Biased mutations and microsatellite variation

Mutation bias is one of the forces that may constrain the variation at microsatellite loci. Here, we study the dynamics of population statistics and the genetic distance between two populations under multiple stepwise mutations with linear bias and random drift. Expressions are derived for these statistics as functions of time, as well as at mutation-drift equilibrium. Applying these expressions to published data on humans and chimpanzees, the regression coefficient of mutation bias on allele size was estimated to be at least between - 0.0064 and -0.013. The assumption of mutational bias produces larger estimates of divergence times than are obtained in its absence; in particular, the time of split between African and non-African human populations is estimated to be between 183,000 and 222,000 years, assuming one-step mutations and no selection. With multistep mutations, the divergence time is estimated to be lower.      

Directional evolution for microsatellite size in maize

Directional evolution in microsatellites is the tendency for microsatellites either to increase or to decrease in size over time between populations. We analyzed 99 microsatellite loci in a sample of 193 maize plants representing the entire pre-Columbian range of this crop for evidence of directional evolution. We took advantage of the known phylogeographic history of maize with the independent movement of maize from its ancestral location in Mexico to North and South America. We show that there is an increase in the average allele size of microsatellites in the geographically derived North and South American groups relative to the ancestral Mexican group. We also show that there is a negative correlation between average allele size and altitude in all three groups. Directional evolution in maize microsatellites can be explained by changes in the mutation rate over time and space, changes in the degree of mutational bias to a larger allele, demographic differences between the ancestral and geographically derived populations, and/or scenarios involving selection on microsatellite size. The occurrence of directional evolution for microsatellite size indicates that the estimation of population parameters with microsatellite data in maize should be done with caution.     

Dynamics of Repeat Polymorphisms under a Forward-Backward Mutation Model: within- and between-Population Variability at Microsatellite Loci

Suggested molecular mechanisms for the generation of new tandem repeats of simple sequences indicate that the microsatellite loci evolve via some form of forward-backward mutation. We provide a mathematical basis for suggesting a measure of genetic distance between populations based on microsatellite variation. Our results indicate that such a genetic distance measure can remain proportional to the divergence time of populations even when the forward-backward mutations produce variable and/or directionally biased alleles size changes. If the population size and the rate of mutation remain constant, then the measure will be proportional to the time of divergence of populations. This genetic distance is expressed in terms of a ratio of components of variance of allele sizes, based on expressions developed for studying population dynamics of quantitative traits. Application of this measure to data on 18 microsatellite loci in nine human populations leads to evolutionary trees consistent with the known ethnohistory of the populations.     

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.     

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.     

Likelihood and approximate likelihood analyses of genetic structure in a linear habitat: performance and robustness to model mis-specification

We evaluate the performance of maximum likelihood (ML) analysis of allele frequency data in a linear array of populations. The parameters are a mutation rate and either the dispersal rate in a stepping stone model or a dispersal rate and a scale parameter in a geometric dispersal model. An approximate procedure known as maximum product of approximate conditional (PAC) likelihood is found to perform as well as ML. Mis-specification biases may occur because the importance sampling algorithm is formally defined in term of mutation and migration rates scaled by the total size of the population, and this size may differ widely in the statistical model and in reality. As could be expected, ML generally performs well when the statistical model is correctly specified. Otherwise, mutation rate estimates are much closer to mutation probability scaled by number of demes in the statistical model than scaled by number of demes in reality when mutation probability is high and dispersal is most limited. This mis-specification bias actually has practical benefits. However, opposite results are found in opposite conditions. Migration rate estimates show roughly similar trends, but they may not always be easily interpreted as low-bias estimates of dispersal rate under any scaling. Estimation of the dispersal scale parameter is also affected by mis-specification of the number of demes, and the different biases compensate each other in such a way that good estimation of the so-called neighborhood size (or more precisely the product of population density and mean-squared parent-offspring dispersal distance) is achieved. Results congruent with these findings are found in an application to a damselfly data set.     

Microsatellite allele frequencies in humans and chimpanzees, with implications for constraints on allele size

The distributions of allele sizes at eight simple-sequence repeat (SSR) or microsatellite loci in chimpanzees are found and compared with the distributions previously obtained from several human populations. At several loci, the differences in average allele size between chimpanzees and humans are sufficiently small that there might be a constraint on the evolution of average allele size. Furthermore, a model that allows for a bias in the mutation process shows that for some loci a weak bias can account for the observations. Several alleles at one of the loci (Mfd 59) were sequenced. Differences between alleles of different lengths were found to be more complex than previously assumed. An 8-base-pair deletion was present in the nonvariable region of the chimpanzee locus. This locus contains a previously unrecognized repeated region, which is imperfect in humans and perfect in chimpanzees. The apparently greater opportunity for mutation conferred by the two perfect repeat regions in chimpanzees is reflected in the higher variance in repeat number at Mfd 59 in chimpanzees than in humans. These data indicate that interspecific differences in allele length are not always attributable to simple changes in the number of repeats.      

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.     

