Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.     

Population Bottlenecks and Nonequilibrium Models in Population Genetics. II. Number of Alleles in a Small Population That Was Formed by a Recent Bottleneck

A model is presented in which a large population in mutation/drift equilibrium undergoes a severe restriction in size and subsequently remains at the small size. The rate of loss of genetic variability has been studied. Allelic loss occurs more rapidly than loss of genic heterozygosity. Rare alleles are lost especially rapidly. The result is a transient deficiency in the total number of alleles observed in samples taken from the reduced population when compared with the number expected in a sample from a steady-state population having the same observed heterozygosity. Alternatively, the population can be considered to possess excess gene diversity if the number of alleles is used as the statistical estimator of mutation rate. The deficit in allele number arises principally from a lack of those alleles that are expected to appear only once or twice in the sample. The magnitude of the allelic deficiency is less, however, than the excess that an earlier study predicted to follow a rapid population expansion. This suggests that populations that have undergone a single bottleneck event, followed by rapid population growth, should have an apparent excess number of alleles, given the observed level of genic heterozygosity and provided that the bottleneck has not occurred very recently. Conversely, such populations will be deficient for observed heterozygosity if allele number is used as the sufficient statistic for the estimation of 4Nev. Populations that have undergone very recent restrictions in size should show the opposite tendencies.     

Simulating allele frequencies in a population and the genetic differentiation of populations under mutation pressure

A method is developed for simulating the allele frequencies in an equilibrium or transient population under the effects of neutral mutation and random drift. The method is based on diffusion theory and is fast so that it can be used to study in detail the distribution of heterozygosity or any quantity that can be expressed as a function of allele frequencies. It has been applied to study the distribution of heterozygosity and the distributions of the frequencies of the first three most frequent alleles in a population. It also has been applied to study the distribution of the number of alleles shared by two populations that were derived from a common stock.     

Sampling for Microsatellite-Based Population Genetic Studies: 25 to 30 Individuals per Population Is Enough to Accurately Estimate Allele Frequencies

One of the most common questions asked before starting a new population genetic study using microsatellite allele frequencies is “how many individuals do I need to sample from each population?” This question has previously been answered by addressing how many individuals are needed to detect all of the alleles present in a population (i.e. rarefaction based analyses). However, we argue that obtaining accurate allele frequencies and accurate estimates of diversity are much more important than detecting all of the alleles, given that very rare alleles (i.e. new mutations) are not very informative for assessing genetic diversity within a population or genetic structure among populations. Here we present a comparison of allele frequencies, expected heterozygosities and genetic distances between real and simulated populations by randomly subsampling 5–100 individuals from four empirical microsatellite genotype datasets (Formica lugubris, Sciurus vulgaris, Thalassarche melanophris, and Himantopus novaezelandia) to create 100 replicate datasets at each sample size. Despite differences in taxon (two birds, one mammal, one insect), population size, number of loci and polymorphism across loci, the degree of differences between simulated and empirical dataset allele frequencies, expected heterozygosities and pairwise F_ST values were almost identical among the four datasets at each sample size. Variability in allele frequency and expected heterozygosity among replicates decreased with increasing sample size, but these decreases were minimal above sample sizes of 25 to 30. Therefore, there appears to be little benefit in sampling more than 25 to 30 individuals per population for population genetic studies based on microsatellite allele frequencies.     

Gene flow and melanism in garter snakes revisited: a comparison of molecular markers and island vs. coalescent models

Within populations, the stochastic effect of genetic drift and deterministic effect of natural selection are potentially weakened or altered by gene flow among populations. The influence of gene flow on Lake Erie populations of the common garter snake has been of particular interest because of a discontinuous colour pattern polymorphism (striped vs. melanistic) that is a target of natural selection. We reassessed the relative contributions of gene flow and genetic drift using genetic data and population size estimates. We compared all combinations of two marker systems and two analytical approaches to the estimation of gene flow rates: allozymes (data previously published), microsatellite DNA (new data), the island model ( F _ST-based approach), and a coalescence-based approach. For the coalescence approach, mutation rates and sampling effects were also investigated. While the two markers produced similar results, gene flow based on F _ST was considerably higher (Nm > 4) than that from the coalescence-based method (Nm < 1). Estimates of gene flow are likely to be inflated by lack of migration-drift equilibrium and changing population size. Potentially low rates of gene flow (Nm < 1), small population size at some sites, and positive correlations of number of microsatellite DNA alleles and island size and between M , mean ratio of number of alleles to range in allele size, and island size suggest that in addition to selection, random genetic drift may influence colour pattern frequencies. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 79, 389–399.     

