General Triallelic Frequency Spectrum Under Demographic Models with Variable Population Size

It is becoming routine to obtain data sets on DNA sequence variation across several thousands of chromosomes, providing unprecedented opportunity to infer the underlying biological and demographic forces. Such data make it vital to study summary statistics that offer enough compression to be tractable, while preserving a great deal of information. One well-studied summary is the site frequency spectrum—the empirical distribution, across segregating sites, of the sample frequency of the derived allele. However, most previous theoretical work has assumed that each site has experienced at most one mutation event in its genealogical history, which becomes less tenable for very large sample sizes. In this work we obtain, in closed form, the predicted frequency spectrum of a site that has experienced at most two mutation events, under very general assumptions about the distribution of branch lengths in the underlying coalescent tree. Among other applications, we obtain the frequency spectrum of a triallelic site in a model of historically varying population size. We demonstrate the utility of our formulas in two settings: First, we show that triallelic sites are more sensitive to the parameters of a population that has experienced historical growth, suggesting that they will have use if they can be incorporated into demographic inference. Second, we investigate a recently proposed alternative mechanism of mutation in which the two derived alleles of a triallelic site are created simultaneously within a single individual, and we develop a test to determine whether it is responsible for the excess of triallelic sites in the human genome.     

Site frequency spectra from genomic SNP surveys

Genomic survey data now permit an unprecedented level of sensitivity in the detection of departures from canonical evolutionary models, including expansions in population size and selective sweeps. Here, we examine the effects of seemingly subtle differences among sampling distributions on goodness of fit analyses of site frequency spectra constructed from single nucleotide polymorphisms. Conditioning on the observation of exactly two alleles in a random sample results in a site frequency spectrum that is independent of the scaled rate of neutral substitution (θ). Other sampling distributions, including conditioning on a single mutational event in the sample genealogy or randomly selecting a single mutation from a genealogy with multiple mutations, have distinct site frequency spectra that show highly significant departures from the predictions of the biallelic model. Some aspects of data filtering may contribute to significant departures of site frequency spectra from expectation, apart from any violation of the standard neutral model.     

Genetic interaction of BBS1 mutations with alleles at other BBS loci can result in non-Mendelian Bardet-Biedl syndrome

Bardet-Biedl syndrome is a genetically and clinically heterogeneous disorder caused by mutations in at least seven loci (BBS1-7), five of which are cloned (BBS1, BBS2, BBS4, BBS6, and BBS7). Genetic and mutational analyses have indicated that, in some families, a combination of three mutant alleles at two loci (triallelic inheritance) is necessary for pathogenesis. To date, four of the five known BBS loci have been implicated in this mode of oligogenic disease transmission. We present a comprehensive analysis of the spectrum, distribution, and involvement in non-Mendelian trait transmission of mutant alleles in BBS1, the most common BBS locus. Analyses of 259 independent families segregating a BBS phenotype indicate that BBS1 participates in complex inheritance and that, in different families, mutations in BBS1 can interact genetically with mutations at each of the other known BBS genes, as well as at unknown loci, to cause the phenotype. Consistent with this model, we identified homozygous M390R alleles, the most frequent BBS1 mutation, in asymptomatic individuals in two families. Moreover, our statistical analyses indicate that the prevalence of the M390R allele in the general population is consistent with an oligogenic rather than a recessive model of disease transmission. The distribution of BBS oligogenic alleles also indicates that all BBS loci might interact genetically with each other, but some genes, especially BBS2 and BBS6, are more likely to participate in triallelic inheritance, suggesting a variable ability of the BBS proteins to interact genetically with each other.     

Human Triallelic Sites: Evidence for a New Mutational Mechanism?

