The relationship between microsatellite slippage mutation rate and the number of repeat units

Microsatellite markers are widely used for genetic studies, but the relationship between microsatellite slippage mutation rate and the number of repeat units remains unclear. In this study, microsatellite distributions in the human genome are collected from public sequence databases. We observe that there is a threshold size for slippage mutations. We consider a model of microsatellite mutation consisting of point mutations and single stepwise slippage mutations. From two sets of equations based on two stochastic processes and equilibrium assumptions, we estimate microsatellite slippage mutation rates without assuming any relationship between microsatellite slippage mutation rate and the number of repeat units. We use the least squares method with constraints to estimate expansion and contraction mutation rates. The estimated slippage mutation rate increases exponentially as the number of repeat units increases. When slippage mutations happen, expansion occurs more frequently for short microsatellites and contraction occurs more frequently for long microsatellites. Our results agree with the length-dependent mutation pattern observed from experimental data, and they explain the scarcity of long microsatellites.     

Complex mutations in a high proportion of microsatellite loci from the protozoan parasite Plasmodium falciparum

Microsatellite loci are generally assumed to evolve via a stepwise mutational process and a battery of statistical techniques has been developed in recent years based on this or related mutation models. It is therefore important to investigate the appropriateness of these models in a wide variety of taxa. We used two approaches to examine mutation patterns in the malaria parasite Plasmodium falciparum: (i) we examined sequence variation at 12 tri-nucleotide repeat loci; and (ii) we analysed patterns of repeat structure and heterozygosity at 114 loci using data from 12 laboratory parasite lines. The sequencing study revealed complex patterns of mutation in five of the 12 loci studied. Alleles at two loci contain indels of 24 bp and 57 bp in flanking regions, while in the other three loci, blocks of imperfect microsatellites appear to be duplicated or inserted; these loci essentially consist of minisatellite repeats, with each repeat unit containing four to eight microsatellites. The survey of heterozygosity revealed a positive relationship between repeat number and microsatellite variability for both di- and trinucleotides, indicating a higher mutation rate in loci with longer repeat arrays. Comparisons of levels of variation in different repeat types indicate that the mutation rate of dinucleotide-bearing loci is 1.6-2.1 times faster than trinucleotides, consistent with the lower mean number of repeats in trinucleotide-bearing loci. However, despite the evidence that microsatellite arrays themselves are evolving in a manner consistent with stepwise mutation model in P. falciparum, the high frequency of complex mutations precludes the use of analytical tools based on this mutation model for many microsatellite-bearing loci in this protozoan. The results call into question the generality of models based on stepwise mutation for analysing microsatellite data, but also demonstrate the ease with which loci that violate model assumptions can be detected using minimal sequencing effort.     

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.     

Likelihood-based estimation of microsatellite mutation rates

Microsatellites are widely used in genetic analyses, many of which require reliable estimates of microsatellite mutation rates, yet the factors determining mutation rates are uncertain. The most straightforward and conclusive method by which to study mutation is direct observation of allele transmissions in parent-child pairs, and studies of this type suggest a positive, possibly exponential, relationship between mutation rate and allele size, together with a bias toward length increase. Except for microsatellites on the Y chromosome, however, previous analyses have not made full use of available data and may have introduced bias: mutations have been identified only where child genotypes could not be generated by transmission from parents' genotypes, so that the probability that a mutation is detected depends on the distribution of allele lengths and varies with allele length. We introduce a likelihood-based approach that has two key advantages over existing methods. First, we can make formal comparisons between competing models of microsatellite evolution; second, we obtain asymptotically unbiased and efficient parameter estimates. Application to data composed of 118,866 parent-offspring transmissions of AC microsatellites supports the hypothesis that mutation rate increases exponentially with microsatellite length, with a suggestion that contractions become more likely than expansions as length increases. This would lead to a stationary distribution for allele length maintained by mutational balance. There is no evidence that contractions and expansions differ in their step size distributions.     

Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.     

Microsatellite variability differs between dinucleotide repeat motifs-evidence from Drosophila melanogaster

Recently, the use of microsatellites as genetic markers has become very popular. While their evolutionary dynamics are not yet fully understood, the emerging picture is that several factors are influencing microsatellite mutation rates. Recent experiments demonstrated a significant effect of repeat motif length on microsatellite mutation rates. Here, we studied the influence of the base composition of the microsatellite. Forty-two microsatellite loci on the second chromosome with the three most abundant dinucleotide repeat motifs (TC/AG, AT/TA, GT/CA) were characterized for six different Drosophila melanogaster populations. Applying ANOVA to the variance in repeat number, we found a significant influence of repeat motif on microsatellite variability. Calculating relative mutation rates, GT/CA appears to have the highest mutation rate, and AT/TA appears to have the lowest. Similar differences in mutation rates were obtained by an alternative method which estimates microsatellite mutation rates from their genomic length distribution.     