Detection of genetic variation with radioactive ligands. III. genetic polymorphism of transcobalamin II in human plasma

We detected genetically determined, electrophoretic variants of vitamin B12 binding proteins, most probably transcobalamin II, in human plasma. Polymorphic variants were observed in all populations tested; the two most common alleles (of at least four detected to date) attain frequencies of greater than 40% in Caucasians and Orientals. The variants are autosomally inherited and are seen as doublets in homozygotes, and four-banded patterns, the sum of two dissimilar homozygote patterns, in heterozygotes. The technique used in this survey, polyacrylamide gel electrophoresis (PAGE) autoradiography of plasma and serum labeled in vitro with 57Co-vitamin B12 is particularly applicable to the study of trace proteins such as the transcobalamins (10(-9)M). Possible functional variation in the TC II allele products is described, and the selective significance of this worldwide polymorphism is considered.     

Selection often overrides the effects of random processes in island populations of Philaenus spumarius (Homoptera)

The influence of various evolutionary factors on the populations of the colour polymorphic meadow spittlebug, Philaenus spumarius (Homoptera), was investigated on islands in the Gulf of Finland. Long-term (30-year) investigations showed that the populations can survive through very narrow bottlenecks, but after strong reduction in the size of a population, random genetic drift may remove alleles or change allele frequencies. One of the factors sustaining the presence of almost all the colour polymorphism alleles in almost all the populations is gene flow. Migration seems to be largely by air and by the sea surface (anemohydrochoric). On one rocky island, gene flow was able to carry the top dominant allele, p^T, to a number of scattered plant stands. However, it was not powerful enough to alter the differences in allele frequencies between populations living on the same island in meadows of different types 3 m or 12 m from each other. It is highly probable that the factor operating is meadow-specific selection. Its action appears to be based on the ecological character of the meadow. In the different meadows, the coverages of the food plants of the spittlebug are dissimilar. Differences in plant assemblages are possibly of importance in maintaining the meadow-specific allele frequencies in the spittlebug populations.     

SNP and haplotype variation in the human genome

We have surveyed and summarized several aspects of DNA variability among humans. The variation described is the result of mutation followed by a combination of drift, migration and selection bringing the frequencies high enough to be observed. This paper describes what we have learned about how DNA variability differs among genes and populations. We sequenced functional regions of a set of 3950 genes. DNA was sampled from 82 unrelated humans: 20 African-Americans, 20 East Asians, 21 Caucasians, 18 Hispanic-Latinos and 3 Native Americans. Different aspects of variability showed a great deal of concordance. In particular, we studied patterns of single nucleotide polymorphism (SNP) allele and haplotype sharing among the four, large sample populations. We also examined how linkage disequilibrium (LD) between SNPs relates to physical distance in the different populations. It is clear from our findings that while many variants are common to all populations, many others have a more restricted distribution. Research that attempts to find genetic variants that explain phenotypic variants must be careful in their choice of study population.     

Mitochondrial iso-citrate dehydrogenase variation in the Australian bush-rat, Rattus fuscipes greyii

Four reproductively isolated populations of the Australian bush-rat, Rattus fuscipes greyii , are polymorphic for electrophoretic variants of the mitochondrial enzyme, NADP-dependent iso-citrate dehydrogenase (M-Idh). The electrophoretic patterns of M-Idh and a small amount of breeding data are in agreement with the hypothesis that the variation is controlled by two alleles at an autosomal locus, Idh-2. In three relatively large populations, the proportion of heterozygotes at the Idh-2 locus ranges from 0.07 to 0.23, while on a small off-shore island it is 0.60. In this latter population there is an excess of heterozygotes which is on the borderline of statistical significance, suggesting that heterotic selection may be maintaining the polymorphism. Populations on eight other small islands are monomorphic for the allele which is the most frequent in the large populations. In most species M-Idh is less variable than most other enzymic proteins and the results presented here constitute one of the few published examples of an extensive M-Idh polymorphism.     