Most SNPs in the human genome are biallelic; however, there are some sites that are triallelic. We show here that there are approximately twice as many triallelic sites as we would expect by chance. This excess does not appear to be caused by natural selection or mutational hotspots. Instead we propose that a new mutation can induce another mutation either within the same individual or subsequently during recombination. We provide evidence for this model by showing that the rarer two alleles at triallelic sites tend to cluster on phylogenetic trees of human haplotypes. However, we find no association between the density of triallelic sites and the rate of recombination, which leads us to suggest that triallelic sites might be generated by the simultaneous production of two new mutations within the same individual on the same genetic background. Under this model we estimate that simultaneous mutation contributes ∼3% of all distinct SNPs. We also show that there is a twofold excess of adjacent SNPs. Approximately half of these seem to be generated simultaneously since they have identical minor allele frequencies. We estimate that the mutation of adjacent nucleotides accounts for a little less than 1% of all SNPs.ALTHOUGH the density of biallelic SNPs in the human genome is reasonably low, there are some sites that have three (triallelic sites) or even four nucleotides segregating in the human population. We show here that there are approximately twice as many triallelic sites as we would expect by chance. There are at least three mutational mechanisms that could potentially generate such an excess of triallelic sites. First, some sites may be hypermutable, and if the mutation rate of at least two pathways (e.g., C → T and C → A) is elevated at such sites, then there will be an excess of triallelic sites. The mutation rate of a site is known to depend upon the adjacent nucleotides, the best known example being the CpG dinucleotide (Coulondre et al. 1978; Bird 1980) at which the frequency of both transition and transversion mutations is elevated. However, other adjacent nucleotides also influence the mutation rate (Blake et al. 1992; Zhao et al. 2003; Hwang and Green 2004). Furthermore, we have recently shown that there is variation in the mutation rate that does not depend upon the identity of the adjacent nucleotides or any specific context (Hodgkinson et al. 2009).Second, it is possible that two of the alleles at a triallelic site are generated simultaneously within a single individual. Point mutations are generally assumed to involve the production of a single new allele per mutation event at a rate that is governed by the effects mentioned above. However, it is not difficult to imagine mechanisms that might induce mutations on both strands of the DNA duplex; for example, the presence of a base mismatch may itself be unstable, so we might go from a G-C base pair to a G-A, which then may mutate to C-A; if DNA replication reads through this mismatch, the G allele will have mutated to both C and T. Alternatively, the mutation may occur across both strands of the duplex at the same time, possibly as a result of a chemical or radiation event. Third, in a similar manner, we might imagine a single SNP inducing subsequent mutations if base mismatches are formed during recombination in heteroduplex DNA.Here we attempt to identify the cause of the excess of triallelic sites by analyzing sequence data around triallelic sites.     

Maintenance of Genetic Variability under the Pressure of Neutral and Deleterious Mutations in a Finite Population

In order to assess the effect of deleterious mutations on various measures of genic variation, approximate formulas have been developed for the frequency spectrum, the mean number of alleles in a sample, and the mean homozygosity; in some particular cases, exact formulas have been obtained. The assumptions made are that two classes of mutations exist, neutral and deleterious, and that selection is strong enough to keep deleterious alleles in low frequencies, the mode of selection being either genic or recessive. The main findings are: (1) If the expected value (q) of the sum of the frequencies of deleterious alleles is about 10% or less, then the presence of deleterious alleles causes only a minor reduction in the mean number of neutral alleles in a sample, as compared to the case of q = 0. Also, the low- and intermediate-frequency parts of the frequency spectrum of neutral alleles are little affected by the presence of deleterious alleles, though the high-frequency part may be changed drastically. (2) The contribution of deleterious mutations to the expected total number of alleles in a sample can be quite large even if q is only 1 or 2%. (3) The mean homozygosity is roughly equal to (1--2q)/(1 + theta 1), where theta 1 is twice the number of new neutral mutations occurring in each generation in the total population. Thus, deleterious mutations increase the mean heterozygosity by about 2q/(1 + theta 1). The present results have been applied to study the controversial problem of how deleterious mutations may affect the testing of the neutral mutation hypothesis.     

Analysis of the Association between the HLA-DQA1 Alleles and the Steroid 21-Hydroxylase Gene Mutations in the Patients with Congenital Adrenal Hyperplasia

In 96 patients with congenital adrenal hyperplasia (CAH) and 50 healthy donors from northwestern Russia the distribution of the HLA-DQA1 alleles and the mutation spectrum and frequency at the CYP21B gene were examined. In the patients with nonclassical (NC) CAH, the distribution of the HLA-DQA1 polymorphic alleles was similar to that in the population sample. In the patients with the salt-wasting form of the disease a statistically significant decrease of the *0401 or *0501major allele frequency was observed. The prevalence of certain HLA-DQA1 genotypes, namely, HLA5, HLA3, and HLA4, was observed in the patients with the NC, salt-wasting (SW), and simple virilizing CAH, respectively. Each clinical group was characterized by a specific spectrum of clinically valuable mutations. An association between theCYP21B mutations most frequently found in case of SW and SV CAH (delB, I2splice, and I172N) and certain HLA-DQA1alleles was demonstrated. The necessity of more precise clinical diagnostics of the NC CAH cases along with detailed examination of this group for determination of the major mutations typical of the NC CAH cases from northwestern Russia is discussed.     

