved roles in vertebrate social and sexual behaviour. Allelic variation at a microsatellite locus in the 5′ regulatory region of these genes is associated with fitness in the bank vole Myodes glareolus. Given the low frequency of long and short alleles at these microsatellite loci in wild bank voles, we used breeding trials to determine whether selection acts against long and short alleles. Female bank voles with intermediate length avpr1a alleles had the highest probability of breeding, while male voles whose avpr1a alleles were very different in length had reduced probability of breeding. Moreover, there was a significant interaction between male and female oxtr genotypes, where potential breeding pairs with dissimilar length alleles had reduced probability of breeding. These data show how genetic variation at microsatellite loci associated with avpr1a and oxtr is associated with fitness, and highlight complex patterns of selection at these loci. More widely, these data show how stabilizing selection might act on allele length frequency distributions at gene-associated microsatellite loci.

Microsatellite evolutionary rate and pattern in Schistocerca gregaria inferred from direct observation of germline mutations

Unravelling variation among taxonomic orders regarding the rate of evolution in microsatellites is crucial for evolutionary biology and population genetics research. The mean mutation rate of microsatellites tends to be lower in arthropods than in vertebrates, but data are scarce and mostly concern accumulation of mutations in model species. Based on parent-offspring segregations and a hierarchical Bayesian model, the mean rate of mutation in the orthopteran insect Schistocerca gregaria was estimated at 2.1e(-4) per generation per untranscribed dinucleotide locus. This is close to vertebrate estimates and one order of magnitude higher than estimates from species of other arthropod orders, such as Drosophila melanogaster and Daphnia pulex. We also found evidence of a directional bias towards expansions even for long alleles and exceptionally large ranges of allele sizes. Finally, at transcribed microsatellites, the mean rate of mutation was half the rate found at untranscribed loci and the mutational model deviated from that usually considered, with most mutations involving multistep changes that avoid disrupting the reading frame. Our direct estimates of mutation rate were discussed in the light of peculiar biological and genomic features of S. gregaria, including specificities in mismatch repair and the dependence of its activity to allele length. Shedding new light on the mutational dynamics of grasshopper microsatellites is of critical importance for a number of research fields. As an illustration, we showed how our findings improve microsatellite application in population genetics, by obtaining a more precise estimation of S. gregaria effective population size from a published data set based on the same microsatellites.

Development of COS-SNP and HRM markers for high-throughput and reliable haplotype-based detection of Lr14a in durum wheat (Triticum durum Desf.)

Leaf rust (Puccinia triticina Eriks. & Henn.) is a major disease affecting durum wheat production. The Lr14a-resistant gene present in the durum wheat cv. Creso and its derivative cv. Colosseo is one of the best characterized leaf-rust resistance sources deployed in durum wheat breeding. Lr14a has been mapped close to the simple sequence repeat markers gwm146, gwm344 and wmc10 in the distal portion of the chromosome arm 7BL, a gene-dense region. The objectives of this study were: (1) to enrich the Lr14a region with single nucleotide polymorphisms (SNPs) and high-resolution melting (HRM)-based markers developed from conserved ortholog set (COS) genes and from sequenced Diversity Array Technology (DArT(®)) markers; (2) to further investigate the gene content and colinearity of this region with the Brachypodium and rice genomes. Ten new COS-SNP and five HRM markers were mapped within an 8.0 cM interval spanning Lr14a. Two HRM markers pinpointed the locus in an interval of <1.0 cM and eight COS-SNPs were mapped 2.1-4.1 cM distal to Lr14a. Each marker was tested for its capacity to predict the state of Lr14a alleles (in particular, Lr14-Creso associated to resistance) in a panel of durum wheat elite germplasm including 164 accessions. Two of the most informative markers were converted into KASPar(®) markers. Single assay markers ubw14 and wPt-4038-HRM designed for agarose gel electrophoresis/KASPar(®) assays and high-resolution melting analysis, respectively, as well as the double-marker combinations ubw14/ubw18, ubw14/ubw35 and wPt-4038-HRM-ubw35 will be useful for germplasm haplotyping and for molecular-assisted breeding.

