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 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.     

A two-locus mutation—Selection model and some of its evolutionary implications

The deterministic properties of a two-locus model with mutation and selection have been investigated. The mutation process is unidirectional, and the model is so constructed that the genetic variation at one locus is selectively neutral in the absence of a mutant allele at the other locus. All genotypes with three or four mutant alleles are deleterious, while the double heterozygotes may have the same fitness as the standard genotype. If one of the mutant alleles becomes fixed in the population, then the other locus will show a regular one-locus mutation-selection balance. Such a boundary equilibrium may be unstable or stable in the full two-locus setting. In the symmetric case, which is analyzed in details, the population will either go to one of the two boundary equilibria, or to a fully polymorphic equilibrium at which both the mutant alleles are rare. The origin of reproductive separation between two populations via the fixation of complementary deleterious mutants at different loci, and the fixation of nonfunctional alleles at duplicated loci, are two biological processes which both can be studied with the present model. In the last part of the paper we show how the results from the deterministic analysis can be used to predict how different factors will influence the rates of evolution in these systems.     

Age‐dependent mutational effects curtail the evolution of senescence by antagonistic pleiotropy

One of the two main hypotheses to account for ageing is antagonistic pleiotropy (AP). This model requires alleles that increase vital rates (reproduction or survival) at early age at the expense of vital rates at late age. An important focus of evolutionary studies has been to assess the relative abundance of AP‐type aging alleles that arise through mutation. Here, we develop theory that predicts that senescence per se reduces the probability that these alleles arise by mutation. A direct result is that these mutations should arise with extremely low frequencies in already senescing populations. This has profound implications for the evolution of life histories because it implies that the adaptive evolution of aging via AP will experience negative feedback. This theory also clarifies the previously inexplicable epistatic patterns of genetic covariance across age‐specific vital rates that are observed in mutation accumulation experiments. We show that this epistasis is an emergent property of aging.     

Comparison of five tandem repeat loci between humans and chimpanzees.

Five tandem repeat loci were studied in humans and chimpanzees using VNTR probes derived from human DNA. Shared alleles were found at three loci and were often the modal allele in one species but never in both. There was no difference in the mean number of alleles per locus. However, these species exhibited substantially different levels of gene diversity, with chimpanzees monomorphic at two loci. Evidence of reduced variability in chimpanzees corroborates earlier comparisons using isozymes and plasma proteins. Molecular mechanisms, population dynamics, or both may be responsible for these differences. Equal numbers of alleles per locus may reflect high mutation rates. By one test, chimpanzees were out of equilibrium at one locus, which may reflect a typing error or population substructure. The long divergence time, and the high probability of backward mutations, precludes accurate estimation of genetic distance between these species.     

The probability of parallel evolution

Abstract How often will natural selection drive parallel evolution at the DNA sequence level? More precisely, what is the probability that selection will cause two populations that live in identical environments to substitute the same beneficial mutation? Here I show that, under fairly general conditions, the answer is simple: if a wild‐type sequence can mutate to n different beneficial mutations, replicate populations will on average fix the same mutation with probability P= 2/(n + 1). This probability, which is derived using extreme value theory, is independent of most biological details, including the length of the gene in question and the precise distribution of fitness effects among alleles. I conclude that the probability of parallel evolution under natural selection is nearly twice as large as that under neutrality.     

Microsatellites in Zea - variability,patterns of mutations,and use for evolutionary studies

To evaluate the performance of microsatellites or simple sequence repeats (SSRs) for evolutionary studies in Zea, 46 microsatellite loci originally derived from maize were applied to diverse arrays of populations that represent all the diploid species of Zea and 101 maize inbreds. Although null phenotypes and amplification of more than two alleles per plant were observed at modest rates, no practical obstacle was encountered for applying maize microsatellites to other Zea species. Sequencing of microsatellite alleles revealed complex patterns of mutation including frequent indels in the regions flanking microsatellite repeats. In one case, all variation at a microsatellite locus came from indels in the flanking region rather than in the repeat motif. Maize microsatellites show great variability within populations and provide a reliable means to measure intraspecific variation. Phylogeographic relationships of Zea populations were successfully reconstructed with good resolution using a genetic distance based on the infinite allele model, indicating that microsatellite loci are useful in evolutionary studies in Zea. Microsatellite loci show a principal division between tropical and temperate inbred lines, and group inbreds within these two broad germplasm groups in a manner that is largely consistent with their known pedigrees. Received: 10 February 2001 / Accepted: 21 May 2001     

Buccal swabs allow efficient and reliable microsatellite genotyping in amphibians

Buccal swabs have recently been used as a minimally invasive sampling method in genetic studies of wild populations, including amphibian species. Yet it is not known to date what is the level of reliability for microsatellite genotypes obtained using such samples. Allelic dropout and false alleles may affect the genotyping derived from buccal samples. Here we quantified the success of microsatellite amplification and the rates of genotyping errors using buccal swabs in two amphibian species, the Alpine newt Triturus alpestris and the Green tree frog Hyla arborea, and we estimated two important parameters for downstream analyses, namely the number of repetitions required to achieve typing reliability and the probability of identity among genotypes. Amplification success was high, and only one locus tested required two to three repetitions to achieve reliable genotypes, showing that buccal swabbing is a very efficient approach allowing good quality DNA retrieval. This sampling method which allows avoiding the controversial toe-clipping will likely prove very useful in the context of amphibian conservation.     