Mutational analysis in Lebanese patients with congenital adrenal hyperplasia due to a deficit in 21-hydroxylase

Molecular defects in the gene encoding steroid 21-hydroxylase (CYP21) result in impairment of adrenal steroid synthesis in patients affected with autosomal-recessive congenital adrenal hyperplasias (CAH). In this study, we report on the molecular screening of six point mutations, large deletions, gene conversion events and duplications in 25 unrelated Lebanese families affected by CAH due to steroid 21-hydroxylase. The methods used (PCR-digestion and southern blot) allowed the detection of 96% of the disease chromosomes. In classical forms, the most frequent mutation was the splice site mutation in intron 2 accounting for 39% of the disease alleles. Gene conversion events accounted for 14% of the alleles, but no large deletions were found. In nonclassical forms, the V281L mutation in exon 7 represent 86% of the tested alleles. Genotype-phenotype correlations were as expected: Delta 8nt, Q318X and gene conversion correspond to SW forms, whereas the intron 2 splice site mutation may give either SW or SV forms; the V281L mutation was responsible for nonclassical forms. The spectrum of mutations underlines the genetic diversity of the Lebanese population. No correlation could be drawn out between mutations and some specific religious communities, except for the Delta 8nt mutation, which is present only in the Christian Maronite group. Molecular study of the CYP21 gene might constitute a good support for clinicians, especially in consanguineous families, for whom we could provide genetic counselling.     

Two novel mutations in the EYS gene are possible major causes of autosomal recessive retinitis pigmentosa in the Japanese population

Retinitis pigmentosa (RP) is a highly heterogeneous genetic disease including autosomal recessive (ar), autosomal dominant (ad), and X-linked inheritance. Recently, arRP has been associated with mutations in EYS (Eyes shut homolog), which is a major causative gene for this disease. This study was conducted to determine the spectrum and frequency of EYS mutations in 100 Japanese arRP patients. To determine the prevalence of EYS mutations, all EYS exons were screened for mutations by polymerase chain reaction amplification, and sequence analysis was performed. We detected 67 sequence alterations in EYS, of which 21 were novel. Of these, 7 were very likely pathogenic mutations, 6 were possible pathogenic mutations, and 54 were predicted non-pathogenic sequence alterations. The minimum observed prevalence of distinct EYS mutations in our study was 18% (18/100, comprising 9 patients with 2 very likely pathogenic mutations and the remaining 9 with only one such mutation). Among these mutations, 2 novel truncating mutations, c.4957_4958insA (p.S1653KfsX2) and c.8868C>A (p.Y2956X), were identified in 16 patients and accounted for 57.1% (20/35 alleles) of the mutated alleles. Although these 2 truncating mutations were not detected in Japanese patients with adRP or Leber's congenital amaurosis, we detected them in Korean arRP patients. Similar to Japanese arRP results, the c.4957_4958insA mutation was more frequently detected than the c.8868C>A mutation. The 18% estimated prevalence of very likely pathogenic mutations in our study suggests a major involvement of EYS in the pathogenesis of arRP in the Japanese population. Mutation spectrum of EYS in 100 Japanese patients, including 13 distinct very likely and possible pathogenic mutations, was largely different from the previously reported spectrum in patients from non-Asian populations. Screening for c.4957_4958insA and c.8868C>A mutations in the EYS gene may therefore be very effective for the genetic testing and counseling of RP patients in Japan.     

