Estimating effective population size from samples of sequences: inefficiency of pairwise and segregating sites as compared to phylogenetic estimates.

It is known that under neutral mutation at a known mutation rate a sample of nucleotide sequences, within which there is assumed to be no recombination, allows estimation of the effective size of an isolated population. This paper investigates the case of very long sequences, where each pair of sequences allows a precise estimate of the divergence time of those two gene copies. The average divergence time of all pairs of copies estimates twice the effective population number and an estimate can also be derived from the number of segregating sites. One can alternatively estimate the genealogy of the copies. This paper shows how a maximum likelihood estimate of the effective population number can be derived from such a genealogical tree. The pairwise and the segregating sites estimates are shown to be much less efficient than this maximum likelihood estimate, and this is verified by computer simulation. The result implies that there is much to gain by explicitly taking the tree structure of these genealogies into account.     

Likelihood analysis of ongoing gene flow and historical association

Abstract.— We develop a Monte Carlo-based likelihood method for estimating migration rates and population divergence times from data at unlinked loci at which mutation rates are sufficiently low that, in the recent past, the effects of mutation can be ignored. The method is applicable to restriction fragment length polymorphisms (RFLPs) and single nucleotide polymorphisms (SNPs) sampled from a subdivided population. The method produces joint maximum-likelihood estimates of the migration rate and the time of population divergence, both scaled by population size, and provides a framework in which to test either for no ongoing gene flow or for population divergence in the distant past. We show the method performs well and provides reasonably accurate estimates of parameters even when the assumptions under which those estimates are obtained are not completely satisfied. Furthermore, we show that, provided that the number of polymorphic loci is sufficiently large, there is some power to distinguish between ongoing gene flow and historical association as causes of genetic similarity between pairs of populations.     

MILDLY DELETERIOUS MUTATIONS IN AVIAN MITOCHONDRIAL DNA: EVIDENCE FROM NEUTRALITY TESTS

To determine whether mildly deleterious mutations (MDMs) are present in nonrecombining genomes such as avian mitochondrial DNA (mtDNA), I analyzed molecular data from 14 studies using the neutrality tests of Tajima (1989a) and McDonald and Kreitman (1991). The presence of MDMs in mtDNA is inferred from trends observed across species in estimates of heterozygosity (θ and π) and by comparisons of polymorphism and divergence using the neutrality index (NI). Assuming neutrality, θ equals π and NI equals one. In this study, however, θ is greater than π more often than expected by chance, which reflects an excess of low-frequency alleles, and NI values presented here and elsewhere are consistently greater than one, which suggests an excess of nonsynonymous mutations within species (polymorphism) relative to between species (divergence). These observations suggest that, within species, there is an excess of rare haplotypes and that these haplotypes are carrying MDMs. The excess rare haplotypes may need to be accounted for when estimating population genetic parameters that assume strict neutrality.     

Estimates of the gene frequency of BRCA1 and its contribution to breast and ovarian cancer incidence.

The majority of multiple-case families that segregate both breast and ovarian cancer in a dominant fashion are due to mutations in the BRCA1 gene on chromosome 17q. In this paper, we have combined penetrance estimates for BRCA1 with the results of two population-based genetic epidemiological studies to estimate the gene frequency of BRCA1. On the assumption that the excess risk of ovarian cancer in first degree relatives of breast cancer patients and the breast cancer excess in relatives of ovarian cancer patients are both entirely accounted for by BRCA1, we estimate that the BRCA1 gene frequency is 0.0006 (95% confidence interval [O.002-0.002]) and that the proportion of breast cancer cases in the general population due to BRCA1 is 5.3% below age 40 years, 2.2% between ages 40 and 49 years, and 1.1% between ages 50 and 70 years. The corresponding estimates for ovarian cancer are 5.7%, 4.6%, and 2.1%, respectively. Our results suggest that the majority of breast cancer families with less than four cases and no ovarian cancer are not due to rare highly penetrant genes such as BRCA1 but are more likely to be due either to chance or to more common genes of lower penetrance.     

Absolute Risk and Loss-of-Lifetime Estimates for Quantitative Risk Assessment

Quantitative risk assessments in public health settings intend to describe the hazard of a specific exposure in a given population on the basis of epidemiological and/or experimental results. Two different risk quantities, the absolute lifetime excess risk and the loss-of-lifetime, which differ in their definition of hazard, are discussed and compared. For both measures estimation procedures are derived and the relationship between the various estimates which are currently in use are investigated. It is shown that the two most common estimators can be written as special cases of a more general concept. This leads to conclusions about the assumptions on which different estimation procedures are implicitly based. For all discussed estimators variance estimates are derived. The analytical results for both risk parameters will be elucidated by an example on lung cancer risk due to residential radon in Germany.     

