The Distribution of Mutant Alleles in a Subdivided Population

The results are presented from a simulation study of the spatial distribution of mutant alleles in a subdivided population. Statistical measures of the spatial pattern are defined in such a way that the same quantities could be measured in a geographic survey of allele frequencies in natural populations. Two types of quantities are discussed in this paper: (1) the occupancy distribution provides information on the presence or absence of the mutant in different numbers of demes; and (2) the conditional frequency distribution provides information about the extent of local differentiation when the mutant is present in different numbers of demes. Properties of these distributions are found for different types of natural selection acting on the mutant. Some results are presented for the same statistical measures based on samples of individuals from a fraction of the total number of demes. The simulation results for intermediate levels of the migration rates are compared with analytic results obtained on the limits of high and low migration rates. The main conclusion is that these measures of the spatial distribution of mutants in a subdivided population have simple properties that could provide a new perspective on data from natural populations.     

Effective Size and F-Statistics of Subdivided Populations. II. Dioecious Species

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.     

Effective Sizes for Subdivided Populations

Many derivations of effective population sizes have been suggested in the literature; however, few account for the breeding structure and none can readily be expanded to subdivided populations. Breeding structures influence gene correlations through their effects on the number of breeding individuals of each sex, the mean number of progeny per female, and the variance in the number of progeny produced by males and females. Additionally, hierarchical structuring in a population is determined by the number of breeding groups and the migration rates of males and females among such groups. This study derives analytical solutions for effective sizes that can be applied to subdivided populations. Parameters that encapsulate breeding structure and subdivision are utilized to derive the traditional inbreeding and variance effective sizes. Also, it is shown that effective sizes can be determined for any hierarchical level of population structure for which gene correlations can accrue. Derivations of effective sizes for the accumulation of gene correlations within breeding groups (coancestral effective size) and among breeding groups (intergroup effective size) are given. The results converge to traditional, single population measures when similar assumptions are applied. In particular, inbreeding and intergroup effective sizes are shown to be special cases of the coancestral effective size, and intergroup and variance effective sizes will be equal if the population census remains constant. Instantaneous solutions for effective sizes, at any time after gene correlation begins to accrue, are given in terms of traditional F statistics or transition equations. All effective sizes are shown to converge upon a common asymptotic value when breeding tactics and migration rates are constant. The asymptotic effective size can be expressed in terms of the fixation indices and the number of breeding groups; however, the rate of approach to the asymptote is dependent upon dispersal rates. For accurate assessment of effective sizes, initial, instantaneous or asymptotic, the expressions must be applied at the lowest levels at which migration among breeding groups is nonrandom. Thus, the expressions may be applicable to lineages within socially structured populations, fragmented populations (if random exchange of genes prevails within each population), or combinations of intra- and interpopulation discontinuities of gene flow. Failure to recognize internal structures of populations may lead to considerable overestimates of inbreeding effective size, while usually underestimating variance effective size.     

