Variance Of Heterozygosity Research Articles

Effects of fine-scale population structure on the distribution of heterozygosity in a long-term study of Antirrhinum majus.

Many studies have quantified the distribution of heterozygosity and relatedness in natural populations, but few have examined the demographic processes driving these patterns. In this study, we take a novel approach by studying how population structure affects both pairwise identity and the distribution of heterozygosity in a natural population of the self-incompatible plant Antirrhinum majus. Excess variance in heterozygosity between individuals is due to identity disequilibrium, which reflects the variance in inbreeding between individuals; it is measured by the statistic g2. We calculated g2 together with FST and pairwise relatedness (Fij) using 91 SNPs in 22,353 individuals collected over 11 years. We find that pairwise Fij declines rapidly over short spatial scales, and the excess variance in heterozygosity between individuals reflects significant variation in inbreeding. Additionally, we detect an excess of individuals with around half the average heterozygosity, indicating either selfing or matings between close relatives. We use 2 types of simulation to ask whether variation in heterozygosity is consistent with fine-scale spatial population structure. First, by simulating offspring using parents drawn from a range of spatial scales, we show that the known pollen dispersal kernel explains g2. Second, we simulate a 1,000-generation pedigree using the known dispersal and spatial distribution and find that the resulting g2 is consistent with that observed from the field data. In contrast, a simulated population with uniform density underestimates g2, indicating that heterogeneous density promotes identity disequilibrium. Our study shows that heterogeneous density and leptokurtic dispersal can together explain the distribution of heterozygosity.

Imbalanced segregation of recombinant haplotypes in hybrid populations reveals inter- and intrachromosomal Dobzhansky-Muller incompatibilities.

Dobzhansky-Muller incompatibilities (DMIs) are a major component of reproductive isolation between species. DMIs imply negative epistasis and are exposed when two diverged populations hybridize. Mapping the locations of DMIs has largely relied on classical genetic mapping. Approaches to date are hampered by low power and the challenge of identifying DMI loci on the same chromosome, because strong initial linkage of parental haplotypes weakens statistical tests. Here, we propose new statistics to infer negative epistasis from haplotype frequencies in hybrid populations. When two divergent populations hybridize, the variance in heterozygosity at two loci decreases faster with time at DMI loci than at random pairs of loci. When two populations hybridize at near-even admixture proportions, the deviation of the observed variance from its expectation becomes negative for the DMI pair. This negative deviation enables us to detect intermediate to strong negative epistasis both within and between chromosomes. In practice, the detection window in hybrid populations depends on the demographic scenario, the recombination rate, and the strength of epistasis. When the initial proportion of the two parental populations is uneven, only strong DMIs can be detected with our method unless migration prevents parental haplotypes from being lost. We use the new statistics to infer candidate DMIs from three hybrid populations of swordtail fish. We identify numerous new DMI candidates, some of which are inferred to interact with several loci within and between chromosomes. Moreover, we discuss our results in the context of an expected enrichment in intrachromosomal over interchromosomal DMIs.

The imprecision of heterozygosity-fitness correlations hinders the detection of inbreeding and inbreeding depression in a threatened species

In nonpedigreed wild populations, inbreeding depression is often quantified through the use of heterozygosity-fitness correlations (HFCs), based on molecular estimates of relatedness. Although such correlations are typically interpreted as evidence of inbreeding depression, by assuming that the marker heterozygosity is a proxy for genome-wide heterozygosity, theory predicts that these relationships should be difficult to detect. Until now, the vast majority of empirical research in this area has been performed on generally outbred, nonbottlenecked populations, but differences in population genetic processes may limit extrapolation of results to threatened populations. Here, we present an analysis of HFCs, and their implications for the interpretation of inbreeding, in a free-ranging pedigreed population of a bottlenecked species: the endangered takahe (Porphyrio hochstetteri). Pedigree-based inbreeding depression has already been detected in this species. Using 23 microsatellite loci, we observed only weak evidence of the expected relationship between multilocus heterozygosity and fitness at individual life-history stages (such as survival to hatching and fledging), and parameter estimates were imprecise (had high error). Furthermore, our molecular data set could not accurately predict the inbreeding status of individuals (as 'inbred' or 'outbred', determined from pedigrees), nor could we show that the observed HFCs were the result of genome-wide identity disequilibrium. These results may be attributed to high variance in heterozygosity within inbreeding classes. This study is an empirical example from a free-ranging endangered species, suggesting that even relatively large numbers (>20) of microsatellites may give poor precision for estimating individual genome-wide heterozygosity. We argue that pedigree methods remain the most effective method of quantifying inbreeding in wild populations, particularly those that have gone through severe bottlenecks.

