Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.     

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.     

Distribution of nucleotide differences between two randomly chosen cistrons in a population of variable size

The distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population is studied here when the population size changes from generation to generation. When genetic variability is measured by heterozygosity (i.e., the probability that two cistrons are different), by the probability that two cistrons differ at two or more nucleotide sites, or by mean number of site differences between cistrons, it is seen that in a population going through a small bottleneck all of these measures decline rapidly but, as soon as population size becomes large, they start to increase owing to new mutations. The amount of reduction in these measures depends not only on the size of bottleneck but also on the rate of population growth. The implications of this study explaining the observed variations in the rates of amino acid substitutions during the evolutionary process are also discussed.     

Heterogeneity of microsatellite mutations within and between loci,and implications for human demographic histories.

Microsatellites have been widely used to reconstruct human evolution. However, the efficient use of these markers relies on information regarding the process producing the observed variation. Here, we present a novel approach to the locus-by-locus characterization of this process. By analyzing somatic mutations in cancer patients, we estimated the distributions of mutation size for each of 20 loci. The same loci were then typed in three ethnically diverse population samples. The generalized stepwise mutation model was used to test the predicted relationship between population and mutation parameters under two demographic scenarios: constant population size and rapid expansion. The agreement between the observed and expected relationship between population and mutation parameters, even when the latter are estimated in cancer patients, confirms that somatic mutations may be useful for investigating the process underlying population variation. Estimated distributions of mutation size differ substantially amongst loci, and mutations of more than one repeat unit are common. A new statistic, the normalized population variance, is introduced for multilocus estimation of demographic parameters, and for testing demographic scenarios. The observed population variation is not consistent with a constant population size. Time estimates of the putative population expansion are in agreement with those obtained by other methods.     

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.     

Test for interaction between two unlinked loci

Despite the growing consensus on the importance of testing gene-gene interactions in genetic studies of complex diseases, the effect of gene-gene interactions has often been defined as a deviance from genetic additive effects, which is essentially treated as a residual term in genetic analysis and leads to low power in detecting the presence of interacting effects. To what extent the definition of gene-gene interaction at population level reflects the genes' biochemical or physiological interaction remains a mystery. In this article, we introduce a novel definition and a new measure of gene-gene interaction between two unlinked loci (or genes). We developed a general theory for studying linkage disequilibrium (LD) patterns in disease population under two-locus disease models. The properties of using the LD measure in a disease population as a function of the measure of gene-gene interaction between two unlinked loci were also investigated. We examined how interaction between two loci creates LD in a disease population and showed that the mathematical formulation of the new definition for gene-gene interaction between two loci was similar to that of the LD between two loci. This finding motived us to develop an LD-based statistic to detect gene-gene interaction between two unlinked loci. The null distribution and type I error rates of the LD-based statistic for testing gene-gene interaction were validated using extensive simulation studies. We found that the new test statistic was more powerful than the traditional logistic regression under three two-locus disease models and demonstrated that the power of the test statistic depends on the measure of gene-gene interaction. We also investigated the impact of using tagging SNPs for testing interaction on the power to detect interaction between two unlinked loci. Finally, to evaluate the performance of our new method, we applied the LD-based statistic to two published data sets. Our results showed that the P values of the LD-based statistic were smaller than those obtained by other approaches, including logistic regression models.     

Forecasting changes in amphibian biodiversity: aiming at a moving target

Amphibian population declines and sudden species' extinctions began to be noted at the beginning of the 1980s. Understanding the causes of the losses is hampered by our poor knowledge of the amphibian fauna in many parts of the world. Amphibian taxa are still being described at a high rate, especially in the tropics, which means that even quantifying species lost as a percentage of the current fauna can be a misleading statistic in some parts of the globe. The number of species that have gone missing is only one measure of the loss of biodiversity. Long-term studies of single-species populations are needed, but this approach has its limits. Amphibian populations often show great annual variation in population size making it difficult, if not impossible, to use short-term studies as a basis for deciding if a population is increasing or decreasing in the long term. Aggregating single studies into databases and searching for patterns of variation is a way of overcoming this limitation. Several databases on species and population time series are available or in development. These records show that declines are continuing worldwide with some species and populations, especially in the tropics and at higher elevations, at greater risk of extinction than others. Unfortunately, amphibian databases with population time series have much less information for the tropics compared to the temperate zone, and less for Africa and Asia compared with Europe and North America. Focusing limited resources using comprehensive statistical designs is a way to maximize the efficiency and effectiveness of monitoring efforts. It is clear that, in the first decades of the twenty-first century, the regions of the globe with the highest diversity of amphibian species will experience the greatest rates of decrease of forests and increase in human population size, fertilizer use, agricultural production, creation of new croplands and irrigation. Many of these changes are likely negatively to affect amphibian species diversity, and their influence must be understood before concluding, at least for amphibians, that the 2010 millennium assessment goal of significantly reversing the rate of loss of Earth's biodiversity can be met.     