The world-wide distribution of allele frequencies at the human dopamine D4 receptor locus

The dopamine D4 receptor gene (DRD4) has an expressed polymorphism in the third exon that may have functional relevance. The polymorphism exists at two levels. At the higher level there is an imperfect tandem repeat of 48 base pairs (bp) coding for 16 amino acids; alleles have been identified with 2 (32 amino acids) to 10 (160 amino acids) repeats. The imperfect nature of the repeats is responsible for a more subtle level of variation since alleles with the same number of repeats can differ in the exact sequences or in the order of the variants of the 48-bp unit. We have undertaken a global survey of this expressed polymorphism as one approach to understanding the evolutionary significance and origins of the polymorphism as well as understanding what selective forces, if any, may be operating at this locus. As the first step, we have determined the repeat number genotype of the DRD4 repeat polymorphism in 1,327 individuals from 36 different populations. The allele frequencies differ considerably among the different populations. The 4-repeat allele was the most prevalent (global mean allele frequency = 64.3%) and appeared in every population with a frequency ranging from 0.16 to 0.96. The 7-repeat allele was the second most common (global mean = 20.6%), appearing quite frequently in the Americas (mean frequency = 48.3%) but only occasionally in East and South Asia (mean frequency = 1.9%). The 2-repeat allele was the third most common (global mean frequency = 8.2%) and was quite frequent in East and South Asia (mean frequency = 18.1%) while uncommon in the Americas (mean frequency = 2.9%) and Africa (mean frequency = 1.7%). The universality of the polymorphism with only three common repeat-number alleles (4, 7, and 2) indicates that the polymorphism is ancient and arose before the global dispersion of modern humans. The diversity of actual allele frequencies for this expressed polymorphism among different populations emphasizes the importance of population considerations in the design and interpretation of any association studies carried out with this polymorphism. Received: 18 July 1995 / Revised: 18 December 1995     

Exact moment calculations for genetic models with migration,mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. In addition, we provide closed-form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.     

On the distribution of allele frequencies in a diffusion model

An expression is derived and values tabulated for the expected allele frequencies and their variances, arranged in decreasing order in a population, from the finite and infinite alleles diffusion model in Watterson (1976). The neutral model and also a model with heterozygote selection are considered. Some observed ABO blood group allele frequencies are compared with the tabulated expected frequencies in the neutral three allele model. This extends the results of Watterson and Guess (1977) who tabulate the expected value of the most common allele. One test of neutrality previously advocated is to consider the distribution of F, the population homozygosity, conditional on G, the product of allele frequencies. However it is shown here that for a large number of alleles, F and G are asymptotically independent, the test would not be a good one in this case. A limit theorem is derived for the distribution of allele frequencies in the neutral model when the mutation rate is large. In this case F is shown to be asymptotically normal. An inequality is derived for the probability that the oldest allele in a population is amongst the r most frequent types. An inequality is also found for the probability that a sample will only contain representatives of the r most frequent allele types in the population.     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

New data on the world distribution of paraoxonase (PON1 Gln 192 --> Arg) gene frequencies

The physiological role of human paraoxonase (PON), a serum enzyme that hydrolyzes organophosphate insecticides and nerve agents, is not clear. Of the three genes in the paraoxonase gene family, PON1 shows a polymorphism, Gln 192 --> Arg, governed by two common alleles named *Q and *R. These determine two different isoforms associated, respectively, with lower and higher activity towards paraoxon, a toxic metabolic product of the insecticide parathion. The *R allele has often been found associated with an increased risk of coronary heart disease. As human populations tend towards greater exposure to environmental changes, including changes in dietary habits and contact with insecticides or other toxic substances, health risks will change as well. In studying the prevention of these newly emerging risks, it could be important to know the distribution of the two alleles in the various world populations. In this paper we report on the genotype and allele frequencies of this polymorphism in different populations, most of which have never been examined for this polymorphism. Samples were taken from mainland Italy, Sardinia, Ethiopia, Benin, and Ecuador. The *R allele frequencies for the samples were: 0.313, 0.248, 0.408, 0.612, and 0.789, respectively. The data show a large variability in allele frequencies, and, in particular, that PON1 allele distribution depends on membership to different geographic populations.     

