Size homoplasy and mutational processes of interrupted microsatellites in two bee species, Apis mellifera and Bombus terrestris (Apidae)

Similar microsatellite electromorphs (PCR products of the same size) can arise from independent mutational events. Such alleles are not identical by descent. This phenomenon, termed size homoplasy, was studied by sequencing electromorphs of two microsatellite loci in which the stretch of basic repeats is interrupted by different short (1-2 bp) DNA motifs. The number and position of these interruptions were established for electromorphs from closely and distantly related populations of honeybees and bumblebees. No sequence difference was found when electromorphs came from the same subspecies or from closely related subspecies, suggesting that they were probably identical by descent. In contrast, sequence differences were often detected in distantly related subspecies, showing that size homoplasy frequently occurs at this level of population differentiation. Size homoplasy is increased by limits to free length variation of alleles, a phenomenon that seems to act on interrupted microsatellites when comparing distantly related taxa, that is, honeybee subspecies from different evolutionary lineages. Electromorph sequences suggest that, within the scope of these limits, large mutation events have occurred frequently at both interrupted loci studied. In good agreement with the molecular data, computations based on the observed heterozygosity and number of electromorphs and simulation studies showed that neither locus fits the one-step stepwise mutant model (SMM). We speculate that interrupted microsatellites in general could be characterized by a higher variance in repeat number and consequently a lower homoplasy rate than pure ones. Hence, interrupted microsatellites should be most appropriate for investigating population differentiation and evolutionary relationship between relatively distant populations.      

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

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

Distribution of nucleotide differences between two randomly chosen cistrons in a population of variable size

The distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population is studied here when the population size changes from generation to generation. When genetic variability is measured by heterozygosity (i.e., the probability that two cistrons are different), by the probability that two cistrons differ at two or more nucleotide sites, or by mean number of site differences between cistrons, it is seen that in a population going through a small bottleneck all of these measures decline rapidly but, as soon as population size becomes large, they start to increase owing to new mutations. The amount of reduction in these measures depends not only on the size of bottleneck but also on the rate of population growth. The implications of this study explaining the observed variations in the rates of amino acid substitutions during the evolutionary process are also discussed.     

Simulation results with stepwise mutation model and their interpretations

Summary Monte Carlo simulations are performed to compare the predictions based on the two presently used theoretical models for studying genetic variations in natural populations, the infinite allele model and the stepwise mutation model. Distribution of heterozygosity is noticed to be similar under these models until the product of population size and mutation rate is large. It is seen that electromorphs with high population frequency usually contain older alleles (at the codon level) than an electromorph of low population frequency. The interpretations of these results in explaining the allelic variations at electrophoretic level is also discussed.Research supported by U.S. Public Health Service General Research Support Grant 5 SO 5 RR 07148 from the University of Texas Health Science Center, Graduate School of Biomedical Sciences, Houston, Texas     

Genetic identity between populations when mutation rates vary within and across loci

A formula is derived for the probability that two genes taken at random from the same locus in two populations isolated at time t ago are of the same allelic type. The model assumed is a neutral one where there are possibly different mutation rates between different alleles. Inequalities are derived for this probability. A particular result is that for a fixed overall mutation rate, the probability is least for the infinite alleles model. Inequalities and approximations are found for Nei's genetic identity at one locus when mutation rates vary, and also for the identity across loci when the overall mutation rates per locus vary. Genetic identity at the molecular level is considered and a probability generating function found for the number of segregating sites between two randomly chosen gametes from two divergent populations, under various models.     

Variance of Neutral Genetic Variances within and between Populations for a Quantitative Character

The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.     

利用分子标记分析遗传多样性时的玉米群体取样策略研究

利用分子标记技术对玉米种质资源进行遗传多样性分析对种质资源的保存和利用具有重要的指导意义。但是,在对地方品种和育种群体这些开放授粉群体进行大规模遗传多样性分析时,取样方法将会严重影响到研究结果和工作效率。本研究用2个育种群体和3个地方品种为试材,利用微卫星(SSR)标记对每个群体100个个体及其组成的不同随机混合样品进行了分子检测。结果表明,不同群体的群体内遗传变异大小存在差异;相同数目的个体随机混合的不同样品间的检测结果基本相同;不同数目的个体混合的样品间存在一定程度的差异,并且与材料本身的遗传变异大小有一定关系。考虑到结果的科学性和工作的可行性,建议在利用分子标记(如SSR)进行地方品种和育种群体的遗传多样性评估时,随机选取30个个体组成混合样(或用15个个体组成2个混合样)来代表1个地方品种或育种群体进行分子鉴定。     

