A note on multidimensional models of neutral mutation

A generalisation of the Ohta-Kimura charge-state model for neutral mutation, in which alleles are represented by points in d-dimensional space, seems appropriate in the light of recent experimental developments. It is noted that existing methods of analysis extend almost trivially to this more general model, and the point is illustrated by calculating the effective number of alleles.     

Evidence for complex mutations at microsatellite loci in Drosophila.

Fifteen lines each of Drosophila melanogaster, D. simulans, and D. sechellia were scored for 19 microsatellite loci. One to four alleles of each locus in each species were sequenced, and microsatellite variability was compared with sequence structure. Only 7 loci had their size variation among species consistent with the occurrence of strictly stepwise mutations in the repeat array, the others showing extensive variability in the flanking region compared to that within the microsatellite itself. Polymorphisms apparently resulting from complex nonstepwise mutations involving the microsatellite were also observed, both within and between species. Maximum number of perfect repeats and variance of repeat count were found to be strongly correlated in microsatellites showing an apparently stepwise mutation pattern. These data indicate that many microsatellite mutation events are more complex than represented even by generalized stepwise mutation models. Care should therefore be taken in inferring population or phylogenetic relationships from microsatellite size data alone. The analysis also indicates, however, that evaluation of sequence structure may allow selection of microsatellites that more closely match the assumptions of stepwise models.     

A Computer Simulation Study of Vntr Population Genetics: Constrained Recombination Rules Out the Infinite Alleles Model

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. We show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. We use sampling theory to confirm the intrinsically poor fit to the infinite alleles model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations.     

Statistics for Microsatellite Variation Based on Coalescence

The stepwise mutation model, which was at one time chiefly of interest in studying the evolution of protein charge-states, has recently undergone a resurgence of interest with the new popularity of microsatellites as phylogenetic markers. In this paper we describe a method which makes it possible to transfer many population genetics results from the standard infinite sites model to the stepwise mutation model. We study in detail the properties of pairwise differences in microsatellite repeat number between randomly chosen alleles. We show that the problem of finding the expected squared distance between two individuals and finding the variance of the squared distance can be reduced for a wide range of population models to finding the mean and mean square coalescence times. In many cases the distributions of coalescence times have already been studied for infinite site problems. In this study we show how to calculate these quantities for several population models. We also calculate the variance in mean squared pairwise distance (an estimator of mutation rate × population size) for samples of arbitrary size and show that this variance does not approach zero as the sample size increases. We can also use our method to study alleles at linked microsatellite loci. We suggest a metric which quantifies the level of association between loci—effectively a measure of linkage disequilibrium. It is shown that there can be linkage disequilibrium between partially linked loci at mutation–drift equilibrium.     

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.     

The number of alleles in electrophoretic experiments

We examine the rate of divergence of the number of distinguishable alleles in a large sample. Our calculations are based on the Ohta-Kimura model for electrophoretic experiments, in which types can only take discrete values, and mutations are selectively neutral.     

鲤鱼微卫星突变速率和模式(英文)

利用150个微卫星分子标记在F1代家系的基因型分析过程中,共有27600个等位基因从亲本向子代传递,其中在5个微卫星座位上检测到6个突变的等位基因。对突变的等位基因数目进行统计分析后得出:鲤鱼平均每个世代每个微卫星座位的突变速率为2.53×10-4。在发现突变的5个位点中,经测序发现,突变序列中插入1个以上的重复单元就导致了突变的发生。这些突变表明,鲤鱼的微卫星突变没有遵循严格的渐变突变模型(stepwise mutation model,SMM)。该文关于鲤鱼微卫星突变速率和模式的研究将会对统计鲤鱼有效群体的统计提供有效参数。     

What phylogeny and gene genealogy analyses reveal about homoplasy in citrus microsatellite alleles

Sixty-five microsatellite alleles amplified from ancestral citrus accessions classified in three separate genera were evaluated for sequence polymorphism to establish the basis of inter- and intra-allelic genetic variation, evaluate the extent of size homoplasy, and determine an appropriate model (stepwise or infinite allele) for analysis of citrus microsatellite alleles. Sequences for each locus were aligned and subsequently used to determine relationships between alleles of different taxa via parsimony. Interallelic size variation at each SSR locus examined was due to changes in repeat copy number with one exception. Sequencing these alleles uncovered new distinct point mutations in the microsatellite region and the region flanking the microsatellite. Several of the point mutations were found to be genus, species, or allele specific, and some mutations were informative about the inferred evolutionary relationships among alleles. Overall, homoplasy was observed in alleles from all three loci, where the core microsatellite repeat was changed causing alleles of the same size class to be identical in state but not identical by descent. Because nearly all changes in allele size (with one exception) were due to expansion or contraction of the repeat motif, this suggests that a stepwise mutation model, which assumes homoplasy may occur, would be the most appropriate for analyzing Citrus SSR data. The collected data indicate that microsatellites can be a useful tool for evaluating Citrus species and two related genera since repeat motifs were reasonably well retained. However, this work also demonstrated that the number of microsatellite alleles is clearly an underestimate of the number of sequence variants present.     

