Effective Size of Nonrandom Mating Populations

Nonrandom mating whereby parents are related is expected to cause a reduction in effective population size because their gene frequencies are correlated and this will increase the genetic drift. The published equation for the variance effective size, Ne, which includes the possibility of nonrandom mating, does not take into account such a correlation, however. Further, previous equations to predict effective sizes in populations with partial sib mating are shown to be different, but also incorrect. In this paper, a corrected form of these equations is derived and checked by stochastic simulation. For the case of stable census number, N, and equal progeny distributions for each sex, the equation is [formula: see text], where Sk2 is the variance of family size and alpha is the departure from Hardy-Weinberg proportions. For a Poisson distribution of family size (Sk2 = 2), it reduces to Ne = N/(1 + alpha), as when inbreeding is due to selfing. When nonrandom mating occurs because there is a specified system of partial inbreeding every generation, alpha can be substituted by Wright's FIS statistic, to give the effective size as a function of the proportion of inbred mates.     

Linkage Disequilibrium Decay and Past Population History in the Human Genome

The fluctuation of population size has not been well studied in the previous studies of theoretical linkage disequilibrium (LD) expectation. In this study, an improved theoretical prediction of LD decay was derived to account for the effects of changes in effective population sizes. The equation was used to estimate effective population size (N_e) assuming a constant N_e and LD at equilibrium, and these N_e estimates implied the past changes of N_e for a certain number of generations until equilibrium, which differed based on recombination rate. As the influence of recent population history on the N_e estimates is larger than old population history, recent changes in population size can be inferred more accurately than old changes. The theoretical predictions based on this improved expression showed accurate agreement with the simulated values. When applied to human genome data, the detailed recent history of human populations was obtained. The inferred past population history of each population showed good correspondence with historical studies. Specifically, four populations (three African ancestries and one Mexican ancestry) showed population growth that was significantly less than that of other populations, and two populations originated from China showed prominent exponential growth. During the examination of overall LD decay in the human genome, a selection pressure on chromosome 14, the gephyrin gene, was observed in all populations.     

Examination of the relationship between inbreeding and population size

This chapter presents a method for examining the relationship between effective population size and accumulated random inbreeding in human populations. Using a linear regression model on 9 Irish isolates, results show that this method is very useful in assessing differential influences on population structure. Inbreeding refers to the level expected at random due to finite population size, offset by migration into the population. The data used consist of effective population size estimates and kinship estimates derived from surnames for 9 isolates on, or near, the west coast of Ireland. Based on the non-parametric correlation results, there is no monotonic relationship between effective population size and the inverse of kinship. The demographic data available show that, with the exception of Garumna, Lettermullen, and the Aran Islands, the other populations changed little in population size during the latter part of the 19th century. The fact that observed kinship is higher than predicted kinship suggests an increse in population size. These analyses suggest that there is little, if any, relationship between population size and inbreeding among these populations, using 1891 effective population size estimates. Given the range of demogrphic, ecological, and cultural environments of human populations, perhaps it is unexpected to see a set of populations adhering strongly to a given theoretical model. The more important aspect of such model fitting is not whether or not a given model shows a significant fit, but rather the analysis of deviations from an expected relationship.     

INBREEDING AND VARIANCE EFFECTIVE SIZES FOR NONRANDOM MATING POPULATIONS

Following an inbreeding approach and assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, I have derived expressions for the inbreeding effective size, N_eI, for a finite diploid population with variable census sizes for three cases: monoecious populations with partial selfing; dioecious populations of equal numbers of males and females with partial sib mating; and unequal numbers of males and females with random mating. For the first two cases, recurrence equations for the inbreeding coefficient are also obtained, which allow inbreeding coefficients to be predicted exactly in both early and late generations. Following the variance of change in gene frequency approach, a general expression for variance effective size, N_eV, is obtained for a population with unequal numbers of male and female individuals, arbitrary family size distribution, and nonrandom mating. All the parameters involved are allowed to change over generations. For some special cases, the equation reduces to the simple expressions approximately as derived by previous authors. Comparisons are made between equations derived by the present study and those obtained by previous authors. Some of the published equations for N_eI and N_eV are shown to be incomplete or incorrect. Stochastic simulations are run to check the results where disagreements with others are involved.     