Recent advances in human quantitative-trait-locus mapping: comparison of methods for selected sibling pairs

During the past few years, there has been a great deal of new work on methods for mapping quantitative-trait loci by use of sibling pairs and sibships. There are several new methods based on linear regression, as well as several more that are based on score statistics. In theory, most of the new methods should be relatively robust to violations of distributional assumptions and to selected sampling, but, in practice, there has been little evaluation of how the methods perform on selected samples. We survey most of the new regression-based statistics and score statistics and propose a few minor variations on the score statistics. We use simulation to evaluate the type I error and the power of all of the statistics, considering (a) population samples of sibling pairs and (b) sibling pairs ascertained on the basis of at least one sibling with a trait value in the top 10% of the distribution. Most of the statistics have correct type I error for selected samples. The statistics proposed by Xu et al. and by Sham and Purcell are generally the most powerful, along with one of our score statistic variants. Even among the methods that are most powerful for "nice" data, some are more robust than others to non-Gaussian trait models and/or misspecified trait parameters.     

Neutral theory in macroecology and population genetics

Current neutral theory in macroecology has many parallels with neutral theory in population genetics, but it also has many distinct features that arise because it focuses mainly on questions at the community level rather than at the population level. Here we highlight the similarities and differences between these two bodies of theories from the aspects of the operational units, definitions of neutrality, basic parameters, driving forces, spatial structure and community assembly rules. Compared with neutral theory in population genetics, whose development spans more than 40 years, neutral theory in ecology, which is only a few years old, is still immature and under-developed. There are many opportunities for major theoretical contributions, some of which can be adopted directly from population genetics, while others will require new theoretical work. We critically discuss these opportunities and theoretical challenges in neutral macroecology, particularly in regard to effective community size, ecological drift, community differentiation and ecological dominance.     

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.     

Accelerated and adaptive evolution of yeast sexual adhesins

There is a recent emergence of interest in the genes involved in gametic recognition as drivers of reproductive isolation. The recent population genomic sequencing of two species of sexually primitive yeasts (Liti G, Carter DM, Moses AM, Warringer J, Parts L, James SA, Davey RP, Roberts IN, Burt A, Koufopanou V et al. [23 co-authors]. 2009. Population genomics of domestic and wild yeasts. Nature 458:337-341.) has provided data for systematic study of the roles these genes play in the early evolution of sex and speciation. Here, we discovered that among genes encoding cell surface proteins, the sexual adhesin genes have evolved significantly more rapidly than others, both within and between Saccharomyces cerevisiae and its closest relative S. paradoxus. This result was supported by analyses using the PAML pairwise model, a modified McDonald-Kreitman test, and the PAML branch model. Moreover, using a combination of a new statistic of neutrality, an information theory-based measure of evolutionary variability, and functional characterization of amino acid changes, we found that a higher proportion of amino acid changes are fixed in the sexual adhesins than in other proteins and a greater proportion of the fixed amino acid changes either between the two species or the two subgroups of S. paradoxus are functionally dissimilar or radically different. These results suggest that the accelerated evolution of sexual adhesin genes may facilitate speciation, or incipient speciation, and promote sexual selection in general.     

Census vs. effective population size in chinook salmon: large- and small-scale environmental perturbation effects

Population viability has often been assessed by census of reproducing adults. Recently this method has been called into question and estimation of the effective population size (Ne) proposed as a complementary method to determine population health. We examined genetic diversity in five populations of chinook salmon (Oncorhynchus tshawytscha) from the upper Fraser River watershed (British Columbia, Canada) at 11 microsatellite loci over 20 years using DNA extracted from archived scale samples. We tested for changes in genetic diversity, calculated the ratio of the number of alleles to the range in allele size to give the statistic M, calculated Ne from the temporal change in allele frequency, used the maximum likelihood method to calculate effective population size (NeM), calculated the harmonic mean of population size, and compared these statistics to annual census estimates. Over the last two decades population size has increased in all five populations of chinook examined; however, Ne calculated for each population was low (81-691) and decreasing over the time interval measured. Values of NeM were low, but substantially higher than Ne calculated using the temporal method. The calculated values for M were generally low (M < 0.70), indicating recent population reductions for all five populations. Large-scale historic barriers to migration and development activities do not appear to account for the low values of Ne; however, available spawning area is positively correlated with Ne. Both Ne and M estimates indicate that these populations are potentially susceptible to inbreeding effects and may lack the ability to respond adaptively to stochastic events. Our findings question the practice of relying exclusively on census estimates for interpreting population health and show the importance of determining genetic diversity within populations.     