分子生态学重要概念——遗传距离及其测度的理论研究概况

综述了遗传距离的概念、背景,有关遗传距离的几种基本的突变模型以及和遗传距离有关的参量和几种常用统计量,指出在处理蛋白质数据、分子数据以及序列数据时,如何选择相应的统计量和可用的软件包,同时还着重指明了各种模型的假设前提,为处理实际的蛋白质或分子数据时选择合适的模型,和对数据的最终解释提供一些帮助。     

A mathematical model of breast cancer development, local treatment and recurrence

Cancer development is a stepwise process through which normal somatic cells acquire mutations which enable them to escape their normal function in the tissue and become self-sufficient in survival. The number of mutations depends on the patient's age, genetic susceptibility and on the exposure of the patient to carcinogens throughout their life. It is believed that in every malignancy 4-6 crucial similar mutations have to occur on cancer-related genes. These genes are classified as oncogenes and tumour suppressor genes (TSGs) which gain or lose their function respectively, after they have received one mutative hit or both of their alleles have been knocked out. With the acquisition of each of the necessary mutations the transformed cell gains a selective advantage over normal cells, and the mutation will spread throughout the tissue via clonal expansion. We present a simplified model of this mutation and expansion process, in which we assume that the loss of two TSGs is sufficient to give rise to a cancer. Our mathematical model of the stepwise development of breast cancer verifies the idea that the normal mutation rate in genes is only sufficient to give rise to a tumour within a clinically observable time if a high number of breast stem cells and TSGs exist or genetic instability is involved as a driving force of the mutation pathway. Furthermore, our model shows that if a mutation occurred in stem cells pre-puberty, and formed a field of cells with this mutation through clonal formation of the breast, it is most likely that a tumour will arise from within this area. We then apply different treatment strategies, namely surgery and adjuvant external beam radiotherapy and targeted intraoperative radiotherapy (TARGIT) and use the model to identify different sources of local recurrence and analyse their prevention.     

Allele Frequencies at Microsatellite Loci: The Stepwise Mutation Model Revisited

We summarize available data on the frequencies of alleles at microsatellite loci in human populations and compare observed distributions of allele frequencies to those generated by a simulation of the stepwise mutation model. We show that observed frequency distributions at 108 loci are consistent with the results of the model under the assumption that mutations cause an increase or decrease in repeat number by one and under the condition that the product Nu, where N is the effective population size and u is the mutation rate, is larger than one. We show that the variance of the distribution of allele sizes is a useful estimator of Nu and performs much better than previously suggested estimators for the stepwise mutation model. In the data, there is no correlation between the mean and variance in allele size at a locus or between the number of alleles and mean allele size, which suggests that the mutation rate at these loci is independent of allele size.     

Neutral two-locus multiple allele models with recombination

General formulae for the homozygosity and variance of linkage disequilibrium are derived for neutral, stationary, two-locus multiple allele models where there is a symmetric type of mutation at each locus. Particular cases examined are K allele models, the infinite alleles model, and the stepwise mutation model. The two-locus infinite allele model is examined at the molecular level and a joint probability generating function is found for the number of heterozygous sites at each locus in two randomly chosen gametes.     

The number of distinguishable alleles according to the Ohta-Kimura model of neutral mutation

We calculate how many alleles one can expect to distinguish in a large sample from a large population which develops according to the Ohta-Kimura model. This number tends to infinity with the sample size, but so slowly that it is bounded for all practical purposes.Research supported by the NSF through a grant to Cornell University     

High somatic instability of a microsatellite locus in a clonal tree,<Emphasis Type="Italic"> Robinia pseudoacacia</Emphasis>

Robinia pseudoacacia L. is a clonal tree species. To investigate a mutation within eight microsatellite loci of R. pseudoacacia, we analyzed DNA samples obtained from different leaf samples within each ramet, leaves from ramets within the genet, and seeds. Of the eight loci, locus Rops15 (AG motif) displayed hypermutability. The mutation rates of Rops15 within each ramet, among ramets within the genet, and offspring were 6.27% (ranging from 0 to 31.1%), 6.11% (from 0 to 25.0%) and 3.78% (from 0 to 10.9%), respectively. The mutation rate increased with allele size (13–71 repeat units). The mutation patterns observed in Rops15 were distinctive in two ways. First, there was a significant bias toward additions over deletions, and both addition and deletion of single repeats were dominant at alleles with lengths less than 232 bp (63 repeats). Second, for the longest allele of 248 bp (71 repeats), the number of losses was higher than the number of gains. These observations suggest that the mutation patterns of microsatellites in R. pseudoacacia may follow a generalized stepwise mutation model, and that the tendency of long alleles to mutate to shorter lengths acts to prevent infinite growth. Finally, the observation of somatic hypermutability at locus Rops15 highlights the need for caution when using highly polymorphic microsatellites for population genetic structure and paternity analysis in tree species.Communicated by H.F. Linskens     