Phenylketonuria mutations in Germany

We report the spectrum of mutations and associated modified haplotypes in patients with phenylketonuria living in Germany. A total of 546 independent alleles was investigated, including 411 of German and 65 of Turkish descent. Mutations were identified for 535 PKU alleles (98%) and there were 91 different mutations. The most common mutation was R408W on 22% of alleles. Two mutations, IVS12+1G→A and IVS10–11G→A accounted for just under 10% of alleles, whereas the remaining mutations were found at relative frequencies of 6% or less; 43 mutations were observed once only. IVS10–11G→A was the most common mutation (38% of alleles) in the subgroup of patients of Turkish descent. Modified haplotypes were determined from the analysis of four silent mutations, three diallelic restriction fragment length polymorphisms, a variable number of tandem repeats minisatellite and a short tandem repeat microsatellite in the phenylalanine hydroxylase gene, showing that a considerable proportion of mutations must have recurred in independent founders; other mutations may have changed chromosomal haplotype backgrounds by gene conversion. The spectrum of PKU mutations in Germany reflects the history of a heterogenous Central European population living at the crossroads of migration throughout the centuries. Received: 11 January 1999 / Accepted: 11 March 1999     

Frequencies of phenylalanine hydroxylase mutations I65T, R252W, R261Q, R261X, IVS10nt11, V388M, R408W, Y414C, and IVS12nt1 in Minas Gerais, Brazil

In order to determine the phenylketonuria (PKU) mutation spectrum in the population of Minas Gerais State, Brazil, 78 unrelated PKU patients found by the neonatal screening program from 1993 to 2003 were tested for nine phenylalanine hydroxylase mutations. These mutations were selected due to their high frequencies in other Brazilian populations and in Portugal, where the largest contingent of the Caucasian component of the Brazilian population originated from. The most frequent mutations were V388M (21%), R261Q (16%), IVS10nt11 (13.4%), I65T (5.7%), and R252W (5%). The frequencies of the other four mutations (R261X, R408W, Y414C, and IVS12nt1) did not reach 2%. By testing these nine mutations, we were able to identify 64% of the PKU alleles in our sample. V388M frequency was higher than in any other known population and almost three times larger than that observed in Portugal, probably reflecting genetic drift. The mutation profile, as well as the relative frequency of the different mutations, suggest that the Minas Gerais population more closely resembles that of Portugal than do the other Brazilian populations that have already been tested.     

Linkage analysis of neurofibromatosis type 1

Summary In order to investigate the molecular basis of phenylketonuria (PKU) in the Polish population, we screened 44 mutant chromosomes from PKU probands for six known mutations, frequently occurring in western European countries, by polymerase chain reaction amplification of their genomic DNA and hybridization with allele-specific oligonucleotides. Our results show that the majority (66%) of all PKU alleles are characterized by three different mutations: in codon 408 (56.8%), codon 158 (6.8%) and codon 261 (2.27%). Of the mutant haplotype 2 alleles, 96% were linked to the mutation in codon 408. Out of five mutant haplotype 4 alleles, three showed the codon 158 mutation, and out of four mutant haplotype 1 alleles, one had the codon 261 mutation. In two families, MspI digests revealed an additional 13.5-kb band similar in length to that previously reported. However, analysis of exon 9 excluded the presence of the T to C transition originally described, indicating a new MspI variant in the Polish population.     

Maintenance of Genetic Variability under the Joint Effect of Mutation, Selection and Random Drift

Formulae are developed for the distribution of allele frequencies (the frequency spectrum), the mean number of alleles in a sample, and the mean and variance of heterozygosity under mutation pressure and under either genic or recessive selection. Numerical computations are carried out by using these formulae and Watterson's (1977) formula for the distribution of allele frequencies under overdominant selection. The following properties are observed: (1) The effect of selection on the distribution of allele frequencies is slight when 4Ns 相似文献   

Recent selection for self‐compatibility in a population of Leavenworthia alabamica

The evolution of self‐compatibility (SC) is the first step in the evolutionary transition in plants from outcrossing enforced by self‐incompatibility (SI) to self‐fertilization. In the Brassicaceae, SI is controlled by alleles of two tightly linked genes at the S‐locus. Despite permitting inbreeding, mutations at the S‐locus leading to SC may be selected if they provide reproductive assurance and/or gain a transmission advantage in a population when SC plants self‐ and outcross. Positive selection can leave a genomic signature in the regions physically linked to the focus of selection when selection has occurred recently. From an SC population of Leavenworthia alabamica with a known nonfunctional mutation at the S‐locus, we collected sequence data from a ～690 Kb region surrounding the S‐locus, as well as from regions not linked to the S‐locus. To test for recent positive selection acting at the S‐locus, we examined polymorphism and the site‐frequency spectra. Using forward simulations, we demonstrate that recent selection of the strength expected for SC at a locus formerly under balancing selection can generate patterns similar to those seen in our empirical data.     