On the number of New World founders: a population genetic portrait of the peopling of the Americas

The founding of New World populations by Asian peoples is the focus of considerable archaeological and genetic research, and there persist important questions on when and how these events occurred. Genetic data offer great potential for the study of human population history, but there are significant challenges in discerning distinct demographic processes. A new method for the study of diverging populations was applied to questions on the founding and history of Amerind-speaking Native American populations. The model permits estimation of founding population sizes, changes in population size, time of population formation, and gene flow. Analyses of data from nine loci are consistent with the general portrait that has emerged from archaeological and other kinds of evidence. The estimated effective size of the founding population for the New World is fewer than 80 individuals, approximately 1% of the effective size of the estimated ancestral Asian population. By adding a splitting parameter to population divergence models it becomes possible to develop detailed portraits of human demographic history. Analyses of Asian and New World data support a model of a recent founding of the New World by a population of quite small effective size.     

Allelic genealogy and human evolution

Genetic variation at most loci examined in human populations indicates that the (effective) population size has been approximately 10(4) for the past 1 Myr and that individuals have been genetically united rather tightly. Also suggested is that the population size has never dropped to a few individuals, even in a single generation. These impose important requirements for the hypotheses for the origin of modern humans: a relatively large population size and frequent migration if populations were geographically subdivided. Any hypothesis that assumes a small number of founding individuals throughout the late Pleistocene can be rejected. Extraordinary polymorphism at some loci of the major histocompatibility complex (Mhc) rules out the past action of severe bottlenecks, or the so-called founder principle, which invokes only a small number of founding individuals when a new species emerges. This conclusion may be extended to the 35-Myr-old history of the human lineage, because some polymorphism at Mhc loci seems to have lasted that long. Furthermore, although the population structure prior to the late Pleistocene is less clear, owing to the insensitivity of Mhc alleles, even to low levels of migration, the nature of Mhc polymorphism suggests that the effective size of populations leading to humans was as large as 10(5). Hence, the effective population size of humans might have become somewhat smaller in most of the late Pleistocene. The reduction could be due either to the then adverse environment in the Old World and/or to the increased migration rate. It is also argued that population explosion fostered by the agriculture revolution has had significant effects on incorporating new alleles into human populations.      

Local extinction and recolonization, species effective population size, and modern human origins

A primary objection from a population genetics perspective to a multiregional model of modern human origins is that the model posits a large census size, whereas genetic data suggest a small effective population size. The relationship between census size and effective size is complex, but arguments based on an island model of migration show that if the effective population size reflects the number of breeding individuals and the effects of population subdivision, then an effective population size of 10,000 is inconsistent with the census size of 500,000 to 1,000,000 that has been suggested by archeological evidence. However, these models have ignored the effects of population extinction and recolonization, which increase the expected variance among demes and reduce the inbreeding effective population size. Using models developed for population extinction and recolonization, we show that a large census size consistent with the multiregional model can be reconciled with an effective population size of 10,000, but genetic variation among demes must be high, reflecting low interdeme migration rates and a colonization process that involves a small number of colonists or kin-structured colonization. Ethnographic and archeological evidence is insufficient to determine whether such demographic conditions existed among Pleistocene human populations, and further work needs to be done. More realistic models that incorporate isolation by distance and heterogeneity in extinction rates and effective deme sizes also need to be developed. However, if true, a process of population extinction and recolonization has interesting implications for human demographic history.     