An Evaluation of Evolutionary Constraints on Microsatellite Loci Using Null Alleles

A test to evaluate constraints on the evolution of single microsatellite loci is described. The test assumes that microsatellite alleles that share the same flanking sequence constitute a series of alleles with a common descent that is distinct from alleles with a mutation in the flanking sequence. Thus two or more different series of alleles at a given locus represent the outcomes of different evolutionary processes. The higher rate of mutations within the repeat region (10(-3) or 10(-4)) compared with that of insertion/deletion or point mutations in adjacent flanking regions (10(-9)) or with that of recombination between the repeat and the point mutation (10(-6) for sequences 100 bp long) provides the rationale for this assumption. Using a two-phase, stepwise mutation model we simulated the evolution of a number of independent series of alleles and constructed the distributions of two similarity indices between pairs of these allele series. Applying this approach to empirical data from locus AG2H46 of Anopheles gambiae resulted in a significant excess of similarity between the main and the null series, indicating that constraints affect allele distribution in this locus. Practical considerations of the test are discussed.     

A Model Allowing Continuous Variation in Electrophoretic Mobility of Neutral Alleles

The infinite-sites model with no recombination is extended to include mutations that affect electrophoretic mobility. The model allows the effect of a single-site mutation to have a continuous effect on mobility. Formulae are obtained for the variance of electrophoretic mobility of alleles after an arbitrary lenght of time. A special case of the general model is the case of stepwise production of neutral alleles with an arbitrary number of steps.     

A high incidence of clustered microsatellite mutations revealed by parent-offspring analysis in the African freshwater snail, <Emphasis Type="BoldItalic">Bulinus forskalii</Emphasis> (Gastropoda,Pulmonata)

Genotyping of 11 microsatellites in 432 offspring from 28 families of the hermaphroditic, freshwater snail Bulinus forskalii detected 10 de novo mutant alleles. This gave an estimated mutation rate of 1.1 × 10^–3 per locus per gamete per generation. There was a trend towards repeat length expansion and, unlike most studies, multi-step mutations predominated, suggesting that the microsatellite mutation process does not conform to a strict stepwise mutation model. Interestingly, the ten mutant alleles appear to have arisen from only six independent germline mutation events within the microsatellite array, with seven of them residing in three mutational clusters. Our results extend observations of clustered microsatellite mutations to another taxonomic group and type of mating system, self-fertile gastropods, and provide compelling evidence of premeiotic germline mutations, a phenomenon that could greatly impact upon our understanding of mutation dynamics but which has received little attention.     

XV-2c and KM.19 haplotype analysis in Chilean patients with cystic fibrosis and unknown CFTR gene mutations

Cystic fibrosis (CF) is caused by mutations in the CFTR gene. More than 1600 mutations have been described, with frequencies that differ worldwide according to the ethnic origin of patients. A small group of mutations are recurrent on several populations. It has been shown that they each tend occur on specific chromosome 7 haplotypes, supporting the notion of a single origin for them. Less than 50% of mutations in Chilean patients have been identified to date. To indirectly assess the possible presence of a predominant founder mutation in the remaining unknown alleles, we evaluated 2 polymorphic markers, XV-2c and KM.19, tightly linked to the CFTR locus. The study was done in Chilean CF patients with unknown or deltaF508 (DeltaF508) CFTR mutations and their haplotypes were compared to affected family-based controls. DeltaF508 showed marked linkage disequilibrium with XV-2c/KM.19 haplotype B, with 90% of alleles on that haplotype. There was no difference in haplotype distribution between unknown mutations and normal controls. These results support a European origin for DeltaF508 alleles in Chilean patients, and make unlikely the presence of a predominant founder mutation in the so-far unknown alleles.     

Allelic frequencies given the sample's common ancestral type

A general formula is derived for finding the expected proportion of genes in a random sample of n genes which are of a particular allelic type given the type of the sample's common ancestor. Expressions of these expectations are obtained for the 2-allele, K-allele, infinitely many alleles, and stepwise mutation models. Numerical examples for the stepwise mutation model are also tabulated.     

Mutability of microsatellites developed for the ant Camponotus consobrinus

Five highly polymorphic (GA)n microsatellite loci are reported for the formicine ant Camponotus consobrinus. The occurrence of many nests with a simple family structure enabled a search for new mutations, 11 of which were found from 3055 informative typings. These mutations were not randomly distributed across loci, 10 of them occurring at the locus Ccon70. The spectrum of mutations across alleles at Ccon70 was also nonrandom, with all of them occurring in alleles in the upper half of the allele size distribution. Six of the Ccon70 mutations decreased allele size. The mutations observed fit the stepwise mutation model well, i.e. mutations could always be assigned to an allele which differed in size from them by one repeat unit. The parental origins of the Ccon70 mutations were established and appear more female biased than vertebrate mutations, significantly so compared with human haemophilia A and primate intron mutations. This result may indicate that the lack of meiosis in males (which are haploid in ants) reduces the mutation rate in that sex relative to species in which both sexes are diploid.