Forward and reverse genetics of rapid-cycling Brassica oleracea

Seeds of rapid-cycling Brassica oleracea were mutagenized with the chemical mutagen, ethylmethane sulfonate. The reverse genetics technique, TILLING, was used on a sample population of 1,000 plants, to determine the mutation profile. The spectrum and frequency of mutations induced by ethylmethane sulfonate was similar to that seen in other diploid species such as Arabidopsis thaliana. These data indicate that the mutagenesis was effective and demonstrate that TILLING represents an efficient reverse genetic technique in B. oleracea that will become more valuable as increasing genomic sequence data become available for this species. The extensive duplication in the B. oleracea genome is believed to result in the genetic redundancy that has been important for the evolution of morphological diversity seen in today’s B. oleracea crops (broccoli, Brussels sprouts, cauliflower, cabbage, kale and kohlrabi). However, our forward genetic screens identified 120 mutants in which some aspect of development was affected. Some of these lines have been characterized genetically and in the majority of these, the mutant trait segregates as a recessive allele affecting a single locus. One dominant mutation (curly leaves) and one semi-dominant mutation (dwarf-like) were also identified. Allelism tests of two groups of mutants (glossy and dwarf) revealed that for some loci, multiple independent alleles have been identified. These data indicate that, despite genetic redundancy, mutation of many individual loci in B. oleracea results in distinct phenotypes. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Dissimilarity of individual microsatellite profiles under different mutation models: Empirical approach

Microsatellites (simple sequence repeats, SSRs) still remain popular molecular markers for studying neutral genetic variation. Two alternative models outline how new microsatellite alleles evolve. Infinite alleles model (IAM) assumes that all possible alleles are equally likely to result from a mutation, while stepwise mutation model (SMM) describes microsatellite evolution as stepwise adding or subtracting single repeat units. Genetic relationships between individuals can be analyzed in higher precision when assuming the SMM scenario with allele size differences as a proxy of genetic distance. If population structure is not predetermined in advance, an empirical data analysis usually includes (a) estimating proximity between individual SSR profiles with a selected dissimilarity measure and (b) determining putative genetic structure of a given set of individuals using methods of clustering and/or ordination for the obtained dissimilarity matrix. We developed new dissimilarity indices between SSR profiles of haploid, diploid, or polyploid organisms assuming different mutation models and compared the performance of these indices for determining genetic structure with population data and with simulations. More specifically, we compared SMM with a constant or variable mutation rate at different SSR loci to IAM using data from natural populations of a freshwater bryozoan Cristatella mucedo (diploid), wheat leaf rust Puccinia triticina (dikaryon), and wheat powdery mildew Blumeria graminis (monokaryon). We show that inferences about population genetic structure are sensitive to the assumed mutation model. With simulations, we found that Bruvo's distance performs generally poorly, while the new metrics are capturing the differences in the genetic structure of the populations.     

Genetic structure of five susceptibility gene regions for coronary artery disease: disequilibria within and among regions

We analyzed two-locus disequilibria for 16 polymorphic loci of seven susceptibility genes for coronary artery disease located in five chromosomal regions distributed across four chromosomes. Included were the genes coding for apolipoprotein B (ApoB, chromosome 2, four marker loci), lipoprotein lipase (LPL, chromosome 8, three marker loci), apolipoproteins AI, CIII, AIV (ApoAI–CIII–AIV, chromosome 11, three marker loci), apolipoprotein E (ApoE, chromosome 19, two marker loci), and the low density lipoprotein receptor (LDLR, chromosome 19, four marker loci). Our sample included 540 unrelated individuals from the Rochester, Minn. population. There were no statistically significant deviations of single-locus genotypes from Hardy-Weinberg equilibrium. The strongest associations within genes were for composite diallelic disequilibria; 17/19 were significant (13 at Pr <0.001, 1 at Pr <0.01, 3 at Pr <0.05). These observations suggest marker alleles within genes have a shared evolutionary history reflected by disequilibria that have not been dissipated by recombination. Disequilibrium was not generally concordant with the physical orderings of markers. Only two significant higher-order disequilibria were observed although 12 triallelic disequilibria were at maximum possible values. We observed 19 statistically significant disequilibria (Pr <0.05; 4 composite diallelic, 13 triallelic, and 2 quadriallelic) between 101 pairs of marker loci, where each locus in a pair was from a different unlinked region. These unexpected results are most likely explained by recent historical factors, including worldwide population expansion and amalgamation with continuous admixture, that influence the genetic structure (organization of alleles and non-alleles into genotypes) of a population. We conclude that disequilibria between loci from unlinked regions may be more extensive than is commonly assumed. Our findings also suggest that it is, on average, at least 15 times more likely to not detect significant disequilibrium among unlinked loci when it is really present than to make a false positive inference. Disequilibria between functional loci within or between regions will impact estimates of genetic variance associated with particular functional mutations within a susceptibility gene region. Received: 15 January 1998 / Accepted: 24 June 1998     