The genetic divergence of two populations

When a population splits in two and the resulting populations evolve independently, genetic divergence may occur due to mutation and genetic drift. This paper considers the influence these factors have on the genetic composition of two samples drawn from the respective populations at some time after the split. Analytical formulas and numerical examples are given of (i) the probability distribution and moments of the allele frequencies, (ii) the number of alleles in common between the samples, and (iii) the probability that the samples are monomorphic.     

The number of lines of descent and fixation probabilities of alleles in the pure genetic drift process: analytical approximations

Analysis of diversity between populations diverged from an evolutionarily small number of generations cannot be done under the assumption that allele frequencies reflect an equilibrium between genetic drift and mutations. An alternative to analysis through coalescence theory is proposed in this situation by developing analytical approximations. Using a Poisson approximation of its distribution, the expected number of genes from one generation whose copies make up the population after a number of generations characterized by fixation index F can be shown to be approximated by 2/F-1, irrespective of population size, and probabilities of fixation of alleles over a finite period of time can be also approximated. These expressions, which were checked numerically, should make it possible to calculate approximate likelihoods for allele frequency distributions promoted by drift.     

Polymorphism of erythrocyte malic enzyme in the goat

Three electrophoretic variants of erythrocyte malic enzyme (ME) in goats were reported. Inheritance data indicate that they are controlled by codominant alleles. The allele frequencies in four Mediterranean populations are given.     

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.     

Dynamics of neutral and selected alleles when the offspring distribution is skewed

We analyze the dynamics of two alternative alleles in a simple model of a population that allows for large family sizes in the distribution of offspring number. This population model was first introduced by Eldon and Wakeley, who described the backward-time genealogical relationships among sampled individuals, assuming neutrality. We study the corresponding forward-time dynamics of allele frequencies, with or without selection. We derive a continuum approximation, analogous to Kimura's diffusion approximation, and we describe three distinct regimes of behavior that correspond to distinct regimes in the coalescent processes of Eldon and Wakeley. We demonstrate that the effect of selection is strongly amplified in the Eldon-Wakeley model, compared to the Wright-Fisher model with the same variance effective population size. Remarkably, an advantageous allele can even be guaranteed to fix in the Eldon-Wakeley model, despite the presence of genetic drift. We compute the selection coefficient required for such behavior in populations of Pacific oysters, based on estimates of their family sizes. Our analysis underscores that populations with the same effective population size may nevertheless experience radically different forms of genetic drift, depending on the reproductive mechanism, with significant consequences for the resulting allele dynamics.     

Patterns of instability of expanded CAG repeats at the ERDA1 locus in general populations.

A highly polymorphic CAG repeat locus, ERDA1, was recently described on human chromosome 17q21.3, with alleles as large as 50-90 repeats and without any disease association in the general population. We have studied allelic distribution at this locus in five human populations and have characterized the mutational patterns by direct observation of 731 meioses. The data show that large alleles (>/=40 CAG repeats) are generally most common in Asian populations, less common in populations of European ancestry, and least common among Africans. We have observed a high intergenerational instability (46. 3%+/-5.1%) of the large alleles. Although the mutation rate is not dependent on parental sex, paternal transmissions have predominantly resulted in contractions, whereas maternal transmissions have yielded expansions. Within this class of large alleles, the mutation rate increases concomitantly with increasing allele size, but the magnitude of repeat size change does not depend on the size of the progenitor allele. Sequencing of specific alleles reveals that the intermediate-sized alleles (30-40 repeats) have CAT/CAC interruptions within the CAG-repeat array. These results indicate that expansion and instability of trinucleotide repeats are not exclusively disease-associated phenomena. The implications of the existence of massively expanded alleles in the general populations are not yet understood.