The Effect of Nonindependent Mate Pairing on the Effective Population Size

The effective population size (N_e) quantifies the effectiveness of genetic drift in finite populations. When generations overlap, theoretical expectations for N_e typically assume that the sampling of offspring genotypes from a given individual is independent among successive breeding events, even though this is not true in many species, including humans. To explore the effects on N_e of nonindependent mate pairing across breeding events, we simulated the genetic drift of mitochondrial DNA, autosomal DNA, and sex chromosome DNA under three mating systems. Nonindependent mate pairing across breeding seasons has no effect when all adults mate pair for life, a small or moderate effect when females reuse stored sperm, and a large effect when there is intense male–male competition for reproduction in a harem social system. If adult females reproduce at a constant rate irrespective of the type of mate pairing, the general effect of nonindependent mate pairing is to decrease N_e for paternally inherited components of the genome. These findings have significant implications for the relative N_e values of different genomic regions, and hence for the expected levels of DNA sequence diversity in these regions.THE effective population size (N_e) is a fundamental parameter of population genetics, which quantifies the effect of genetic drift, the stochastic change in allele frequencies over time in a population of finite size (Wright 1931). The magnitude of N_e affects both the level of genetic variability within a population and the efficiency with which populations retain mildly beneficial mutations and purge mildly deleterious ones. This influences a myriad of genetic phenomena, such as the level of DNA sequence polymorphism, the rate of substitution of nonsynonymous and functional noncoding nucleotide positions, the abundance of transposable elements, levels of variation, and the rate of evolution of gene expression, the persistence of duplicate genes, and genome size and organization (Lynch 2007; Charlesworth 2009). There are a variety of definitions of N_e; here we use the definition in terms of the mean coalescence time of a pair of neutral alleles, which is given by 2N_e (Charlesworth 2009). This definition has the useful feature that the expected pairwise nucleotide site diversity under the widely used infinite sites model is equal to 4N_eμ, where μ is the neutral mutation rate (Kimura 1971).As a result of differences in their ploidy level and mode of inheritance, autosomal DNA (aDNA), the X chromosome (xDNA), the Y chromosome (yDNA), and maternally transmitted organelle DNA such as mitochondrial DNA (mtDNA) generally have a different N_e values. Under certain conditions, such as constant population size, discrete generations, a Poisson distribution of reproductive success, and a sex ratio equal to one, the relative N_e values of these genomic regions (N_e-a, N_e-x, N_e-mt, and N_e-y) are expected to be 4:3:1:1 (Charlesworth 2009). This is because aDNA is biparentally inherited and diploid; xDNA is biparentally inherited, diploid in females, and haploid in males (with female heterogamety, the reverse applies to the Z chromosome), and yDNA (the W chromosome, with female heterogamety) and mtDNA are both effectively uniparentally inherited and haploid in most species.However, several characteristics of natural populations, such as unequal numbers of males and females and nonrandom variation in reproductive success, can affect the value of N_e, even for populations with discrete generations (reviewed in Caballero 1994; Hedrick 2007; Charlesworth 2009). In addition, natural selection at sites linked to neutral markers also has the potential to increase N_e (under balancing selection) (Charlesworth 2006) or to decrease N_e (with background selection or selective sweeps) (Hudson and Kaplan 1988; Charlesworth et al. 1993). Because the nature of natural selection varies in different genomic regions, especially in relation to the rate of recombination, N_e may also vary among unlinked regions with the same ploidy and mode of inheritance, for example, different portions of an autosomal chromosome (Gossmann et al. 2011). In natural populations, these factors can skew the relative N_e values away from the 4:3:1:1 expectation. Even when the effects of natural selection and “nonideal” demography are ignored, the 4:3:1:1 relation still has a large variance when applied to individual loci (Hudson and Turelli 2003).When generations overlap, an additional source of possible deviations from these idealized relations arises from variation among individuals in survival and reproductive success among breeding seasons (Felsenstein 1971; Hill 1972, 1979; Johnson 1977) and from sex differences in demographic parameters and stochastic changes in population size (Engen et al. 2007). In contrast, the effect of a high variance in reproductive success caused by male–male competition is lessened when generations overlap for many breeding seasons (Nunney 1993; Charlesworth 2001). Conversely, overlapping generations with nonindependent mate pairing across breeding seasons could increase the variance in reproductive success. For example, in humans, paternity is correlated with paternal confidence in paternity (Anderson 2006), and married individuals tend to repeatedly produce offspring with each other more frequently than expected by chance. Nonindependent mate pairing among breeding seasons occurs in many other species as well—for example, long-term pair bonding in prairie voles (DeVries et al. 1995), harems in gorillas (Gatti et al. 2004), and sperm storage in fruit flies (Neubaum and Wolfner 1999).Current theoretical models that allow calculation of the effective population size with overlapping generations and age structure make several simplifying assumptions, notably constant sizes of each age class, sufficiently large numbers of individuals in each age class that second-order terms in their reciprocals can be neglected, and independent sampling of offspring genotypes from the same individual reproducing at different times (Hill 1972; Nunney 1991, 1993; Caballero 1994; Charlesworth 1994, 2001). The latter assumption in particular makes it difficult to provide accurate expressions for species such as humans and Drosophila, which reproduce nonindependently because of long-term pair bonds and sperm storage, respectively (Charlesworth 2001).The goal of this study is therefore to explore the consequences of nonindependence of reproductive events across time in different social systems and with different age structures, using simulations of genetic drift in two types of age-structured populations, under different scenarios of independent and nonindependent mate pairing among breeding events. We have explored how these scenarios affect the relative values of N_e-a, N_e-x, N_e-mt, and N_e-y using the infinite alleles model of mutation (Kimura and Crow 1964), with particular emphasis on comparisons of similar mating systems that differ in the extent of nonindependence among breeding events.     