The intron 7 donor splice site transition: a second Tay-Sachs disease mutation in French Canada

Mutations at the hexosaminidase A (HEXA) gene which cause Tay-Sachs disease (TSD) have elevated frequency in the Ashkenazi Jewish and French-Canadian populations. We report a novel TSD allele in the French-Canadian population associated with the infantile form of the disease. The mutation, a GA transition at the +1 position of intron 7, abolishes the donor splice site. Cultured human fibroblasts from a compound heterozygote for this transition (and for a deletion mutation) produce no detectable HEXA mRNA. The intron 7+1 mutation occurs in the base adjacent to the site of the adult-onset TSD mutation (G805A). In both mutations a restriction site for the endonuclease EcoRII is abolished. Unambiguous diagnosis, therefore, requires allele-specific oligonucleotide hybridization to distinguish between these two mutant alleles. The intron 7+1 mutation has been detected in three unrelated families. Obligate heterozygotes for the intron 7+1 mutation were born in the Saguenay-Lac-St-Jean region of Quebec. The most recent ancestors common to obligate carriers of this mutation were from the Charlevoix region of the province of Quebec. This mutation thus has a different geographic centre of diffusion and is probably less common than the exon 1 deletion TSD mutation in French Canadians. Neither mutation has been detected in France, the ancestral homeland of French Canada.     

Isolation of polymorphic microsatellite markers for Begonia sutherlandii Hook. f.

Seven polymorphic microsatellite loci have been characterized for investigating population structure in the patchily distributed herb Begonia sutherlandii. Two loci (BSU3 and BSU4) exhibited population specific null alleles; primer redesign and allele sequencing for one of these loci showed two transition mutations in the original primer site. Two loci exhibited imperfect repeat polymorphisms due to single base pair indels in the flanking region (locus BSU6) and in the microsatellite region itself (BSU7). Transversion mutations were also found in the microsatellite region of locus BSU7. The remaining three loci amplified in all individuals tested and appeared to conform to a simple stepwise mutation pattern.     

Muller's ratchet and the pattern of variation at a neutral locus

The levels and patterns of variation at a neutral locus are analyzed in a haploid asexual population undergoing accumulation of deleterious mutations due to Muller's ratchet. We find that the movement of Muller's ratchet can be associated with a considerable reduction in genetic diversity below classical neutral expectation. The extent to which variability is reduced is a function of the deleterious mutation rate, the fitness effects of the mutations, and the population size. Approximate analytical expressions for the expected genetic diversity are compared with simulation results under two different models of deleterious mutations: a model where all deleterious mutations have equal effects and a model where there are two classes of deleterious mutations. We also find that Muller's ratchet can produce a considerable distortion in the neutral frequency spectrum toward an excess of rare variants.     

Estimating the total number of alleles using a sample coverage method.

Previously reported methods for estimating the number of different alleles at a single locus in a population have not described a useful general result. Using the number of alleles observed in a sample gives an underestimate for the true number of alleles. The similar problem of estimating the number of species in a population was first investigated in 1943. In this article we use the sample coverage method proposed by Chao and Lee in 1992 to estimate the number of alleles in a population when there are unequal allele frequencies. Simulation studies under the recurrent mutation model show that, for reasonable sample sizes, a significantly better estimate of the true number can be obtained than that using only the observed alleles. Results under the stepwise mutation model and infinite-allele model are presented. Possible applications include improving the characterization of the prior distribution for the allele frequencies, adjusting the estimates of genetic diversity, and estimating the range of microsatellite alleles.