Mutation and evolution of microsatellite loci in Neurospora

The patterns of mutation and evolution at 13 microsatellite loci were studied in the filamentous fungal genus Neurospora. First, a detailed investigation was performed on five microsatellite loci by sequencing each microsatellite, together with its nonrepetitive flanking regions, from a set of 147 individuals from eight species of Neurospora. To elucidate the genealogical relationships among microsatellite alleles, repeat number was mapped onto trees constructed from flanking-sequence data. This approach allowed the potentially convergent microsatellite mutations to be placed in the evolutionary context of the less rapidly evolving flanking regions, revealing the complexities of the mutational processes that have generated the allelic diversity conventionally assessed in population genetic studies. In addition to changes in repeat number, frequent substitution mutations within the microsatellites were detected, as were substitutions and insertion/deletions within the flanking regions. By comparing microsatellite and flanking-sequence divergence, clear evidence of interspecific allele length homoplasy and microsatellite mutational saturation was observed, suggesting that these loci are not appropriate for inferring phylogenetic relationships among species. In contrast, little evidence of intraspecific mutational saturation was observed, confirming the utility of these loci for population-level analyses. Frequency distributions of alleles within species were generally consistent with the stepwise mutational model. By comparing variation within species at the microsatellites and the flanking-sequence, estimated microsatellite mutation rates were approximately 2500 times greater than mutation rates of flanking DNA and were consistent with estimates from yeast and fruit flies. A positive relationship between repeat number and variance in repeat number was significant across three genealogical depths, suggesting that longer microsatellite alleles are more mutable than shorter alleles. To test if the observed patterns of microsatellite variation and mutation could be generalized, an additional eight microsatellite loci were characterized and sequenced from a subset of the same Neurospora individuals.     

A power analysis of microsatellite-based statistics for inferring past population growth

We present results concerning the power to detect past population growth using three microsatellite-based statistics available in the current literature: (1) that based on between-locus variability, (2) that based on the shape of allele size distribution, and (3) that based on the imbalance between variance and heterozygosity at a locus. The analysis is based on the single-step stepwise mutation model. The power of the statistics is evaluated for constant, as well as variable, mutation rates across loci. The latter case is important, since it is a standard procedure to pool data collected at a number of loci, and mutation rates at microsatellite loci are known to be different. Our analysis indicates that the statistic based on the imbalance between allele size variance and heterozygosity at a locus has the highest power for detection of population growth, particularly when mutation rates vary across loci.     

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.     

New algorithms for Luria-Delbrück fluctuation analysis

Fluctuation analysis is the most widely used approach in estimating microbial mutation rates. Development of methods for point and interval estimation of mutation rates has long been hampered by lack of closed form expressions for the probability mass function of the number of mutants in a parallel culture. This paper uses sequence convolution to derive exact algorithms for computing the score function and observed Fisher information, leading to efficient computation of maximum likelihood estimates and profile likelihood based confidence intervals for the expected number of mutations occurring in a test tube. These algorithms and their implementation in SALVADOR 2.0 facilitate routine use of modern statistical techniques in fluctuation analysis by biologists engaged in mutation research.     

Allelic variation at (TAA)n microsatellite loci in a world collection of chickpea (Cicer arietinum L.) germplasm

A set of 12 randomly selected (TAA)_n microsatellite loci of the cultivated chickpea (Cicer arietinum L.) were screened in a worldwide sample comprising 72 landraces, four improved cultivars and two wild species of the primary gene pool (C. reticulatum and C. echinosperum) to determine the level and pattern of polymorphism in these populations. A single fragment was amplified from all the accessions with each of 12 sequence-tagged microsatellite site markers, except for one locus where no fragment was obtained from either of the two wild species. There was a high degree of intraspecific polymorphism at these microsatellite loci, although isozymes, conventional RFLPs and RAPDs show very little or no polymorphism. Overall, the repeat number at a locus (excluding null alleles) ranged from 7 to 42. The average number of alleles per locus was 14.1 and the average genetic diversity was 0.86. Based on the estimates obtained, 11 out of the 12 frequency distributions of alleles at the loci tested can be considered to be non-normal. A significant positive correlation between the average number of repeats (size of the locus) and the amount of variation was observed, indicating that replication slippage may be the molecular mechanism involved in generation of variability at the loci. A comparison between the infinite allele and stepwise mutation models revealed that for 11 out of the 12 loci the number of alleles observed fell in between the values predicted by the two models. Phylogenetic analysis of microsatellite polymorphism in C. arietinum showed no relationship between accession and geographic origin, which is compatible with the recent expansion of this crop throughout the world. Received: 18 September 1998 / Accepted: 2 December 1998     

Towards Improvements in the Estimation of the Coalescent: Implications for the Most Effective Use of Y Chromosome Short Tandem Repeat Mutation Rates

Over the past two decades, many short tandem repeat (STR) microsatellite loci on the human Y chromosome have been identified together with mutation rate estimates for the individual loci. These have been used to estimate the coalescent age, or the time to the most recent common ancestor (TMRCA) expressed in generations, in conjunction with the average square difference measure (ASD), an unbiased point estimator of TMRCA based upon the average within-locus allele variance between haplotypes. The ASD estimator, in turn, depends on accurate mutation rate estimates to be able to produce good approximations of the coalescent age of a sample. Here, a comparison is made between three published sets of per locus mutation rate estimates as they are applied to the calculation of the coalescent age for real and simulated population samples. A novel evaluation method is developed for estimating the degree of conformity of any Y chromosome STR locus of interest to the strict stepwise mutation model and specific recommendations are made regarding the suitability of thirty-two commonly used Y-STR loci for the purpose of estimating the coalescent. The use of the geometric mean for averaging ASD and across loci is shown to improve the consistency of the resulting estimates, with decreased sensitivity to outliers and to the number of STR loci compared or the particular set of mutation rates selected.     