Effective Size and F-Statistics of Subdivided Populations. I. Monoecious Species with Partial Selfing

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.     

The Effective Population Size of Malaria Mosquitoes: Large Impact of Vector Control

Malaria vectors in sub-Saharan Africa have proven themselves very difficult adversaries in the global struggle against malaria. Decades of anti-vector interventions have yielded mixed results—with successful reductions in transmission in some areas and limited impacts in others. These varying successes can be ascribed to a lack of universally effective vector control tools, as well as the development of insecticide resistance in mosquito populations. Understanding the impact of vector control on mosquito populations is crucial for planning new interventions and evaluating existing ones. However, estimates of population size changes in response to control efforts are often inaccurate because of limitations and biases in collection methods. Attempts to evaluate the impact of vector control on mosquito effective population size (N_e) have produced inconclusive results thus far. Therefore, we obtained data for 13–15 microsatellite markers for more than 1,500 mosquitoes representing multiple time points for seven populations of three important vector species—Anopheles gambiae, An. melas, and An. moucheti—in Equatorial Guinea. These populations were exposed to indoor residual spraying or long-lasting insecticidal nets in recent years. For comparison, we also analyzed data from two populations that have no history of organized vector control. We used Approximate Bayesian Computation to reconstruct their demographic history, allowing us to evaluate the impact of these interventions on the effective population size. In six of the seven study populations, vector control had a dramatic impact on the effective population size, reducing N_e between 55%–87%, the exception being a single An. melas population. In contrast, the two negative control populations did not experience a reduction in effective population size. This study is the first to conclusively link anti-vector intervention programs in Africa to sharply reduced effective population sizes of malaria vectors.     

A Phylogenetic Estimator of Effective Population Size or Mutation Rate

A new estimator of the essential parameter θ = 4N(e)μ from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where N(e) is the effective population size and μ is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators of the parameter and is substantially smaller than that of any existing estimator. The high efficiency of the new estimator is achieved by making full use of phylogenetic information in a sample of DNA sequences from a population. An example of estimating θ by the new method is presented using the mitochondrial sequences from an American Indian population.     

Analyzing Gene-Frequency Data When the Effective Population Size Is Finite

The statistical methods used by Schaffer, Yardley and Anderson (1977) and by Gibson et al. (1979) to analyze the variation in allele frequencies in two common types of experimental procedure, where the effective population size is finite, are extended to a more general situation involving a greater range of experiments. The analysis developed is more sensitive in detecting changes in allele frequency due to both fluctuating and balancing selection, as well as to directional selection. The error involved in many studies due to ignoring the effective population size structure would appear to be large. The range of hypotheses that can be considered may be increased as well. Finally, the method of determining bounds for the effective population size, when a particular genetic model is known to hold for a data set, is also outlined.     

Effective Population Size Dynamics and the Demographic Collapse of Bornean Orang-Utans