HOW ARE DELETERIOUS MUTATIONS PURGED? DRIFT VERSUS NONRANDOM MATING

Accumulation of deleterious mutations has important consequences for the evolution of mating systems and the persistence of small populations. It is well established that consanguineous mating can purge a part of the mutation load and that lethal mutations can also be purged in small populations. However, the efficiency of purging in natural populations, due to either consanguineous mating or to reduced population size, has been questioned. Consequences of consanguineous mating systems and small population size are often equated under "inbreeding" because both increase homozygosity, and selection is though to be more efficient against homozygous deleterious alleles. I show that two processes of purging that I call "purging by drift" and "purging by nonrandom mating" have to be distinguished. Conditions under which the two ways of purging are effective are derived. Nonrandom mating can purge deleterious mutations regardless of their dominance level, whereas only highly recessive mutations can be purged by drift. Both types of purging are limited by population size, and sharp thresholds separate domains where purging is either effective or not. The limitations derived here on the efficiency of purging are compatible with some experimental studies. Implications of these results for conservation and evolution of mating systems are discussed.     

Why proof of safety is much more difficult than proof of hazard

On the basis of simple, generally accepted biostatistical and public health principles, it is shown that for environmental health hazards a proof of safety is much more difficult than a proof of hazard. The effective sample sizes required for proof of safety are orders of magnitude greater than what is feasible in biostatistical-epidemiological studies. Although many assurances of safety "in the name of science" have been issued by government agencies and others, few if any of these assurances are statistically valid.     

Test for a population expansion after a drastic reduction in population size using DNA sequence data

Populations may, during their evolutionary history, go through drastic changes in population size due to bottlenecks or founder events upon colonization of new areas. This involves a subsample of haplotypes, causing the allele frequencies to be different from the original population. In addition, the period of recovery after a bottleneck can be of considerable length. If reproduction is unequal among individuals but random with regard to haplotype, large deviations from the patterns expected in a stable population may result. By means of computer simulation, I have analysed the patterns arising when populations undergo bottlenecks and then slowly recover, and used two new statistical tests for the detection of the bottleneck. A test based on the variance of the relative frequency of haplotypes had generally high power even at low sample size (n=25). This statistic was most powerful after very strong bottlenecks and lost power with increasing propagule size. A test based on the variance of the pairwise differences shows slightly less power. As expected, power was reduced when migration into the founder population was allowed from the source population. This suggests that the test is particularly suited for detecting relatively recent and strong bottlenecks, and thus may be a valuable tool for identifying population events on a fine temporal scale, such as colonisations after the last glaciation.     

Detection of reduction in population size using data from microsatellite loci

We demonstrate that the mean ratio of the number of alleles to the range in allele size, which we term M, calculated from a population sample of microsatellite loci, can be used to detect reductions in population size. Using simulations, we show that, for a general class of mutation models, the value of M decreases when a population is reduced in size. The magnitude of the decrease is positively correlated with the severity and duration of the reduction in size. We also find that the rate of recovery of M following a reduction in size is positively correlated with post-reduction population size, but that recovery occurs in both small and large populations. This indicates that M can distinguish between populations that have been recently reduced in size and those which have been small for a long time. We employ M to develop a statistical test for recent reductions in population size that can detect such changes for more than 100 generations with the post-reduction demographic scenarios we examine. We also compute M for a variety of populations and species using microsatellite data collected from the literature. We find that the value of M consistently predicts the reported demographic history for these populations. This method, and others like it, promises to be an important tool for the conservation and management of populations that are in need of intervention or recovery.     

Comparative evaluation of a new effective population size estimator based on approximate bayesian computation

We describe and evaluate a new estimator of the effective population size (N(e)), a critical parameter in evolutionary and conservation biology. This new "SummStat" N(e) estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N(e). Simulations of a Wright-Fisher population with known N(e) show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N(e) values. We also address the paucity of information about the relative performance of N(e) estimators by comparing the SummStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated using initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and N(e) < or = 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N(e). The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any potentially informative summary statistic from population genetic data.     

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.     

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.     

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.