Genotypic selection in Daphnia populations consisting of inbred sibships

The genetic basis of fitness reduction associated with inbreeding is still poorly understood. Here we use associations between allozyme genotypes and fitness to investigate the genetic basis of inbreeding depression in experimental outdoor populations of the water flea, Daphnia magna. In Daphnia, a phase of clonal reproduction follows hatching from sexually produced resting eggs, and changes in genotype frequencies during the clonal phase can be used to estimate fitness. Our experiment resembles natural colonization of ponds in that single clones colonize an empty pool, expand asexually and produce sexual offspring by selfing (sisters mate with their clonal brothers). These offspring diapause and form populations consisting of selfed sibships in the following spring. In 12 of 13 experimental populations, genotypes of selfed hatchlings after diapause conformed to Mendelian expectations. During the subsequent ca. 10 asexual generations, however, genotype frequencies changed significantly at 19 of 27 single loci studied within populations, mostly in favour of heterozygotes, with heterozygosity at multiple loci affecting the change in genotype frequency multiplicatively. Because variance in heterozygosity among siblings at a given marker reflects only heterozygosity in the chromosomal region around this marker, our results suggest that selection at fitness-associated loci in the chromosomal regions near the markers were responsible for these changes. The genotype frequency changes were more consistent with selection acting on linked loci than on the allozymes themselves. Taken together, the evidence for abundant selection in the chromosomal regions of the markers and the fact that changes in genotype frequencies became apparent only after several generations of clonal selection, point to a genetic load consisting of many alleles of small or intermediate effects, which is consistent with the strong genetic differentiation and repeated genetic bottlenecks in the metapopulation from which the animals for this study were obtained.

Computer Program for Calculating Within-Population Variance of Heterozygosity

Computer Program for Calculating Within-Population Variance of Heterozygosity

A study on a nearly neutral mutation model in finite populations.

As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, sigma, of the distribution of the mutant effect. If 4N sigma is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4N sigma is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4N sigma is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4N sigma is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.

GENETIC VARIABILITY MAINTAINED BY MUTATION AND OVERDOMINANT SELECTION IN FINITE POPULATIONS

Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Itô and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2Ns (N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient (s) to mutation rate (nu) is large and the mean heterozygosity (h) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.

MAINTENANCE OF GENETIC VARIABILITY UNDER THE JOINT EFFECT OF MUTATION, SELECTION AND RANDOM DRIFT

Formulae are developed for the distribution of allele frequencies (the frequency spectrum), the mean number of alleles in a sample, and the mean and variance of heterozygosity under mutation pressure and under either genic or recessive selection. Numerical computations are carried out by using these formulae and Watterson's (1977) formula for the distribution of allele frequencies under overdominant selection. The following properties are observed: (1) The effect of selection on the distribution of allele frequencies is slight when 4Ns </= 4, but becomes strong when 4Ns becomes larger than 10, where N denotes the effective size and s the selective difference between alleles. Genic selection and recessive selection tend to force the distribution to be U-shaped, whereas overdominant selection has the opposite tendency. (2) The mean total number of alleles in a sample is much more strongly affected by selection than the mean number of rare alleles in a sample. (3) Even slight heterozygote advantage, as small as 10(-5), increases considerably the mean heterozygosity of a population, as compared to the case of neutral mutations. On the other hand, even slight genic or recessive selection causes a great reduction in heterozygosity when population size is large. (4) As a test statistic, the variance of heterozygosity can be used to detect the presence of selection, though it is not efficient when the selection intensity is very weak, say when 4Ns is around 4 or less. A model, which is somewhat similar to Ohta's (1976) model of slightly deleterious mutations, has been proposed to explain the following general patterns of genic variation: (i) There seems to be an upper limit for the observed average heterozygosities. (ii) The distribution of allele frequencies is U-shaped for every species surveyed. (iii) Most of the species surveyed tend to have an excess of rare alleles as compared with that expected under the neutral mutation hypothesis.

Is there a pattern of gene differentiation in the Indian populations.

Indian populations divided into a number of endogamous groups consisting of different castes, languages, religions, and tribes provide unique opportunities for examining the extent and nature of genetic differentiation at a microevolutionary stage. The genetic relationships between some of these Indian population groups have been examined using electrophoretic data from several biochemical loci in a gene diversity analysis. Does this type of analysis provide any insight into what causes such gene differentiation? What patterns of genetic variation emerge from these empirical findings? Answers are sought by relating the observed heterozygosity, genetic distance, and allied statistics to a mutation-drift hypothesis. The statistics used are: (1) interlocus mean and variance of heterozygosity, (2) mean and variance of genetic distance, and (3) correlation of heterozygosity and gene identity. The observed relationships between these sets of statistics agree well with the ones predicted by the hypothesis that different alleles at protein loci are selectively equivalent and gene frequency change occurs predominantly due to genetic drift.

Maintenance of genetic variability under mutation and selection pressures in a finite population.

Formulas are developed for the distribution of allele frequencies and the mean and variance of heterozygosity under mutation and selection pressures. In large populations, even slight selection drastically changes the shape of the distribution of allele frequencies and reduces heterozygosity. On the other hand, the number of rare alleles in a sample is much less affected by selection. Under genic selection, heterozygosity may decrease with increasing population size. As a test statistic, the variance of heterozygosity can be used to detect the presence of selection, though it is not efficient when selection is very slight.

Infinite allele model with varying mutation rate.

Available data suggest that the variation in mutation rate among protein loci follows the gamma distribution. Thus, taking into account this variation, formulae are developed for the distribution of allele frequencies, mean and variance of heterozygosity, expected number of alleles, proportion of polymorphic loci, and genetic distance. These formulae should be more appropriate for the analysis of gene frequency data for protein loci than equivalent formulae with constant mutation rate.