Bornean orang-utans experienced a major demographic decline and local extirpations during the Pleistocene and Holocene due to climate change, the arrival of modern humans, of farmers and recent commercially-driven habitat loss and fragmentation. The recent loss of habitat and its dramatic fragmentation has affected the patterns of genetic variability and differentiation among the remaining populations and increased the extinction risk of the most isolated ones. However, the contribution of recent demographic events to such genetic patterns is still not fully clear. Indeed, it can be difficult to separate the effects of recent anthropogenic fragmentation from the genetic signature of prehistoric demographic events. Here, we investigated the genetic structure and population size dynamics of orang-utans from different sites. Altogether 126 individuals were analyzed and a full-likelihood Bayesian approach was applied. All sites exhibited clear signals of population decline. Population structure is known to generate spurious bottleneck signals and we found that it does indeed contribute to the signals observed. However, population structure alone does not easily explain the observed patterns. The dating of the population decline varied across sites but was always within the 200–2000 years period. This suggests that in some sites at least, orang-utan populations were affected by demographic events that started before the recent anthropogenic effects that occurred in Borneo. These results do not mean that the recent forest exploitation did not leave its genetic mark on orang-utans but suggests that the genetic pool of orang-utans is also impacted by more ancient events. While we cannot identify the main cause for this decline, our results suggests that the decline may be related to the arrival of the first farmers or climatic events, and that more theoretical work is needed to understand how multiple demographic events impact the genome of species and how we can assess their relative contributions.     

Genome-Wide Estimates of Coancestry,Inbreeding and Effective Population Size in the Spanish Holstein Population

Estimates of effective population size in the Holstein cattle breed have usually been low despite the large number of animals that constitute this breed. Effective population size is inversely related to the rates at which coancestry and inbreeding increase and these rates have been high as a consequence of intense and accurate selection. Traditionally, coancestry and inbreeding coefficients have been calculated from pedigree data. However, the development of genome-wide single nucleotide polymorphisms has increased the interest of calculating these coefficients from molecular data in order to improve their accuracy. In this study, genomic estimates of coancestry, inbreeding and effective population size were obtained in the Spanish Holstein population and then compared with pedigree-based estimates. A total of 11,135 animals genotyped with the Illumina BovineSNP50 BeadChip were available for the study. After applying filtering criteria, the final genomic dataset included 36,693 autosomal SNPs and 10,569 animals. Pedigree data from those genotyped animals included 31,203 animals. These individuals represented only the last five generations in order to homogenise the amount of pedigree information across animals. Genomic estimates of coancestry and inbreeding were obtained from identity by descent segments (coancestry) or runs of homozygosity (inbreeding). The results indicate that the percentage of variance of pedigree-based coancestry estimates explained by genomic coancestry estimates was higher than that for inbreeding. Estimates of effective population size obtained from genome-wide and pedigree information were consistent and ranged from about 66 to 79. These low values emphasize the need of controlling the rate of increase of coancestry and inbreeding in Holstein selection programmes.     

Historical Analysis of Genetic Variation Reveals Low Effective Population Size in a Northern Pike (Esox Lucius) Population

Effective population size (N(e)) of a natural fish population was estimated from temporal changes in allele frequencies at seven microsatellite loci. Use of a historical collection of fish scales made it possible to increase the precision of estimates by increasing the time interval between samples and to use an equation developed for discrete generations without correcting for demographic parameters. Estimates of N(e) for the time intervals 1961-1977 and 1977-1993 were 35 and 72, respectively. For the entire interval, 1961-1993, the estimate of N(e) was 48 when based on a weighted mean derived from the above two estimates or 125 when calculated from 1961 and 1993 samples only. Corresponding ratios of effective size to adult census size ranged from 0.03 to 0.14. An N(e) of 48 over a 32-year period would imply that this population lost as much as 8% of its heterozygosity in that time. Results suggest the potential for using genetic methods based on microsatellite loci data to compare historical trends in N(e) with population dynamic parameters. Such comparisons will help to evaluate the relationship between genetic diversity and long-term persistence of natural populations.     

Adaptive Protein Evolution in Animals and the Effective Population Size Hypothesis