Mutation rate at swine microsatellite loci

During genotyping of 38 microsatellites for QTL (quantitative trait loci) mapping in three F₂ swine populations, five mutant alleles were detected in a total of 66,436 parent-offspring transfers of microsatellite alleles, which gives an overall mutation rate of 7.52×10^–5 per locus per generation. No significant (P<0.05) association between mutation rates and other factors (i.e., GC contents in the flanking regions, heterozygosity, and repeat number) was revealed. Detailed sequencing showed that four out of five mutant alleles were caused by insertions of one to five repeats, respectively. The other mutant allele was produced by either an insertion of three repeats or a change of 30 base pairs (a deletion of 16 CT repeats and an insertion of one CA repeat). An insertion of one base pair in the flanking region of a microsatellite was also detected. Together, these data indicate that expansions are more common than contractions among microsatellites and that the mutation processes are very complicated, do not fit with the strict stepwise mutation model and may vary from locus to locus.     

DNA-based parentage verification in two Australian goat herds

This study aimed to evaluate a set of DNA markers for their effectiveness in parentage inference, to quantify the level of pedigree errors in Australian Angora and Cashmere goat herds using different pedigree recording methods, and to investigate genotype mismatches between parent and offspring. The 14 microsatellite markers evaluated in this study provided a high level of power (probability of exclusion, PE >99.70%) for parentage testing. The extent of PE depended on polymorphic information content (PIC) and number of alleles for each marker. The minimum number of MS markers essential for accurate determination of parentage was 12, when neither parent is known (PE1) and 10, when one parent is known (PE2). In both populations, the error rates of recorded sire and dam pedigree were significant, averaging around 12%. The error rates of sire and dam pedigree varied considerably between the two populations, reflecting management differences on the two properties. Of 14 MS markers, one locus, SRCRSP07, had null alleles present in the heterozygous state. This null allele was revealed by mismatches of genotypes of parent-offspring pairs. Highly significant deviation from Hardy–Weinberg Equilibrium and significant heterozygote deficiency was also observed at this locus.     

Microsatellite evolution in the 5′ UTR of theHLA-F gene

In order to understand evolutionary aspects of the highly polymorphicHLA-F microsatellite (heterozygosity>90%), several alleles of primates were characterized. 576 meioses from 35 CEPH families were investigated for regular transmission. Furthermore 364 healthy, non-related individuals belonging to four populations from distant ethnic groups were analysed to determine the applicability of this locus in population studies. Sequencing revealed alternate (GAGGAA)_n blocks spaced by (GAA)_n repeats in all primates analysed. The mutation rate of this locus amounts to 1.5%. The mutational patterns follow approximately the one step mutation model. Differential analysis suggests that mutation rates depend on the repeat length. Paternal mutation rates exceed maternal ones. The presence of both allele classes in all human populations investigated indicates that this polymorphism predated raciation. Evidence is provided that the short alleles originated from the longer ones by deletion. Finally the differential analysis of each allele class corroborates the biological history of the studied populations as traced by other genetic markers.     

Analysis of somatic mutations at human minisatellite loci in tumors and cell lines

Hypervariable human minisatellite loci show a substantial level of germline instability, and spontaneous mutation rates to new length alleles have been measured directly by pedigree analysis. We now show that mutation events altering the number of minisatellite repeat units are not restricted to the germline, but also arise in other tissues. Mutant alleles can be detected at a very low frequency in lymphoblastoid cell lines and at much higher frequencies in clonal tumor cell populations, most particularly in gastrointestinal adenocarcinomas. Mutant alleles in these tumors are usually present at a dosage equal to or greater than that of the progenitor allele, indicating that most or all of the tumor cells carry the same clonally derived mutant allele. As with germline mutation, the incidence of somatic mutations in tumors varies from locus to locus, with the same locus showing the highest level of germline and somatic instability. Most length changes, as those in the germline, are of only a few repeat units; however, very large changes are also observed, implying that such mutations can occur in the absence of meiosis.     

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.     