Factors Influencing Ascertainment Bias of Microsatellite Allele Sizes: Impact on Estimates of Mutation Rates

Microsatellite loci play an important role as markers for identification, disease gene mapping, and evolutionary studies. Mutation rate, which is of fundamental importance, can be obtained from interspecies comparisons, which, however, are subject to ascertainment bias. This bias arises, for example, when a locus is selected on the basis of its large allele size in one species (cognate species 1), in which it is first discovered. This bias is reflected in average allele length in any noncognate species 2 being smaller than that in species 1. This phenomenon was observed in various pairs of species, including comparisons of allele sizes in human and chimpanzee. Various mechanisms were proposed to explain observed differences in mean allele lengths between two species. Here, we examine the framework of a single-step asymmetric and unrestricted stepwise mutation model with genetic drift. Analysis is based on coalescent theory. Analytical results are confirmed by simulations using the simuPOP software. The mechanism of ascertainment bias in this model is a tighter correlation of allele sizes within a cognate species 1 than of allele sizes in two different species 1 and 2. We present computations of the expected average allele size difference, given the mutation rate, population sizes of species 1 and 2, time of separation of species 1 and 2, and the age of the allele. We show that when the past demographic histories of the cognate and noncognate taxa are different, the rate and directionality of mutations affect the allele sizes in the two taxa differently from the simple effect of ascertainment bias. This effect may exaggerate or reverse the effect of difference in mutation rates. We reanalyze literature data, which indicate that despite the bias, the microsatellite mutation rate estimate in the ancestral population is consistently greater than that in either human or chimpanzee and the mutation rate estimate in human exceeds or equals that in chimpanzee with the rate of allele length expansion in human being greater than that in chimpanzee. We also demonstrate that population bottlenecks and expansions in the recent human history have little impact on our conclusions.     

The Evolution of Latent Genes in Subdivided Populations

We define latent genes as phenotypically silent DNA sequences which may be reactivated by various genetic mechanisms. Of interest is how they and their functional counterparts can be maintained at high frequency in the face of mutation and selection pressure. We propose a two-deme, three-allele model incorporating viability selection, mutation and migration in haploid populations. It is shown that polymorphism for the three alleles can be easily maintained for a wide range of biologically meaningful parameter values. Computer simulations were employed to gain qualitative insight into the global dynamics of the system. It was found that the dynamics of the latent allele is closely correlated with that of the functional allele. In addition, bias in the migration rates can strengthen or weaken selective conditions for preservation of the functional and latent alleles.     

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

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

An Evaluation of Genetic Distances for Use with Microsatellite Loci

Mutations of alleles at microsatellite loci tend to result in alleles with repeat scores similar to those of the alleles from which they were derived. Therefore the difference in repeat score between alleles carries information about the amount of time that has passed since they shared a common ancestral allele. This information is ignored by genetic distances based on the infinite alleles model. Here we develop a genetic distance based on the stepwise mutation model that includes allelic repeat score. We adapt earlier treatments of the stepwise mutation model to show analytically that the expectation of this distance is a linear function of time. We then use computer simulations to evaluate the overall reliability of this distance and to compare it with allele sharing and Nei's distance. We find that no distance is uniformly superior for all purposes, but that for phylogenetic reconstruction of taxa that are sufficiently diverged, our new distance is preferable.     

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.     

Ancestral alleles and population origins: inferences depend on mutation rate.

Previous studies have found that at most human loci, ancestral alleles are "African," in the sense that they reach their highest frequency there. Conventional wisdom holds that this reflects a recent African origin of modern humans. This paper challenges that view by showing that the empirical pattern (of elevated allele frequencies within Africa) is not as pervasive as has been thought. We confirm this African bias in a set of mainly protein-coding loci, but find a smaller bias in Alu insertion polymorphisms, and an even smaller bias in noncoding loci. Thus, the strong bias that was originally observed must reflect some factor that varies among data sets--something other than population history. This factor may be the per-locus mutation rate: the African bias is most pronounced in loci where this rate is high. The distribution of ancestral alleles among populations has been studied using 2 methods. One of these involves comparing the fractions of loci that reach maximal frequency in each population. The other compares the average frequencies of ancestral alleles. The first of these methods reflects history in a manner that depends on the mutation rate. When that rate is high, ancestral alleles at most loci reach their highest frequency in the ancestral population. When that rate is low, the reverse is true. The other method--comparing averages--is unresponsive. Average ancestral allele frequencies are affected neither by mutation rate nor by the history of population size and migration. In the absence of selection and ascertainment bias, they should be the same everywhere. This is true of one data set, but not of 2 others. This also suggests the action of some factor, such as selection or ascertainment bias, that varies among data sets.     