The Episode of Genetic Drift Defining the Migration of Humans out of Africa Is Derived from a Large East African Population Size

Human genetic variation particularly in Africa is still poorly understood. This is despite a consensus on the large African effective population size compared to populations from other continents. Based on sequencing of the mitochondrial Cytochrome C Oxidase subunit II (MT-CO2), and genome wide microsatellite data we observe evidence suggesting the effective size (Ne) of humans to be larger than the current estimates, with a foci of increased genetic diversity in east Africa, and a population size of east Africans being at least 2-6 fold larger than other populations. Both phylogenetic and network analysis indicate that east Africans possess more ancestral lineages in comparison to various continental populations placing them at the root of the human evolutionary tree. Our results also affirm east Africa as the likely spot from which migration towards Asia has taken place. The study reflects the spectacular level of sequence variation within east Africans in comparison to the global sample, and appeals for further studies that may contribute towards filling the existing gaps in the database. The implication of these data to current genomic research, as well as the need to carry out defined studies of human genetic variation that includes more African populations; particularly east Africans is paramount.     

Likelihood and Bayes estimation of ancestral population sizes in hominoids using data from multiple loci

Polymorphisms in an ancestral population can cause conflicts between gene trees and the species tree. Such conflicts can be used to estimate ancestral population sizes when data from multiple loci are available. In this article I extend previous work for estimating ancestral population sizes to analyze sequence data from three species under a finite-site nucleotide substitution model. Both maximum-likelihood (ML) and Bayes methods are implemented for joint estimation of the two speciation dates and the two population size parameters. Both methods account for uncertainties in the gene tree due to few informative sites at each locus and make an efficient use of information in the data. The Bayes algorithm using Markov chain Monte Carlo (MCMC) enjoys a computational advantage over ML and also provides a framework for incorporating prior information about the parameters. The methods are applied to a data set of 53 nuclear noncoding contigs from human, chimpanzee, and gorilla published by Chen and Li. Estimates of the effective population size for the common ancestor of humans and chimpanzees by both ML and Bayes methods are approximately 12,000-21,000, comparable to estimates for modern humans, and do not support the notion of a dramatic size reduction in early human populations. Estimates published previously from the same data are several times larger and appear to be biased due to methodological deficiency. The divergence between humans and chimpanzees is dated at approximately 5.2 million years ago and the gorilla divergence 1.1-1.7 million years earlier. The analysis suggests that typical data sets contain useful information about the ancestral population sizes and that it is advantageous to analyze data of several species simultaneously.     

The importance of control populations for the identification and management of genetic diversity

A fundamental criterion for recognizing species or populations as potentially endangered is the presence/absence of genetic diversity. However, the lack of control populations in many studies of natural systems deprives one from unambiguous criteria for evaluating the genetic effects of small population size and its potential effects on fitness. In this study, I present an example of how the lack of adequate controls may lead to erroneous conclusions for understanding the role that population size may play in the preservation of genetic diversity and fitness of natural populations. The genetic analysis of a population of greater prairie chickens from Illinois, USA, between two time periods (1974–1987 and 1988–1993) in which the studied population experienced a substantial reduction in size and fitness showed no apparent associations between population size and genetic diversity. However, genetic analysis of museum specimens from early this century indicated that Illinois prairie chickens had originally higher levels of genetic diversity, which suggest the Illinois population was already bottlenecked by the 1970s. This study emphasizes the importance of using historical controls to evaluate the temporal dynamics of genetic variability in natural populations. The large number of museum collections worldwide may provide a valuable source of genetic information from past populations, particularly in species currently endangered as a result of human activities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantifying the Human Impacts on Papua New Guinea Reef Fish Communities across Space and Time

Describing the drivers of species loss and of community change are important goals in both conservation and ecology. However, it is difficult to determine whether exploited species decline due to direct effects of harvesting or due to other environmental perturbations brought about by proximity to human populations. Here we quantify differences in species richness of coral reef fish communities along a human population gradient in Papua New Guinea to understand the relative impacts of fishing and environmental perturbation. Using data from published species lists we categorize the reef fishes as either fished or non-fished based on their body size and reports from the published literature. Species diversity for both fished and non-fished groups decreases as the size of the local human population increases, and this relationship is stronger in species that are fished. Additionally, comparison of modern and museum collections show that modern reef communities have proportionally fewer fished species relative to 19^th century ones. Together these findings show that the reef fish communities of Papua New Guinea experience multiple anthropogenic stressors and that even at low human population levels targeted species experience population declines across both time and space.     