Evolutionary Relationship of DNA Sequences in Finite Populations

With the aim of analyzing and interpreting data on DNA polymorphism obtained by DNA sequencing or restriction enzyme technique, a mathematical theory on the expected evolutionary relationship among DNA sequences (nucleons) sampled is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. The statistical property of the number of nucleotide differences between randomly chosen nucleons and that of heterozygosity or nucleon diversity is investigated using this theory. These studies indicate that the estimates of the average number of nucleotide differences and nucleon diversity have a large variance, and a large part of this variance is due to stochastic factors. Therefore, increasing sample size does not help reduce the variance significantly. The distribution of sample allele (nucleomorph) frequencies is also studied, and it is shown that a small number of samples are sufficient in order to know the distribution pattern.     

Microsatellite size homoplasy, SSCP, and population structure: a case study in the freshwater snail Bulinus truncatus

The extent of microsatellite size homoplasy, as well as its effect on several population genetics statistics, was investigated in natural populations using the single-strand conformation polymorphism (SSCP) method. The analysis was conducted using 240 individuals from 13 populations of the freshwater snail Bulinus truncatus at a GT(n)CT(m) compound microsatellite locus. We showed that SSCP can be used to uncover, at least partly, size homoplasy in the core sequence of this category of loci. Eight conformers (SSCP variants) were detected among the three size variants (electromorphs). Sequencing revealed that each conformer corresponded to a different combination of repeats in the GT(n) and CT(m) arrays. Part of this additional variability was detected within populations, resulting in a substantial increase in gene diversity in four populations. Additional variability also changed the values of parameters used to analyze population differentiation among populations: pairwise tests of differentiation were significant much more often with conformers than with electromorphs. On the other hand, pairwise estimates of F(st) were either smaller or larger with conformers than with electromorphs, depending on whether or not electromorphs were shared among populations. However, estimates of F(st) (or analogs) over all populations were very similar, ranging between 0.66 and 0.75. Our results were consistent with the theoretical prediction that homoplasy should not always lead to stronger population structure. Finally, conformer sequences and electromorph size distribution suggested that single-point and/or stepwise mutations occurring simultaneously in the different repeated arrays of compound microsatellites produce sequence variation without size variation and hence generate more size homoplasy than expected under a simple stepwise mutation model.     

Allele frequencies in a multidimensional Wright-Fisher model with general mutation

A formula is obtained for the probability that two genes at a single locus, sampled at random from a population at time t, are of particular types. The model assumed is a diffusion approximation to a neutral Wright-Fisher model in which mutation is general and not necessarily symmetric. An example is given of a population in which one allele has a high mutation rate, and the others have an equal, low mutation rate. The matrix Q, with elements given by the probability of sampling two alleles of particular types, is calculated exactly and approximately for this case. A formula is given for the distribution of the number of segregating sites occurring in two randomly sampled finite sequences of completely linked sites, with general mutation at a site and identical mutation structure between sites.     

Genetic distance and electrophoretic identity of proteins between taxa

Summary The relationship between amino acid substitution and charge change of proteins in the evolutionary process is studied by using a stochastic model. A mathematical formula is developed for the electrophoretic identity of proteins between two different taxa for a given number of average codon differences per protein locus. Using this formula, a reference figure is constructed for estimating the average number of codon differences per locus between taxa.     

Complex mutational patterns and size homoplasy at maize microsatellite loci

Microsatellite markers have become one of the most popular tools for germplasm characterization, population genetics and evolutionary studies. To investigate the mutational mechanisms of maize microsatellites, nucleotide sequence information was obtained for ten loci. In addition, Single-Strand Conformation Polymorphism (SSCP) analysis was conducted to assess the occurrence of size homoplasy. Sequence analysis of 54 alleles revealed a complex pattern of mutation at 8/10 loci, with only 2 loci showing allele variation strictly consistent with stepwise mutations. The overall allelic diversity resulted from changes in the number of repeat units, base substitutions, and indels within repetitive and non-repetitive segments. Thirty-one electromorphs sampled from six maize landraces were considered for SSCP analysis. The number of conformers per electromorph ranged from 1 to 7, with 74.2% of the electromorphs showing more than one conformer. Size homoplasy was apparent within landraces and populations. Variation in the amount of size homoplasy was observed within and between loci, although no differences were detected among populations. The results of the present study provide useful information on the interpretation of genetic data derived from microsatellite markers. Further efforts are still needed to determine the impact of these findings on the estimation of population parameters and on the inference of phylogenetic relationships in maize investigations. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

