Genetic Variation and Random Drift in Autotetraploid Populations

The rate of decay of genetic variation is determined for randomly mating autotetraploid populations of finite size, and the equilibrium homozygosity under mutation and random drift is calculated. It is shown that heterozygosity is lost at a slower rate than in diploid populations, and that the equilibrium heterozygosity with mutation and random drift is higher than for diploids. Outcrossing populations as well as populations that randomly self are analyzed. A method of comparing genetic variation between autotetraploid and diploid populations is proposed. Our treatment suggests that the ``gametic homozygosity' provides a unified approach for comparing genotypes within a population as well as comparing genetic variation between populations with different levels of ploidy.     

Environmental variance in male mating success modulates the positive versus negative impacts of sexual selection on genetic load

Sexual selection on males is predicted to increase population fitness, and delay population extinction, when mating success negatively covaries with genetic load across individuals. However, such benefits of sexual selection could be counteracted by simultaneous increases in genome-wide drift resulting from reduced effective population size caused by increased variance in fitness. Resulting fixation of deleterious mutations could be greatest in small populations, and when environmental variation in mating traits partially decouples sexual selection from underlying genetic variation. The net consequences of sexual selection for genetic load and population persistence are therefore likely to be context dependent, but such variation has not been examined. We use a genetically explicit individual-based model to show that weak sexual selection can increase population persistence time compared to random mating. However, for stronger sexual selection such positive effects can be overturned by the detrimental effects of increased genome-wide drift. Furthermore, the relative strengths of mutation-purging and drift critically depend on the environmental variance in the male mating trait. Specifically, increasing environmental variance caused stronger sexual selection to elevate deleterious mutation fixation rate and mean selection coefficient, driving rapid accumulation of drift load and decreasing population persistence times. These results highlight an intricate balance between conflicting positive and negative consequences of sexual selection on genetic load, even in the absence of sexually antagonistic selection. They imply that environmental variances in key mating traits, and intrinsic genetic drift, should be properly factored into future theoretical and empirical studies of the evolution of population fitness under sexual selection.     

Relationship between heterozygosity and genetic distance in the three major races of man

In pairwise comparisons of gene frequency data from the three major races of man, the single locus measures of the heterozygosity within and the genetic distance between races are shown to be strongly correlated across the loci coding for red cell proteins and enzymes. The intercept of the regression line of genetic distance on heterozygosity in protein enzyme loci is statistically insignificant. These findings suggest that the genetic variability at the enzyme and protein loci in man is probably maintained by a balance of mutation and random genetic drift. At the blood group loci, however, the observed relationship between genetic distance and heterozygosity does not follow the expectation of the neutral mutation hypothesis. These observations are discussed in terms of the changes in probability of identical monomorphism in two populations during the process of gene differentiation.     

Optimum number of marker loci for estimating outcrossing in plant populations

Summary For the measurements of outcrossing rates in plant populations, current electrophoretic procedures permit many loci to be scored per individual progeny. Given that the total experimental effort or cost is limited, the choice exists then between assaying a large number of loci on a restricted number of individuals, or assaying a large number of individuals at a few loci. Using simple models and the criterion of minimising the variance of the estimate, several factors which affect this choice are considered (levels of polymorphism, heterozygosity, linkage disequilibrium, pollen or outcrossing heterogeneity). The general conclusion is that the actual level of outcrossing is a major factor in determining experimental strategy. Maximum efficiency for estimating outcrossing in predominantly inbreeding plants comes from large samples assayed for few polymorphic loci. In contrast, in predominantly outcrossing plants, more loci should be assayed at the expense of sample size for improved statistical efficiency.     

STATISTICAL ANALYSIS OF HETEROZYGOSITY DATA: INDEPENDENT SAMPLE COMPARISONS

The distribution of mean heterozygosities under an infinite allele model with constant mutation rate was examined through simulation studies. It was found that, although the variance of the distribution decreases with increasing numbers of loci examined as expected, the shape of the distribution may remain skewed or bimodal. The distribution becomes symmetrical for increasing mean heterozygosity levels and numbers of loci. As a result, parametric statistical tests may not be valid for making comparisons among populations or species. Independent sample t-tests were examined in detail to determine the frequency of rejection of the null hypothesis when pairs of samples are drawn from populations with the same mean heterozygosity. Differing numbers of loci and levels of mean heterozygosity were examined. For mean heterozygosity levels above 7.5%, t-tests provide the proper rejection rate, with as few as five loci. When mean heterozygosity is as low as 2.5%, the t-test is conservative even when 40 loci are examined in each population. Independent sample t-tests were then examined for their power to detect true differences between populations as the degree of difference and number of loci vary. Although large differences can be found with high certainty, differences on the order of 5% heterozygosity may require that large numbers of loci (>40) be examined in order to be 80% or more certain of detecting them. In addition, it is emphasized that, for small numbers of loci (<25), the statistical detection of differences of interesting magnitude requires that relatively rare sampling events occur and that much larger differences be observed among the samples than exist for the population means. Two reasons exist for the lack of sensitivity of the test procedures. First, when mean heterozygosity levels are low, the non-normality of the sample means is perhaps most important. Second, even when mean heterozygosity levels are high or when sample sizes are large enough so sample means are approximately normally distributed, the intrinsically high interlocus variance of heterozygosity estimates makes the tests insensitive to the presence of heterozygosity differences that might be biologically meaningful. Finally, the implications of the results of this study are discussed with regard to observed low levels of correlation between heterozygosity and other explanatory variables.     