COVARIATION OF SELFING RATES WITH PARENTAL GENE FIXATION INDICES WITHIN POPULATIONS OF MIMULUS GUTTATUS

Wright's gene fixation index F and two single-locus effective selfing rates—the selfing rate at loci with fixed alleles, and the selfing rate at loci without fixed alleles—were estimated in five populations of Mimulus guttatus. These two effective selfing rates describe the inbreeding observed at a single locus when both uniparental and biparental inbreeding are practiced. Estimates were made using progeny arrays assayed for six allozyme loci and two morphological loci exhibiting dominance. The average of the two selfing rates computed for subpopulations (ca. 10 m diameter) ranged from 24% to 59%, with a mean of 37%. When computed for populations (ca. 1 km diameter), average selfing rates were about 10% higher. In four populations, the selfing rate at loci with fixed alleles was higher than the selfing rate at loci without fixed alleles. Thus, the covariance of selfing with parental gene fixation was positive. In one of the populations, estimates for individual plants sampled along a transect gave positive correlations for selfing rates and for gene-fixation indices between adjacent plants. A highly positive correlation between selfing rate and gene fixation of individual plants was also observed. In another population, the covariance of selfing with gene fixation was higher for a locus causing leaf spots than for allozyme loci. This covariance is partially caused by 1) variation in homozygosity among neighborhoods and 2) biparental inbreeding within neighborhoods. The consequences of this covariance are discussed.     

Mutating away from your enemies: The evolution of mutation rate in a host–parasite system

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host–parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.     

A STOCHASTIC SIMULATION STUDY ON SPECIATION BY SEXUAL SELECTION

A two-locus multi-allele sexual isolation model incorporating mutation and genetic drift which was first proposed by Nei et al. (1983) is studied here. One locus controls the male mating character, and the other controls female receptivity. All females are assumed to have equal mating success. Therefore, the frequencies of female receptivity alleles are changed by mutation, drift, and hitchhiking with male character alleles. Without hitchhiking, development of sexual isolation between allopatric populations proceeds faster in smaller populations, as expected. The hitchhiking effect, by triggering the mutual reinforcement of mating behavior of both sexes (or the runaway process, Fisher [1958]), speeds up the evolution of sexual isolation significantly. For populations with 2Nv ≤ 0.2 (N = population size, ν = mutation rate), the rates of divergence all approach the maximum possible rate. Sympatric sexual isolation develops quite frequently if two favorable conditions are met: 1) There is no selection on female phenotype (except in some limited cases), and 2) The population size is large enough to carry several female receptivity alleles. Because of stochastic factors, these alleles may lead to the formation of two discrete groups of females, each group receptive to males of different mating characters. The formation of sympatric sexually-isolated groups is also aided significantly, at the incipient stage, by the runaway process.     

ClonEstiMate,a Bayesian method for quantifying rates of clonality of populations genotyped at two‐time steps

Partial clonality is commonly used in eukaryotes and has large consequences for their evolution and ecology. Assessing accurately the relative importance of clonal vs. sexual reproduction matters for studying and managing such species. Here, we proposed a Bayesian approach, ClonEstiMate, to infer rates of clonality c from populations sampled twice over a short time interval, ideally one generation time. The method relies on the likelihood of the transitions between genotype frequencies of ancestral and descendent populations, using an extended Wright–Fisher model explicitly integrating reproductive modes. Our model provides posterior probability distribution of inferred c, given the assumed rates of mutation, as well as inbreeding and selfing when occurring. Tested under various conditions, this model provided accurate inferences of c, especially when the amount of information was modest, that is low sample sizes, few loci, low polymorphism and strong linkage disequilibrium. Inferences remained robust when mutation models and rates were misinformed. However, the method was sensitive to moderate frequencies of null alleles and when the time interval between required samplings exceeding two generations. Misinformed rates on mating modes (inbreeding and selfing) also resulted in biased inferences. Our method was tested on eleven data sets covering five partially clonal species, for which the extent of clonality was formerly deciphered. It delivered highly consistent results with previous information on the biology of those species. ClonEstiMate represents a powerful tool for detecting and inferring clonality in finite populations, genotyped with SNPs or microsatellites. It is freely available at https://www6.rennes.inra.fr/igepp_eng/Productions/Software .     

The transition density for multiple neutral alleles

For a single genetic locus with multiple alleles, Littler and Fackerall (1975, Biometrics 31, 117–123) found the transition density of the allelic proportions in the case of no mutation and no selection. Their method is found to be suitable for a model in which symmetric mutation is allowed between alleles. The sampling probabilities and moments are found. Watterson's (1977, Genetics 85, 789–814) test for selection is found to be non-robust for non-stationary populations.     

The influence of spatial inhomogeneities on neutral models of geographical variation : I. Formulation

The influence of spatial variation in the carrying capacity and migration rate of a geographical barrier on the one-dimensional stepping-stone model is studied. The monoecious, diploid population is subdivided into an infinite linear array of panmictic colonies that exchange gametes. In each deme, the rate of self-fertilization is equal to the reciprocal of the number of individuals in that deme. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to new alleles at the same rate. In the diffusion approximation, a partial differential equation that incorporates spatial (and temporal) variation in the carrying capacity and migration rate is derived for the probability of identity. Transition conditions that simultaneously take into account discontinuities in the carrying capacity and migration rate are established: the probability of identity is continuous, but its partial derivatives are not, their ratio being a simple function of the carrying capacities and migrational variance on the two sides of the inhomogeneity. The partial derivatives of the probability of identity are continuous across a geographical barrier, whereas the probability of identity itself has a discontinuity proportional to the partial derivative at the barrier, the constant of proportionality being a measure of the difficulty of crossing the barrier.