THE INFLUENCE OF SELF-FERTILIZATION AND POPULATION DYNAMICS ON THE GENETIC STRUCTURE OF SUBDIVIDED POPULATIONS: A CASE STUDY USING MICROSATELLITE MARKERS IN THE FRESHWATER SNAIL BULINUS TRUNCATUS

The distribution of neutral genetic variability within and among sets of populations results from the combined actions of genetic drift, migration, extinction and recolonization processes, mutation, and the mating system. We here analyzed these factors in 38 populations of the hermaphroditic snail Bulinus truncatus. The sampling area covered a large part of the species range. The variability was analyzed using four polymorphic microsatellite loci. A very large number of alleles (up to 55) was found at the level of the whole study. Observed heterozygote deficiencies within populations are consistent with very high selfing rates, generally above 0.80, in all populations. These should depress the variability within populations, because of low effective size, genetic hitchhiking, and background selection, whatever the model of mutation assumed. However, that some populations exhibit much more variability than others suggests that historical demographic processes (e.g., population size variation, bottlenecks, or founding events) may play a significant role. A hierarchical analysis of the distribution of the variability across populations indicates a strong pattern of isolation by distance, whatever the geographical scale considered. Our analysis also illustrates how the mutation rate may affect population differentiation, as different mutation rates result in different levels of homoplasy at microsatellite loci. The effects of both genetic drift and gene flow vary with the temporal and spatial scales considered in B. truncatus populations.     

Genetic screens for factors involved in the notum bristle loss of interspecific hybrids between Drosophila melanogaster and D. simulans

Interspecific cross is a powerful means to uncover hidden within- and between-species variation in populations. One example is a bristle loss phenotype of hybrids between Drosophila melanogaster and D. simulans, although both the pure species have exactly the same pattern of bristle formation on the notum. There exists a large amount of genetic variability in the simulans populations with respect to the number of missing bristles in hybrids, and the variation is largely attributable to simulans X chromosomes. Using nine molecular markers, I screened the simulans X chromosome for genetic factors that were responsible for the differences between a pair of simulans lines with high (H) and low (L) missing bristle numbers. Together with duplication-rescue experiments, a single major quantitative locus was mapped to a 13F-14F region. Importantly, this region accounted for most of the differences between H and L lines in three other independent pairs, suggesting segregation of H and L alleles at the single locus in different populations. Moreover, a deficiency screening uncovered several regions with factors that potentially cause the hybrid bristle loss due to epistatic interactions with the other factors.     

Variation of Microsatellite Size Homoplasy Across Electromorphs, Loci, and Populations in Three Invertebrate Species

Size homoplasy was analyzed at microsatellite loci by sequencing electromorphs, that is, variants of the same size (base pairs). This study was conducted using five interrupted and/or compound loci in three invertebrate species, the honey bee Apis mellifera, the bumble bee Bombus terrestris, and the freshwater snail Bulinus truncatus. The 15 electromorphs sequenced turned out to hide 31 alleles (i.e., variants identical in sequence). Variation in the amount of size homoplasy was detected among electromorphs and loci. From one to seven alleles were detected per electromorph, and one locus did not show any size homoplasy in both bee species. The amount of size homoplasy was related to the sequencing effort, since the number of alleles was correlated with the number of copies of electromorphs sequenced, but also with the molecular structure of the core sequence at each locus. Size homoplasy within populations was detected only three times, meaning that size homoplasy was detected mostly among populations. We analyzed population structure, estimating F _st and a genetic distance, based on either electromorphs or alleles. Whereas little difference was found in A. mellifera, uncovering size homoplasy led to a more marked population structure in B. terrestris and B. truncatus. We also showed in A. mellifera that the detection of size homoplasy may alter phylogenetic reconstructions. Received: 21 July 1997 / Accepted: 29 January 1998     

The Island Model of Population Differentiation: A General Solution

The island model deals with a species which is subdivided into a number of discrete finite populations, races or subspecies, between which some migration occurs. If the number of populations is small, an assumption of equal rates of migration between each pair of populations may be reasonable approximation. Mutation at a constant rate to novel alleles may also be assumed.-A general solution is given for the process of population divergence under this model following subdivision of a single parental population, expressed in terms of the observed average frequency of heterozygotes within and between subpopulations at a randomly chosen set of independently segregating loci. No restriction is imposed on the magnitude of the migration or mutation rates involved, nor on the number of populations exchanging migrants.-The properties of two fundamental measures of genetic divergence are deduced from the theory. One is a parameter related to varphi, the coefficient of kinship, and the other, gamma, measures the rate of mutational divergence between the sub-populations.     