Genetic diversity of microsatellite loci in hierarchically structured populations

Microsatellite loci are widely used for investigating patterns of genetic variation within and among populations. Those patterns are in turn determined by population sizes, migration rates, and mutation rates. We provide exact expressions for the first two moments of the allele frequency distribution in a stochastic model appropriate for studying microsatellite evolution with migration, mutation, and drift under the assumption that the range of allele sizes is bounded. Using these results, we study the behavior of several measures related to Wright's F(ST), including Slatkin's R(ST). Our analytical approximations for F(ST) and R(ST) show that familiar relationships between N(e)m and F(ST) or R(ST) hold when the migration and mutation rates are small. Using the exact expressions for F(ST) and R(ST), our numerical results show that, when the migration and mutation rates are large, these relationships no longer hold. Our numerical results also show that the diversity measures most closely related to F(ST) depend on mutation rates, mutational models (stepwise versus two-phase), migration rates, and population sizes. Surprisingly, R(ST) is relatively insensitive to the mutation rates and mutational models. The differing behaviors of R(ST) and F(ST) suggest that properties of the among-population distribution of allele frequencies may allow the roles of mutation and migration in producing patterns of diversity to be distinguished, a topic of continuing investigation.

Inference on population history and model checking using DNA sequence and microsatellite data with the software DIYABC (v1.0)

BACKGROUND

Approximate Bayesian computation (ABC) is a recent flexible class of Monte-Carlo algorithms increasingly used to make model-based inference on complex evolutionary scenarios that have acted on natural populations. The software DIYABC offers a user-friendly interface allowing non-expert users to consider population histories involving any combination of population divergences, admixtures and population size changes. We here describe and illustrate new developments of this software that mainly include (i) inference from DNA sequence data in addition or separately to microsatellite data, (ii) the possibility to analyze five categories of loci considering balanced or non balanced sex ratios: autosomal diploid, autosomal haploid, X-linked, Y-linked and mitochondrial, and (iii) the possibility to perform model checking computation to assess the "goodness-of-fit" of a model, a feature of ABC analysis that has been so far neglected.

RESULTS

We used controlled simulated data sets generated under evolutionary scenarios involving various divergence and admixture events to evaluate the effect of mixing autosomal microsatellite, mtDNA and/or nuclear autosomal DNA sequence data on inferences. This evaluation included the comparison of competing scenarios and the quantification of their relative support, and the estimation of parameter posterior distributions under a given scenario. We also considered a set of scenarios often compared when making ABC inferences on the routes of introduction of invasive species to illustrate the interest of the new model checking option of DIYABC to assess model misfit.

CONCLUSIONS

Our new developments of the integrated software DIYABC should be particularly useful to make inference on complex evolutionary scenarios involving both recent and ancient historical events and using various types of molecular markers in diploid or haploid organisms. They offer a handy way for non-expert users to achieve model checking computation within an ABC framework, hence filling up a gap of ABC analysis. The software DIYABC V1.0 is freely available at http://www1.montpellier.inra.fr/CBGP/diyabc.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother-sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea-Japan land separation.

Bayesian analysis of an admixture model with mutations and arbitrarily linked markers

We introduce here a Bayesian analysis of a classical admixture model in which all parameters are simultaneously estimated. Our approach follows the approximate Bayesian computation (ABC) framework, relying on massive simulations and a rejection-regression algorithm. Although computationally intensive, this approach can easily deal with complex mutation models and partially linked loci, and it can be thoroughly validated without much additional computation cost. Compared to a recent maximum-likelihood (ML) method, the ABC approach leads to similarly accurate estimates of admixture proportions in the case of recent admixture events, but it is found superior when the admixture is more ancient. All other parameters of the admixture model such as the divergence time between parental populations, the admixture time, and the population sizes are also well estimated, unlike the ML method. The use of partially linked markers does not introduce any particular bias in the estimation of admixture, but ML confidence intervals are found too narrow if linkage is not specifically accounted for. The application of our method to an artificially admixed domestic bee population from northwest Italy suggests that the admixture occurred in the last 10-40 generations and that the parental Apis mellifera and A. ligustica populations were completely separated since the last glacial maximum.