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.     

Microsatellite Variation in Honey Bee (Apis Mellifera L.) Populations: Hierarchical Genetic Structure and Test of the Infinite Allele and Stepwise Mutation Models

Samples from nine populations belonging to three African (intermissa, scutellata and capensis) and four European (mellifera, ligustica, carnica and cecropia) Apis mellifera subspecies were scored for seven microsatellite loci. A large amount of genetic variation (between seven and 30 alleles per locus) was detected. Average heterozygosity and average number of alleles were significantly higher in African than in European subspecies, in agreement with larger effective population sizes in Africa. Microsatellite analyses confirmed that A. mellifera evolved in three distinct and deeply differentiated lineages previously detected by morphological and mitochondrial DNA studies. Dendrogram analysis of workers from a given population indicated that super-sisters cluster together when using a sufficient number of microsatellite data whereas half-sisters do not. An index of classification was derived to summarize the clustering of different taxonomic levels in large phylogenetic trees based on individual genotypes. Finally, individual population X loci data were used to test the adequacy of the two alternative mutation models, the infinite allele model (IAM) and the stepwise mutation models. The better fit overall of the IAM probably results from the majority of the microsatellites used including repeats of two or three different length motifs (compound microsatellites).     

Wave-of-advance models of the diffusion of the Y chromosome haplogroup R1b1b2 in Europe

Whether or not the spread of agriculture in Europe was accompanied by movements of people is a long-standing question in archeology and anthropology, which has been frequently addressed with the help of population genetic data. Estimates on dates of expansion and geographic origins obtained from genetic data are however sensitive to the calibration of mutation rates and to the mathematical models used to perform inference. For instance, recent data on the Y chromosome haplogroup R1b1b2 (M269) have either suggested a Neolithic origin for European paternal lineages or a more ancient Paleolithic origin depending on the calibration of Y-STR mutation rates. Here we examine the date of expansion and the geographic origin of hgR1b1b2 considering two current estimates of mutation rates in a total of fourteen realistic wave-of-advance models. We report that a range expansion dating to the Paleolithic is unlikely to explain the observed geographical distribution of microsatellite diversity, and that whether the data is informative with respect to the spread of agriculture in Europe depends on the mutation rate assumption in a critical way.     

Gene flow and functional connectivity in the natterjack toad

Functional connectivity is a key factor for the persistence of many specialist species in fragmented landscapes. However, connectivity estimates have rarely been validated by the observation of dispersal movements. In this study, we estimated functional connectivity of a real landscape by modelling dispersal for the endangered natterjack toad (Bufo calamita) using cost distance. Cost distance allows the evaluation of 'effective distances', which are distances corrected for the costs involved in moving between habitat patches in spatially explicit landscapes. We parameterized cost-distance models using the results of our previous experimental investigation of natterjack's movement behaviour. These model predictions (connectivity estimates from the GIS study) were then confronted to genetic-based dispersal rates between natterjack populations in the same landscape using Mantel tests. Dispersal rates between the populations were inferred from variation at six microsatellite loci. Based on these results, we conclude that matrix structure has a strong effect on dispersal rates. Moreover, we found that cost distances generated by habitat preferences explained dispersal rates better than did the Euclidian distances, or the connectivity estimate based on patch-specific resistances (patch viscosity). This study is a clear example of how landscape genetics can validate operational functional connectivity estimates.     

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.     

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.     

Gene flow and melanism in garter snakes revisited: a comparison of molecular markers and island vs. coalescent models

Within populations, the stochastic effect of genetic drift and deterministic effect of natural selection are potentially weakened or altered by gene flow among populations. The influence of gene flow on Lake Erie populations of the common garter snake has been of particular interest because of a discontinuous colour pattern polymorphism (striped vs. melanistic) that is a target of natural selection. We reassessed the relative contributions of gene flow and genetic drift using genetic data and population size estimates. We compared all combinations of two marker systems and two analytical approaches to the estimation of gene flow rates: allozymes (data previously published), microsatellite DNA (new data), the island model ( F _ST-based approach), and a coalescence-based approach. For the coalescence approach, mutation rates and sampling effects were also investigated. While the two markers produced similar results, gene flow based on F _ST was considerably higher (Nm > 4) than that from the coalescence-based method (Nm < 1). Estimates of gene flow are likely to be inflated by lack of migration-drift equilibrium and changing population size. Potentially low rates of gene flow (Nm < 1), small population size at some sites, and positive correlations of number of microsatellite DNA alleles and island size and between M , mean ratio of number of alleles to range in allele size, and island size suggest that in addition to selection, random genetic drift may influence colour pattern frequencies. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 79, 389–399.