Variation in estimated recombination rates across human populations

Recently it has been reported that recombination hotspots appear to be highly variable between humans and chimpanzees, and there is evidence for between-person variability in hotspots, and evolutionary transience. To understand the nature of variation in human recombination rates, it is important to describe patterns of variability across populations. Direct measurement of recombination rates remains infeasible on a large scale, and population-genetic approaches can be imprecise, and are affected by demographic history. Reports to date have suggested broad similarity in recombination rates at large genomic scales and across human populations. Here, we examine recombination rate estimates at a finer population and genomic scale: 28 worldwide populations and 107 SNPs in a 1 Mb stretch of chromosome 22q. We employ analysis of variance of recombination rate estimates, corrected for differences in effective population size using genome-wide microsatellite mutation rate estimates. We find substantial variation in fine-scale rates between populations, but reduced variation within continental groups. All effects examined (SNP-pair, region, population and interactions) were highly significant. Adjustment for effective population size made little difference to the conclusions. Observed hotspots tended to be conserved across populations, albeit at varying intensities. This holds particularly for populations from the same region, and also to a considerable degree across geographical regions. However, some hotspots appear to be population-specific. Several results from studies on the population history of humans are in accordance with our analysis. Our results suggest that between-population variation in DNA sequences may underly recombination rate variation.     

Information-theoretic identification of predictive SNPs and supervised visualization of genome-wide association studies

The size, dimensionality and the limited range of the data values makes visualization of single nucleotide polymorphism (SNP) datasets challenging. The purpose of this study is to evaluate the usefulness of 3D VizStruct, a novel multi-dimensional data visualization technique for SNP datasets capable of identifying informative SNPs in genome-wide association studies. VizStruct is an interactive visualization technique that reduces multi-dimensional data to three dimensions using a combination of the discrete Fourier transform and the Kullback–Leibler divergence. The performance of 3D VizStruct was challenged with several diverse, biologically relevant published datasets including the human lipoprotein lipase (LPL) gene locus, the human Y-chromosome in several populations and a multi-locus genotype dataset of coral samples from four populations. In every case, the SNPs and or polymorphic markers identified by the 3D VizStruct mapping were predictive of the underlying biology.     

Assessing the effects of human mixing patterns on human immunodeficiency virus-1 interhost phylogenetics through social network simulation

Geneticists seeking to understand HIV-1 evolution among human hosts generally assume that hosts represent a panmictic population. Social science research demonstrates that the network patterns over which HIV-1 spreads are highly nonrandom, but the effect of these patterns on the genetic diversity of HIV-1 and other sexually transmitted pathogens has yet to be thoroughly examined. In addition, interhost phylogenetic models rarely account explicitly for genetic diversity arising from intrahost dynamics. This study outlines a graph-theoretic framework (exponential random graph modeling, ERGM) for the estimation, inference, and simulation of dynamic partnership networks. This approach is used to simulate HIV-1 transmission and evolution under eight mixing patterns resembling those observed in empirical human populations, while simultaneously incorporating intrahost viral diversity. Models of parametric growth fit panmictic populations well, yielding estimates of total viral effective population on the order of the product of infected host size and intrahost effective viral population size. Populations exhibiting patterns of nonrandom mixing differ more widely in estimates of effective population size they yield, however, and reconstructions of population dynamics can exhibit severe errors if panmixis is assumed. I discuss implications for HIV-1 phylogenetics and the potential for ERGM to provide a general framework for addressing these issues.     