Small population size and extremely low levels of genetic diversity in island populations of the platypus, Ornithorhynchus anatinus

Genetic diversity generally underpins population resilience and persistence. Reductions in population size and absence of gene flow can lead to reductions in genetic diversity, reproductive fitness, and a limited ability to adapt to environmental change increasing the risk of extinction. Island populations are typically small and isolated, and as a result, inbreeding and reduced genetic diversity elevate their extinction risk. Two island populations of the platypus, Ornithorhynchus anatinus, exist; a naturally occurring population on King Island in Bass Strait and a recently introduced population on Kangaroo Island off the coast of South Australia. Here we assessed the genetic diversity within these two island populations and contrasted these patterns with genetic diversity estimates in areas from which the populations are likely to have been founded. On Kangaroo Island, we also modeled live capture data to determine estimates of population size. Levels of genetic diversity in King Island platypuses are perilously low, with eight of 13 microsatellite loci fixed, likely reflecting their small population size and prolonged isolation. Estimates of heterozygosity detected by microsatellites (H(E)= 0.032) are among the lowest level of genetic diversity recorded by this method in a naturally outbreeding vertebrate population. In contrast, estimates of genetic diversity on Kangaroo Island are somewhat higher. However, estimates of small population size and the limited founders combined with genetic isolation are likely to lead to further losses of genetic diversity through time for the Kangaroo Island platypus population. Implications for the future of these and similarly isolated or genetically depauperate populations are discussed.     

On estimating critical population size for an endangered species in the presence of environmental stochasticity

A stationary second order autoregressive process with Gaussian noise, which was linked to survivorship and reproductive success by logistic transformations, was used as a model for an environmental process. Computer experiments in Monte Carlo integration, with the objective of exploring the sensitivity of estimates of mean critical population size to variations in the parameters of the environmental process, were then conducted. These experiments suggest that estimates of mean critical population size are very sensitive to the form of the autocorrelation function of the stationary environmental process. For the most part, those experiments in which the autocorrelation function was strictly positive not only resulted in the largest estimates of mean critical population size but also led to the highest levels of environmental stochasticity as measured by its coefficient of variation. As in previous work, these experiments suggest that concerted efforts should be made to model those environmental factors that are critical to the survivability of an endangered species in assessing its chances for continued existence.     

Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci

The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be approximately 20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.     

Modelling the past and future of whales and whaling

Historical reconstruction of the population dynamics of whales before, during and after exploitation is crucial to marine ecological restoration and for the consideration of future commercial whaling. Population dynamic models used by the International Whaling Commission require historical catch records, estimates of intrinsic rates of increase and current abundance, all of which are subject to considerable uncertainty. Population genetic parameters can be used for independent estimates of historical demography, but also have large uncertainty, particularly for rates of mutational substitution and gene flow. At present, demographic and genetic estimates of pre-exploitation abundance differ by an order of magnitude and, consequently, suggest vastly different baselines for judging recovery. Here, we review these two approaches and suggest the need for a synthetic analytical framework to evaluate uncertainty in key parameters. Such a framework could have broad application to modelling both historical and contemporary population dynamics in other exploited species.     

The interaction among evolutionary forces in the pathogenic fungus Mycosphaerella graminicola

The population genetic dynamic of a species is driven by interactions among mutation, migration, drift, mating system, and selection, but it is rare to have sufficient empirical data to estimate values for all of these forces and to allow comparison of the relative magnitudes of these evolutionary forces. We combined data from a mark-release-recapture experiment, extensive population surveys, and computer simulations to evaluate interactions among these evolutionary forces in the pathogenic fungus Mycosphaerella graminicola. The results from these studies showed that, on average, the immigration rate was 0.027, the fraction of outcrossing individuals was 0.035, and the selection coefficient associated with immigrants was 0.106 each generation. We also estimated that effective population sizes for this fungus were larger than 24,000 and the mutation rate for the RFLP markers used in surveys and field experiments was approximately 4 x 10(-5). Computer simulations based on these estimates indicate that, on average, the global population of M. graminicola has reached equilibrium. Population genetic parameters including number of alleles, gene diversity, and population subdivision estimated from the computer simulations were surprisingly close to empirical estimates. Simulations also revealed that random drift is the major evolutionary force decreasing genetic variation in this fungus, followed by natural selection. The major force adding to genetic variation was mutation, followed by gene flow and sexual recombination. Gene flow played the leading role in decreasing population subdivision while natural selection was the major factor increasing population subdivision.     