Rate and directionality of mutations and effects of allele size constraints at anonymous, gene-associated, and disease-causing trinucleotide loci.

We studied the patterns of within- and between-population variation at 29 trinucleotide loci in a random sample of 200 healthy individuals from four diverse populations: Germans, Nigerians, Chinese, and New Guinea highlanders. The loci were grouped as disease-causing (seven loci with CAG repeats), gene-associated (seven loci with CAG/CCG repeats and eight loci with AAT repeats), or anonymous (seven loci with AAT repeats). We used heterozygosity and variance of allele size (expressed in units of repeat counts) as measures of within-population variability and GST (based on heterozygosity as well as on allele size variance) as the measure of genetic differentiation between populations. Our observations are: (1) locus type is the major significant factor for differences in within-population genetic variability; (2) the disease-causing CAG repeats (in the nondisease range of repeat counts) have the highest within-population variation, followed by the AAT-repeat anonymous loci, the AAT-repeat gene-associated loci, and the CAG/CTG-repeat gene-associated loci; (3) an imbalance index beta, the ratio of the estimates of the product of effective population size and mutation rate based on allele size variance and heterozygosity, is the largest for disease-causing loci, followed by AAT- and CAG/CCG-repeat gene-associated loci and AAT-repeat anonymous loci; (4) mean allele size correlates positively with allele size variance for AAT- and CAG/CCG-repeat gene-associated loci and negatively for anonymous loci; and (5) GST is highest for the disease-causing loci. These observations are explained by specific differences of rates and patterns of mutations in these four groups of trinucleotide loci, taking into consideration the effects of the past demographic history of the modern human population.     

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.     

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.     

Genetic analysis of microsatellite polymorphism in the Elliot's Pheasant (Syrmaticus ellioti) in China

In this study, we reported the population genetic analyses in the Elliot's Pheasant(Syrnaticus ellioti) using seven polymorphism microsatellite loci based on 105 individuals from 4 geographical populations. Departures from Hardy-Weinberg equilibrium were found in four geographical populations. The average number of alleles was 8.86, with a total of 62 alleles across 7 loci; observed heterozygosity (HO) was generally low and the average number was 0.504. For the seven microsatellite loci, the polymorphism information content ranged from 0.549 to 0.860, with an average number 0.712. Population bottlenecks of the four geographical populations were tested by infinite allele mutation model, step-wise mutation model and two-phase mutation model, which found that each population had experienced bottleneck effect during the recent period. Fst analysis across all geographical populations indicated that the genetic differentiaton between the Guizhou geographical population and the Hunan geographical population was highly significant (P<0.001), a finding supported by the far genetic relationship showed by the neighbor-joining tree of four geographical populations based on Nei's unbiased genetic distances. Using hierarchical analysis of molecular variance (Guizhou geographical population relative to all others pooled), we found a low level of the genetic variation among geographical populations and that between groups. However, differences among populations relative to the total sample explained most of the genetic variance (92.84%), which was significant.     

Recombination disequilibrium in ideal and natural populations

Following Hardy-Weinberg disequilibrium (HWD) occurring at a single locus and linkage disequilibrium (LD) between two loci in generations, we here proposed the third genetic disequilibrium in a population: recombination disequilibrium (RD). RD is a measurement of crossover interference among multiple loci in a random mating population. In natural populations besides recombination interference, RD may also be due to selection, mutation, gene conversion, drift and/or migration. Therefore, similarly to LD, RD will also reflect the history of natural selection and mutation. In breeding populations, RD purely results from recombination interference and hence can be used to build or evaluate and correct a linkage map. Practical examples from F₂, testcross and human populations indeed demonstrate that RD is useful for measuring recombination interference between two short intervals and evaluating linkage maps. As with LD, RD will be important for studying genetic mapping, association of haplotypes with disease, plant breading and population history.     

Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.     

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.     

Isolation and characterization of 13 polymorphic microsatellite loci from the clam shrimp Eulimnadia texana (Crustacea: Spinicaudata)

Thirteen polymorphic microsatellite loci were isolated and characterized from the clam shrimp Eulimnadia texana. In analyses of 20–50 individuals from two populations the number of alleles ranged from two to seven with observed heterozygosity ranging between 0.00 and 0.37. The low values for heterozygosity were not unexpected for a group characterized by its unusual androdioecious mating system, in which males compete with self‐compatible hermaphrodites for offspring production. These microsatellites are likely to be useful for further evolutionary investigations of this rare mating system in these crustaceans.     