Reconstruction of microsatellite mutation history reveals a strong and consistent deletion bias in invasive clonal snails,Potamopyrgus antipodarum

Direct observations of mutations and comparative analyses suggest that nuclear microsatellites show a tendency to expand, with reports of deletion biases limited to very long alleles or a few loci in multilocus studies. Here we investigate microsatellite evolution in clonal snails, Potamopyrgus antipodarum, since their introduction to Britain in the 19th century, using an analysis based on minimum spanning networks of multilocus microsatellite genotypes. British populations consist of a small number of highly distinct genotype groups with very few outlying genotypes, suggesting clonal lineages containing minor variation generated by mutation. Network patterns suggest that a single introduced genotype was the ancestor of all extant variation and also provide support for wholly apomictic reproduction within the most common clonal lineage (group A). Microsatellites within group A showed a strong tendency to delete repeats, with an overall bias exceeding 88%, irrespective of the exact method used to infer mutations. This highly unusual pattern of deletion bias is consistent across populations and loci and is unrelated to allele size. We suggest that for persistence of microsatellites in this clone, some change in the mutation mechanism must have occurred in relatively recent evolutionary time. Possible causes of such a change in mechanism are discussed.     

Mutation Patterns at Dinucleotide Microsatellite Loci in Humans

Microsatellites are a major type of molecular markers in genetics studies. Their mutational dynamics are not clear. We investigated the patterns and characteristics of 97 mutation events unambiguously identified, from 53 multigenerational pedigrees with 630 subjects, at 362 autosomal dinucleotide microsatellite loci. A size-dependent mutation bias (in which long alleles are biased toward contraction, whereas short alleles are biased toward expansion) is observed. There is a statistically significant negative relationship between the magnitude (repeat numbers changed during mutation) and direction (contraction or expansion) of mutations and standardized allele size. Contrasting with earlier findings in humans, most mutation events (63%) in our study are multistep events that involve changes of more than one repeat unit. There was no correlation between mutation rate and recombination rate. Our data indicate that mutational dynamics at microsatellite loci are more complicated than the generalized stepwise mutation models.     

Evolutionary and statistical properties of three genetic distances

Many genetic distances have been developed to summarize allele frequency differences between populations. I review the evolutionary and statistical properties of three popular genetic distances: DS, DA, and theta;, using computer simulation of two simple evolutionary histories: an isolation model of population divergence and an equilibrium migration model. The effect of effective population size, mutation rate, and mutation mechanism upon the parametric value between pairs of populations in these models explored, and the unique properties of each distance are described. The effect of these evolutionary parameters on study design is also investigated and similar results are found for each genetic distance in each model of evolution: large sample sizes are warranted when populations are relatively genetically similar; and loci with more alleles produce better estimates of genetic distance.     

844ins68 in the cystathionine beta-synthase gene in Israel and review of its distribution in the world

The 844ins68 allele in the cystathionine beta-synthase gene is always found in cis with the T833C mutation further indicating that its origin is monophyletic and that it might be a useful anthropogenetic marker. Its frequency was examined in 1087 randomly chosen subjects from Israel (twelve Jewish communities and Palestinians), and found to range from 0.034 to 0.125. The heterogeneity among the Jewish communities spans most of the range encountered among Caucasoid populations and is in accordance both with other genetic markers examined in the Jewish communities and with genetic distance and discriminant analyses. 844ins68 cannot distinguish between various European regions, because of the marked heterogeneity of the allele frequency distribution in Europe. This distribution of the insertion does not follow a recognised pattern of any known colonisation process. Its use as a reliable anthropogenetic marker discriminating between the major human groups may also be problematic until more populations are sampled.     

An unbiased estimator of gene diversity in samples containing related individuals

Gene diversity is sometimes estimated from samples that contain inbred or related individuals. If inbred or related individuals are included in a sample, then the standard estimator for gene diversity produces a downward bias caused by an inflation of the variance of estimated allele frequencies. We develop an unbiased estimator for gene diversity that relies on kinship coefficients for pairs of individuals with known relationship and that reduces to the standard estimator when all individuals are noninbred and unrelated. Applying our estimator to data simulated based on allele frequencies observed for microsatellite loci in human populations, we find that the new estimator performs favorably compared with the standard estimator in terms of bias and similarly in terms of mean squared error. For human population-genetic data, we find that a close linear relationship previously seen between gene diversity and distance from East Africa is preserved when adjusting for the inclusion of close relatives.     

Genetic diversity and population structure of the invasive alien red swamp crayfish

High genetic diversity is thought to characterize successful invasive species, as the potential to adapt to new environments is enhanced and inbreeding is reduced. The red swamp crayfish, Procambarus clarkii, native to northeastern Mexico and south-central USA was introduced to Nanjing, China from Japan in 1929. Little is known about the genetic diversity and population structure of this species in China. We examined the genetic diversity and population structure of six P. clarkii populations using nine polymorphic microsatellites. Among the six populations, Nanjing population showed the highest allele number, allele richness and gene diversity, which is consistent with records indicating Nanjing may be the first site of introduction. In all six populations, significant heterozygote deficit was observed, suggesting founder effects and non-random mating. Analysis of bottleneck under infinite allele model, stepwise mutation model and two-phased model of mutation revealed evidence of a recent bottleneck in all these populations. Pairwise genetic distance analysis, AMOVA and assignment tests demonstrated high genetic differentiation between populations. Pairwise genetic distance did not fit the pairwise geographic distance, suggesting that human mediated dispersal have played a role in the population expansion and genetic differentiation.