Population growth enhances the mean fixation time of neutral mutations and the persistence of neutral variation

A fundamental result of population genetics states that a new mutation, at an unlinked neutral locus in a randomly mating diploid population, has a mean time of fixation of ～4N(e) generations, where N(e) is the effective population size. This result is based on an assumption of fixed population size, which does not universally hold in natural populations. Here, we analyze such neutral fixations in populations of changing size within the framework of the diffusion approximation. General expressions are derived for the mean and variance of the fixation time in changing populations. Some explicit results are given for two cases: (i) the effective population size undergoes a sudden change, representing a sudden population expansion or a sudden bottleneck; (ii) the effective population changes linearly for a limited period of time and then remains constant. Additionally, a lower bound for the mean time of fixation is obtained for an effective population size that increases with time, and this is applied to exponentially growing populations. The results obtained in this work show, among other things, that for populations that increase in size, the mean time of fixation can be enhanced, sometimes substantially so, over 4N(e,0) generations, where N(e,0) is the effective population size at the time the mutation arises. Such an enhancement is associated with (i) an increased probability of neutral polymorphism in a population and (ii) an enhanced persistence of high-frequency neutral variation, which is the variation most likely to be observed.     

Contrasting signatures of population growth for mitochondrial DNA and Y chromosomes among human populations in Africa

A history of Pleistocene population expansion has been inferred from the frequency spectrum of polymorphism in the mitochondrial DNA (mtDNA) of many human populations. Similar patterns are not typically observed for autosomal and X-linked loci. One explanation for this discrepancy is a recent population bottleneck, with different rates of recovery for haploid and autosomal loci as a result of their different effective population sizes. This hypothesis predicts that mitochondrial and Y chromosomal DNA will show a similar skew in the frequency spectrum in populations that have experienced a recent increase in effective population size. We test this hypothesis by resequencing 6.6 kb of noncoding Y chromosomal DNA and 780 basepairs of the mtDNA cytochrome c oxidase subunit III (COIII) gene in 172 males from 5 African populations. Four tests of population expansion are employed for each locus in each population: Fu's Fs statistic, the R(2) statistic, coalescent simulations, and the mismatch distribution. Consistent with previous results, patterns of mtDNA polymorphism better fit a model of constant population size for food-gathering populations and a model of population expansion for food-producing populations. In contrast, none of the tests reveal evidence of Y chromosome growth for either food-gatherers or food-producers. The distinct mtDNA and Y chromosome polymorphism patterns most likely reflect sex-biased demographic processes in the recent history of African populations. We hypothesize that males experienced smaller effective population sizes and/or lower rates of migration during the Bantu expansion, which occurred over the last 5,000 years.     

Shortcut predictions for fitness properties at the mutation-selection-drift balance and for its buildup after size reduction under different management strategies

For populations at the mutation-selection-drift (MSD) balance, I develop approximate analytical expressions giving expectations for the number of deleterious alleles per gamete, the number of loci at which any individual is homozygous for deleterious alleles, the inbreeding depression rate, and the additive and dominant components of fitness variance. These predictions are compared to diffusion ones, showing good agreement under a wide range of situations. I also give approximated analytical predictions for the changes in mean and additive variance for fitness when a population approaches a new equilibrium after its effective size is reduced to a stable value. Results are derived for populations maintained with equal family contribution or with no management after size reduction, when selection acts through viability or fertility differences. Predictions are compared to previously published results obtained from transition matrices or stochastic simulations, a good qualitative fit being obtained. Predictions are also obtained for populations of various sizes under different sets of plausible mutational parameters. They are compared to available empirical results for Drosophila, and conservation implications are discussed.     

Effect of changes in population size on genetic microdifferentiation

Changes in local population size are expected to have an effect on the degree of genetic microdifferentiation. A decrease in population size is expected to lead to an increase in microdifferentiation, and an increase in population size to a decrease in microdifferentiation. These expectations are routinely used with historical and/or demographic data to evaluate changes in estimates of microdifferentiation obtained over time for human populations. Here I look more closely at these expectations by using simple mathematical models that relate a change in average effective population size to the degree of microdifferentiation. The direction of change in microdifferentiation is influenced by the migration structure of the populations and the proximity of the region to an equilibrium state. A change in population size always leads to a new equilibrium, but the speed at which this new equilibrium is reached depends on migration and time depth. A decline in population size in one generation always leads to an immediate increase in the degree of microdifferentiation. An increase in population size in one generation could lead to an initial decrease or increase in the degree of microdifferentiation or to no change at all. Consideration of the parameters of the models shows under what conditions such changes occur. The relevance of these models is explored using summary data from a number of human populations.     

Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.