Simulation of the effect of population size on the evolution of the recombination fraction

A study, by means of computer simulation, has been performed on the evolution of recombination rate modifier genes in a system with three diallelic loci (A, B and C). The locus C, selectively neutral, is responsible for the modification of the recombination fraction between the major loci (A and B) which are subjected to selection. Two models have been analysed, the modifier allele being recessive in one of them, and codominant in the other, with infinite and finite populations. Distinct initial genic frequencies of the major loci and different selection coefficients have been utilised. We have found that the frequency of the allele which favours recombination increases in finite populations, and decreases slightly in infinite populations. These results are consistent with previous theory; presumably, selection favours alleles reducing recombination between epistatically interacting loci in a infinite population, since this reduces the breakup of advantageous combinations of alleles. However, in finite populations, selection favours the breakup of the random linkage disequilibria which are produced by random drift.     

Breeding designs for recombinant inbred advanced intercross lines

Recombinant inbred lines derived from an advanced intercross, in which multiple generations of mating have increased the density of recombination breakpoints, are powerful tools for mapping the loci underlying complex traits. We investigated the effects of intercross breeding designs on the utility of such lines for mapping. The simplest design, random pair mating with each pair contributing exactly two offspring to the next generation, performed as well as the most extreme inbreeding avoidance scheme at expanding the genetic map, increasing fine-mapping resolution, and controlling genetic drift. Circular mating designs offer negligible advantages for controlling drift and exhibit greatly reduced map expansion. Random-mating designs with variance in offspring number are also poor at increasing mapping resolution. Given equal contributions of each parent to the next generation, the constraint of monogamy has no impact on the qualities of the final population of inbred lines. We find that the easiest crosses to perform are well suited to the task of generating populations of highly recombinant inbred lines.     

Microsatellite DNA variability in the populations of muskoxen <Emphasis Type="Italic">Ovibos moschatus</Emphasis> transplanted into the Russian North

The muskoxen populations introduced to the Taimyr Peninsula and Wrangel Island in 1974 to 1975 were examined for sequence variation at seven microsatellite loci. Donor material originated from the populations of Banks Island (Canada) and Eastern Greenland. Relative to the allele frequencies, both introduced populations demonstrated rather strong deviation from the populations of the native range. At the same time, population allelic structures evidenced that they were closer to the Greenland populations. Estimates of genetic diversity at microsatellite loci (expected heterozygosity and the allele number) in the introduced muskoxen were found to be high for populations originating from a small number of founder individuals. In the immigrants, linkage disequilibrium and deviation of the genotype frequencies from the Hardy-Weinberg proportions were observed, which was mainly caused by the deficit of heterozygotes. The same pattern was also typical of native populations and was explained in terms of specific population structure and demographic processes. The latter were manifested as a periodic decline of the effective population size, resulting in the prevailing influence of genetic drift and inbreeding. The consequences of genetic drift were not as dramatic, as could be expected, which may be explained by a high mutation rate of neutral microsatellite loci and fast growth of the new populations.     

The Exact Distributions of F IS under Partial Asexuality in Small Finite Populations with Mutation

Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient F _IS. Understanding how those mating systems impact the possible distributions of F _IS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of F _IS, the probabilities of positive and negative F _IS, the probabilities of fixation and the probabilities to observe changes in the sign of F _IS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive F _IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F _IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F _IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F _IS spectrum, including strong positive F _IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.     

The Variance of the Number of Loci Having a Given Gene Frequency

Considering a random mating population of finite size, the variance of the number of loci having a given gene frequency was derived under the assumption of a steady flux of mutations. The variance of average heterozygosity among populations was also derived under the same assumption. It was shown that these variances are proportional to the population size if the mutants are selectively neutral, and they are inversely proportional to the selection coefficient if the mutants are selectively advantageous and additive in their fitness.     

Statistical Studies on Protein Polymorphism in Natural Populations I. Distribution of Single Locus Heterozygosity

Surveying the literature, the frequency distribution of single-locus heterozygosity among protein loci was examined in 95 vertebrate and 34 invertebrate species with the aim of testing the validity of the mutation-drift hypothesis. This distribution did not differ significantly from that expected under the mutation-drift hypothesis for any of the species examined when tested by the Kolmogorov-Smirnov goodness-of-fit statistic. The agreement between the observed interlocus variance of heterozygosity and its theoretical expectation was also satisfactory. There was an indication that variation in the mutation rate among loci inflates the interlocus variance of heterozygosity. The variance of heterozygosity for a homologous locus among different species was also studied. This variance generally agreed with the theoretical value very well, though in some groups of Drosophila species there was a significant discrepancy. The observed relationship between average heterozygosity and the proportion of polymorphic loci was in good agreement with the theoretical relationship. It was concluded that, with respect to the pattern of distribution of heterozygosity, the majority of data on protein polymorphisms are consistent with the mutation-drift hypothesis. After examining alternative possible explanations involving selection, it was concluded that the present data cannot be explained adequately without considering a large effect of random genetic drift, whether there is selection or not.