The benefits of increasing the number of microsatellites utilized in genetic population studies: an empirical perspective

One of the key issues concerning the application of microsatellite DNA data in evolutionary studies is how the number of loci applied may influence the stability of genetic distances and corresponding phylograms. While computer simulations have suggested that over 30 microsatellites are required for accurate evolutionary inference, we show that a median of only six loci have been generally applied in studies of wild populations. Factors contributing to this contrast include: i) uncertainty regarding the potential benefits that can be gained from a realistic increase in the number of loci used; and ii) the lack of empirical studies assessing the influence of the number of microsatellites on the reliability of genetic distance estimation and phylogeny construction. In order to address these issues, we applied resampling techniques to microsatellite data in widely distributed populations of European grayling (Thymallus thymallus, Salmonidae). In agreement with expectations based on simulated data, we demonstrate empirically that the stability of commonly used genetic distances (DCE, DA and (deltamu)2) and the corresponding neighbor-joining phylograms is positively associated with the number of microsatellites utilized. For instance, increasing the number of loci from six to 17 resulted in a striking 75% increase in the proportion of DCE phylogram nodes supported by a bootstrap estimate of over 70%. Our results demonstrate that even moderately increasing the number of loci can be very beneficial--a finding extremely relevant for studies of natural populations for which optimally high microsatellite numbers are out of reach. Furthermore, the number of loci most commonly used to date may lead to erroneous inference of the evolutionary relationships between populations.

Comparative analysis on the genetic relatedness of Sorghum bicolor accessions from Southern Africa by RAPDs, AFLPs and SSRs

In order to get an overview on the genetic relatedness of sorghum (Sorghum bicolor) landraces and cultivars grown in low-input conditions of small-scale farming systems, 46 sorghum accessions derived from Southern Africa were evaluated on the basis of amplified fragment length polymorphism (AFLPs), random amplified polymorphic DNAs (RAPDs) and simple sequence repeats (SSRs). By this approach all sorghum accessions were uniquely fingerprinted by all marker systems. Mean genetic similarity was estimated at 0.88 based on RAPDs, 0.85 using AFLPs and 0.31 based on SSRs. In addition to this, genetic distance based on SSR data was estimated at 57 according to a stepwise mutation model (Deltamu-SSR). All UPGMA-clusters showed a good fit to the similarity estimates (AFLPs: r = 0.92; RAPDs: r = 0.88; SSRs: r = 0.87; Deltamu-SSRs: r = 0.85). By UPGMA-clustering two main clusters were built on all marker systems comprising landraces on the one hand and newly developed varieties on the other hand. Further sub-groupings were not unequivocal. Genetic diversity (H, DI) was estimated on a similar level within landraces and breeding varieties. Comparing the three approaches to each other, RAPD and AFLP similarity indices were highly correlated (r = 0.81), while the Spearman's rank correlation coefficient between SSRs and AFLPs was r = 0.57 and r = 0.51 between RAPDs and SSRs. Applying a stepwise mutation model on the SSR data resulted in an intermediate correlation coefficient between Deltamu-SSRs and AFLPs (r = 0.66) and RAPDs ( r = 0.67), respectively, while SSRs and Deltamu-SSRs showed a lower correlation coefficient (r = 0.52). The highest bootstrap probabilities were found using AFLPs (56% on average) while SSR, Deltamu-SSR and RAPD-based similarity estimates had low mean bootstrap probabilities (24%, 27%, 30%, respectively). The coefficient of variation (CV) of the estimated genetic similarity decreased with an increasing number of bands and was lowest using AFLPs.

Genetic effects on microsatellite diversity in wild emmer wheat (Triticum dicoccoides) at the Yehudiyya microsite, Israel

This study investigated allele size constraints and clustering, and genetic effects on microsatellite (simple sequence repeat, SSR) diversity at 28 loci comprising seven types of tandem repeated dinucleotide motifs in a natural population of wild emmer wheat, Triticum dicoccoides, from a shade vs sun microsite in Yehudiyya, northeast of the Sea of Galilee, Israel. It was found that allele distribution at SSR loci is clustered and constrained with lower or higher boundary. This may imply that SSR have functional significance and natural constraints. Genetic factors, involving genome, chromosome, motif, and locus significantly affected SSR diversity. Genome B appeared to have a larger average repeat number (ARN), but lower variance in repeat number (sigma(ARN)(2)), and smaller number of alleles per locus than genome A. SSRs with compound motifs showed larger ARN than those with perfect motifs. The effects of replication slippage and recombinational effects (eg, unequal crossing over) on SSR diversity varied with SSR motifs. Ecological stresses (sun vs shade) may affect mutational mechanisms, influencing the level of SSR diversity by both processes.