The number of heterozygous loci between two randomly chosen completely linked sequences of loci in two subdivided population models

The stationary probability distribution of the number of heterozygous loci in two randomly chosen sequences of completely linked infinite alleles loci, with mutation at each locus, is found in the island model for within and between islands. Results for an infinite site model are found as a limit. A single charge state locus is also studied in the island model and distributions found for the charge difference between two genes. Similar results are derived for a stepping stone model.     

The effect of newly induced mutations on the fitness of genotypes and populations of yeast (Saccharomyces cerevisiae)

This paper analyses the fate of artificially induced mutations and their importance to the fitness of populations of the yeast, Saccharomyces cerevisiae, an increasingly important model organism in population genetics.

Diploid strains, treated with UV and EMS, were cultured asexually for approximately 540 generations and under conditions where the asexual growth was interrupted by a sexual phase.

Growth rates of 100 randomly sampled diploid clones were estimated at the beginning and at the end of the experiment. After the induction of sporulation the growth rates of 100 randomly sampled spores were measured. UV and EMS treatment decreases the average growth rate of the clones significantly but increases the variability in comparison to the untreated control. After selection over approximately 540 generations, variability in growth rates was reduced to that of the untreated control. No increase in mean population fitness was observed. However, the results show that after selection there still exists a large amount of hidden genetic variability in the populations which is revealed when the clones are cultivated in environments other than those in which selection took place. A sexual phase increased the reduction of the induced variability.     

Contrasting patterns of gene diversity between microsatellites and mitochondrial SNPs in farm and wild Atlantic salmon

Levels of genetic variability at 12 microsatellite loci and 19 single nucleotide polymorphisms in mitochondrial DNA were studied in four farm strains and four wild populations of Atlantic salmon. Within populations, the farm strains showed significantly lower allelic richness and expected heterozygosity than wild populations at the 12 microsatellite loci, but a significantly higher genetic variability with respect to observed number of haplotypes and haplotype diversity in mtDNA. Significant differences in allele- and haplotype-frequencies were observed between farm strains and wild populations, as well as between different farm strains and between different wild populations. The large genetic differentiation at mitochondrial DNA between wild populations (F_ST = 0.24), suggests that the farm strains attained a high mitochondrial genetic variability when created from different wild populations seven generations ago. A large proportion of this variability remains despite an expected lower effective population size for mitochondrial than nuclear DNA. This is best explained by the particular mating schemes in the breeding programmes, with 2–4 females per male. Our observations suggest that for some genetic polymorphisms farm populations might currently hold equal or higher genetic variability than wild populations, but lower overall genetic variability. In the short-term, genetic interactions between escaped farm salmon and wild salmon might increase genetic variability in wild populations, for some, but not most, genetic polymorphisms. In the long term, further losses of genetic variability in farm populations are expected for all genetic polymorphisms, and genetic variability in wild populations will be reduced if escapes of farm salmon continue.     

Genetic profile of cosmopolitan populations: effects of hidden subdivision

Natural populations of many organisms exhibit excess of rare alleles in comparison with the predictions of the neutral mutation hypothesis. It has been shown before that either a population bottleneck or the presence of slightly deleterious mutations can explain this phenomenon. A third explanation is presented in this work, showing that hidden subdivision within a population can also lead to an excess of rare alleles in the total population when the expectations of the neutral model are based on the allele frequency profile of the entire population data. With two examples (mitochondrial DNA-morph distribution and isozyme allele frequency distributions), it is shown that most cosmopolitan human populations exhibit excess of rare as well as total allele counts, when these are compared with the expectations of the neutral mutation hypothesis. The mitochondrial data demonstrate that such excesses can be detected from genetic variation at a single locus as well, and this is not due to stochastic error of allele frequency distributions. Contrast of the present observations with the allele frequency profiles in agglomerated tribal populations from South and Central America shows that even when the neutral expectations hold for individual subpopulations, if all subpopulations are grouped into a single population, the pooled data exhibit an excess of total number of alleles that is mainly due to the excess of rare alleles. Therefore, a primary cause of the excess number of rare alleles could be the hidden subdivision, and the magnitude of the excess indicates the extent of substructuring. The two components of hidden subdivision are: 1) Number of subpopulations, and 2) the average genetic distance among them. The implications of this observation in estimating mutation rate are discussed indicating the difficulties of comparing mutation rates from different population surveys.