The rate at which genomes adapt to environmental changes and the prevalence of adaptive processes in molecular evolution are two controversial issues in current evolutionary genetics. Previous attempts to quantify the genome-wide rate of adaptation through amino-acid substitution have revealed a surprising diversity of patterns, with some species (e.g. Drosophila) experiencing a very high adaptive rate, while other (e.g. humans) are dominated by nearly-neutral processes. It has been suggested that this discrepancy reflects between-species differences in effective population size. Published studies, however, were mainly focused on model organisms, and relied on disparate data sets and methodologies, so that an overview of the prevalence of adaptive protein evolution in nature is currently lacking. Here we extend existing estimators of the amino-acid adaptive rate by explicitly modelling the effect of favourable mutations on non-synonymous polymorphism patterns, and we apply these methods to a newly-built, homogeneous data set of 44 non-model animal species pairs. Data analysis uncovers a major contribution of adaptive evolution to the amino-acid substitution process across all major metazoan phyla—with the notable exception of humans and primates. The proportion of adaptive amino-acid substitution is found to be positively correlated to species effective population size. This relationship, however, appears to be primarily driven by a decreased rate of nearly-neutral amino-acid substitution because of more efficient purifying selection in large populations. Our results reveal that adaptive processes dominate the evolution of proteins in most animal species, but do not corroborate the hypothesis that adaptive substitutions accumulate at a faster rate in large populations. Implications regarding the factors influencing the rate of adaptive evolution and positive selection detection in humans vs. other organisms are discussed.     

Effects of Overlapping Generations on Linkage Disequilibrium Estimates of Effective Population Size

Use of single-sample genetic methods to estimate effective population size has skyrocketed in recent years. Although the underlying models assume discrete generations, they are widely applied to age-structured species. We simulated genetic data for 21 iteroparous animal and plant species to evaluate two untested hypotheses regarding performance of the single-sample method based on linkage disequilibrium (LD): (1) estimates based on single-cohort samples reflect the effective number of breeders in one reproductive cycle (N_b), and (2) mixed-age samples reflect the effective size per generation (N_e). We calculated true N_e and N_b, using the model species’ vital rates, and verified these with individual-based simulations. We show that single-cohort samples should be equally influenced by N_b and N_e and confirm this with simulated results: N^b was a linear (r² = 0.98) function of the harmonic mean of N_e and N_b. We provide a quantitative bias correction for raw N^b based on the ratio N_b/N_e, which can be estimated from two or three simple life history traits. Bias-adjusted estimates were within 5% of true N_b for all 21 study species and proved robust when challenged with new data. Mixed-age adult samples produced downwardly biased estimates in all species, which we attribute to a two-locus Wahlund effect (mixture LD) caused by combining parents from different cohorts in a single sample. Results from this study will facilitate interpretation of rapidly accumulating genetic estimates in terms of both N_e (which influences long-term evolutionary processes) and N_b (which is more important for understanding eco-evolutionary dynamics and mating systems).     

Evidence for Variation in the Effective Population Size of Animal Mitochondrial DNA

Background

It has recently been shown that levels of diversity in mitochondrial DNA are remarkably constant across animals of diverse census population sizes and ecologies, which has led to the suggestion that the effective population of mitochondrial DNA may be relatively constant.

Results

Here we present several lines of evidence that suggest, to the contrary, that the effective population size of mtDNA does vary, and that the variation can be substantial. First, we show that levels of mitochondrial and nuclear diversity are correlated within all groups of animals we surveyed. Second, we show that the effectiveness of selection on non-synonymous mutations, as measured by the ratio of the numbers of non-synonymous and synonymous polymorphisms, is negatively correlated to levels of mitochondrial diversity. Finally, we estimate the effective population size of mitochondrial DNA in selected mammalian groups and show that it varies by at least an order of magnitude.

Conclusions

We conclude that there is variation in the effective population size of mitochondria. Furthermore we suggest that the relative constancy of DNA diversity may be due to a negative correlation between the effective population size and the mutation rate per generation.     

DNA Polymorphism in a Subdivided Population: The Expected Number of Segregating Sites in the Two-Subpopulation Model

Using the two subpopulation model, the expected numbers of segregating sites in a number of DNA sequences randomly sampled from a subdivided population were examined for several types of population subdivisions. It is shown that, in the case where the pattern of migration is symmetrical such as the finite island model, the expected number of segregating sites is independent of the migration rate when two or three DNA sequences are randomly sampled from the same subpopulation, but depends on the migration rate when more than three DNA sequences are sampled. It is also shown that the population subdivision can increase the amount of DNA polymorphism even in a subpopulation in some cases.