Homoplasy and mutation model at microsatellite loci and their consequences for population genetics analysis

Homoplasy has recently attracted the attention of population geneticists, as a consequence of the popularity of highly variable stepwise mutating markers such as microsatellites. Microsatellite alleles generally refer to DNA fragments of different size (electromorphs). Electromorphs are identical in state (i.e. have identical size), but are not necessarily identical by descent due to convergent mutation(s). Homoplasy occurring at microsatellites is thus referred to as size homoplasy. Using new analytical developments and computer simulations, we first evaluate the effect of the mutation rate, the mutation model, the effective population size and the time of divergence between populations on size homoplasy at the within and between population levels. We then review the few experimental studies that used various molecular techniques to detect size homoplasious events at some microsatellite loci. The relationship between this molecularly accessible size homoplasy size and the actual amount of size homoplasy is not trivial, the former being considerably influenced by the molecular structure of microsatellite core sequences. In a third section, we show that homoplasy at microsatellite electromorphs does not represent a significant problem for many types of population genetics analyses realized by molecular ecologists, the large amount of variability at microsatellite loci often compensating for their homoplasious evolution. The situations where size homoplasy may be more problematic involve high mutation rates and large population sizes together with strong allele size constraints.

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.

Dynamics of microsatellite divergence under stepwise mutation and proportional slippage/point mutation models

Recently Kruglyak, Durrett, Schug, and Aquadro showed that microsatellite equilibrium distributions can result from a balance between polymerase slippage and point mutations. Here, we introduce an elaboration of their model that keeps track of all parts of a perfect repeat and a simplification that ignores point mutations. We develop a detailed mathematical theory for these models that exhibits properties of microsatellite distributions, such as positive skewness of allele lengths, that are consistent with data but are inconsistent with the predictions of the stepwise mutation model. We use our theoretical results to analyze the successes and failures of the genetic distances (delta(mu))(2) and D(SW) when used to date four divergences: African vs. non-African human populations, humans vs. chimpanzees, Drosophila melanogaster vs. D. simulans, and sheep vs. cattle. The influence of point mutations explains some of the problems with the last two examples, as does the fact that these genetic distances have large stochastic variance. However, we find that these two features are not enough to explain the problems of dating the human-chimpanzee split. One possible explanation of this phenomenon is that long microsatellites have a mutational bias that favors contractions over expansions.

Juxtaposed microsatellite systems as diagnostic markers for admixture: an empirical evaluation with brown trout (Salmo trutta) as model organism

A juxtaposed microsatellite system (JMS) is composed of two microsatellite repeat arrays separated by a sequence of less than 200 bp and more than 20 bp. This paper presents the first empirical evaluation of JMSs for the study of genetic admixture induced by man, with brown trout (Salmo trutta) as model organism. Two distinct admixture situations were studied: native populations from streams of the Atlantic basin and of the Mediterranean basin, respectively, all stocked with domestic strains originating from the Atlantic basin. For these two situations, we first evaluated by simulation the ability of JMSs to differentiate between alien alleles and naturally shared homoplasious or ancestral alleles, and thus to behave as diagnostic markers for admixture. Simulations indicated that JMSs are expected to be reliable diagnostic markers in most divergent (i.e. Mediterranean) populations and nonreliable diagnostic markers in most closely related (i.e. Atlantic) populations. Three JMSs were genotyped in domestic strains as well as in nonstocked and stocked populations of brown trout sampled in different rivers of the Mediterranean and Atlantic basins. The observed distributions of JMS haplotypes were consistent with simulation predictions confirming that JMSs were reliable diagnostic markers only over a given proportion of the species range, i.e. in substantially divergent populations. JMSs also reinforced the diagnostic character of three microsatellite sites for the studied Mediterranean populations. This last result is consistent with our simulation results which showed that, although much less frequently than at JMSs, diagnostic markers are likely to be found at single site microsatellites provided that the native Mediterranean population has a sufficiently small effective population size. For each population of the Mediterranean basin admixture coefficients did not differ significantly across JMSs and mean admixture coefficients sometimes differ among populations. The interpretation of the origin of JMS haplotypes based on the allele length variants was supported by nucleotide sequence analysis.

A test for concordance between the multilocus genealogies of genes and microsatellites in the pathogenic fungus Coccidioides immitis

Uncovering the correct phylogeny of closely related species requires analysis of multiple gene genealogies or, alternatively, genealogies inferred from the multiple alleles found at highly polymorphic loci, such as microsatellites. However, a concern in using microsatellites is that constraints on allele sizes may occur, resulting in homoplasious distributions of alleles, leading to incorrect phylogenies. Seven microsatellites from the pathogenic fungus Coccidioides immitis were sequenced for 20 clinical isolates chosen to represent the known genetic diversity of the pathogen. An organismal phylogeny for C. immitis was inferred from microsatellite-flanking sequence polymorphisms and other restriction fragment length polymorphism-containing loci. Two microsatellite genetic distances were then used to determine phylogenies for C. immitis, and the trees found by these three methods were compared. Congruence between the organismal and microsatellite phylogenies occurred when microsatellite distances were based on simple allele frequency data. However, complex mutation events at some loci made distances based on stepwise mutation models unreliable. Estimates of times of divergence for the two species of C. immitis based on microsatellites were significantly lower than those calculated from flanking sequence, most likely due to constraints on microsatellite allele sizes. Flanking-sequence insertions/deletions significantly decreased the accuracy of genealogical information inferred from microsatellite loci and caused interspecific length homoplasies at one of the seven loci. Our analysis shows that microsatellites are useful phylogenetic markers, although care should be taken to choose loci with appropriate flanking sequences when they are intended for use in evolutionary studies.

An empirical exploration of the (delta mu)2 genetic distance for 213 human microsatellite markers

Microsatellites are now used ubiquitously as genetic markers. One important application is to the assessment of population subdivision and phylogenetic relatedness. Such applications require a method of estimation of genetic distance. Here we examine the most widely used measure of microsatellite genetic distance, Goldstein et al.'s delta-mu squared ([delta mu]2), with respect to a large data set of 213 markers typed across samples from four diverse human populations. We find that (delta mu)2 yields plausible interpopulation distances. For the first time, we report significant interpopulation differences in mean microsatellite length, although the effect of these differences on (delta mu)2 is negligible. However, we also show that the method is extremely sensitive to one or two loci that contribute extreme values, even when a sample size of >200 loci is used. Some of these extreme loci can be removed on the grounds that some alleles carry large indels, but for others there is no clear justification for exclusion a priori. Our data suggest a rather recent African/non-African split, with an upper limit of some 70,000-80,000 years ago.

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 </= 500) and migration rates are moderate (Nm approximately 2), violations to the assumption used to derive the Nm estimators lead to biased results. Under ideal conditions, i.e. large sample sizes (ns >/= 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 </= 10) and the number of loci scored is low (nl < 20). These are the conditions under which many real investigations are carried out and therefore we conclude that in many cases the most conservative approach is to use FST.

Microsatellite and trinucleotide-repeat evolution: evidence for mutational bias and different rates of evolution in different lineages

Microsatellites are stretches of repetitive DNA, where individual repeat units comprise one to six bases. These sequences are often highly polymorphic with respect to repeat number and include trinucleotide repeats, which are abnormally expanded in a number of diseases. It has been widely assumed that microsatellite loci are as likely to gain and lose repeats when they mutate. In this review, we present population genetic and empirical data arguing that microsatellites, including normal alleles at trinucleotide-repeat disease loci, are more likely to expand in length when they mutate. In addition, our experiments suggest that the rates of expansion of such sequences differ in related species.

Single-locus tests of microsatellite evolution: multi-step mutations and constraints on allele size

We evaluate some common simulation procedures as well as a recently developed likelihood method used for testing hypotheses regarding microsatellite evolution. Results from simulated data revealed that the tests for the detection of multi-step mutations in general have some power, whereas tests for the presence of constraints on the repeat number have only very limited power. The tests were applied to population data obtained from nine different baleen whale populations. High agreement was found between results obtained using the simulation-based approach and results obtained using a likelihood ratio test. In four of the nine population samples the tests rejected the one-step mutation model. In two instances the significant deviation was due to excess of heterozygosity and in two instances to a reduced level of heterozygosity relative to the expectations under the stepwise mutation model. The former significant deviation was consistent with occasional multi-step mutations, whereas the latter may indicate the presence of constraints on the number of repeats.