Admixture in a biologically African caste of black Americans

Social and historical factors account for much of the variation in European ancestry among different Black American populations, including that of McNary, Arizona. The Black population of McNary is socioculturally and geographically isolated. Admixture estimates based upon reflectometry and serological data suggest that this population has less than 5% European ancestry. Anthropometric and hemoglobin data also suggest that this population is more African in ancestry than other Black American populations. Admixture estimates for the population are complicated by several factors. Genetic drift has probably affected Black McNary; estimated effective population size (Ne) is 52.11 and the coefficient of breeding isolation is less than 50. Frequencies of the alleles B, O, and r support this hypothesis; they are quite atypical for a Black American group. Selective migration and occupational selection may also have influenced the current genetic composition of Black McNary. Over 80% of the Black residents of McNary were born in backwoods lumbering towns in the American South. Most Black families in McNary trace their economic reliance on lumbering back several generations. Historical sources and demographic data from Black McNary suggest that Southern Black millworking families formed an endogamous unit that produced this caste, which has a relatively small amount of European ancestry.     

Multilocus methods for estimating population sizes, migration rates and divergence time, with applications to the divergence of Drosophila pseudoobscura and D. persimilis

The genetic study of diverging, closely related populations is required for basic questions on demography and speciation, as well as for biodiversity and conservation research. However, it is often unclear whether divergence is due simply to separation or whether populations have also experienced gene flow. These questions can be addressed with a full model of population separation with gene flow, by applying a Markov chain Monte Carlo method for estimating the posterior probability distribution of model parameters. We have generalized this method and made it applicable to data from multiple unlinked loci. These loci can vary in their modes of inheritance, and inheritance scalars can be implemented either as constants or as parameters to be estimated. By treating inheritance scalars as parameters it is also possible to address variation among loci in the impact via linkage of recurrent selective sweeps or background selection. These methods are applied to a large multilocus data set from Drosophila pseudoobscura and D. persimilis. The species are estimated to have diverged approximately 500,000 years ago. Several loci have nonzero estimates of gene flow since the initial separation of the species, with considerable variation in gene flow estimates among loci, in both directions between the species.     

Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates

1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5.1%. 4. Significant density regulation was present in 53.6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.     

内蒙古赛罕乌拉自然保护区东北马鹿种群遗传多样性与性别结构分析

东北马鹿(Cervuscanadensis)种群面临着地理隔绝和生境破碎化等问题,对其种群遗传多样性和性别结构的研究,有助于了解其隔离种群的生存现状,为保护与管理工作提供科学依据.本研究利用8对微卫星分子标记,对内蒙古赛罕乌拉国家级自然保护区的456份马鹿粪便样品进行遗传多样性分析.结果识别出2015年冬季56只个体,...     

Do polymorphic loci require large sample sizes to estimate genetic distances?

The coefficient of variation of estimates of three genetic distances (standard genetic distance of Nei, chord distance, FST) was examined with computer simulation to determine if large samples (per population) are necessary to precisely estimate genetic distances at loci with high levels of polymorphism. These simulations showed that loci with high mutation rates produce estimates of genetic distance with lower coefficients of variation than loci with lower mutation rates--without requiring larger sample sizes from each population. In addition, the rate at which increasing sample sizes decreases the coefficient of variation of estimates of genetic distances was shown to be approximately determined by the value of FST between the populations being sampled. When FST was greater than 0.05, sampling fewer than 20 individuals (per population) should be sufficient. When FST was less than 0.01, sampling 100 individuals (per population) or more will be useful.     

Estimation of some population parameters of Drosophila limbata V. Roser in a greenhouse

Summary Size and survival rate of a population of Drosophila limbata in a cucumber greenhouse in the vicinity of Groningen, The Netherlands, were estimated twice in the summer of 1975 by mark-release-recapture experiments, using the Fisher-Ford model. The second time, an independent check was carried out by directly estimating the number of emergences. At the end of June, estimated population size was about 13,600, with a survival rate per day of 53.4%, at the end of July population size was estimated at 49,600, with a survival rate per day of 83.4%. The number of emergences per day was at the end of July 5,300, which is reasonably in line with the expectation from the mark-release-recapture experiment. At the end of June there was an excess of females, later there was an excess of males. Reliability of estimates, differences between estimates and growth of the population are discussed. Extrapolation from these data leads to an estimate of 3 million adult flies as the total maximum population size in the local area.     

Dispersal, gene flow, and population structure

The accuracy of gene flow estimates is unknown in most natural populations because direct estimates of dispersal are often not possible. These estimates can be highly imprecise or even biased because population genetic structure reflects more than a simple balance between genetic drift and gene flow. Most of the models used to estimate gene flow also assume very simple patterns of movement. As a result, multiple interpretations of population structure involving contemporary gene flow, departures from equilibrium, and other factors are almost always possible. One way to isolate the relative contribution of gene flow to population genetic differentiation is to utilize comparative methods. Population genetic statistics such as FST, heterozygosity and Nei's D can be compared between species with differing dispersal abilities if these species are otherwise phylogenetically, geographically and demographically comparable. Accordingly, the available literature was searched for all groups that meet these criteria to determine whether broad conclusions regarding the relationships between dispersal, population genetic structure, and gene flow estimates are possible. Allozyme and mtDNA data were summarized for 27 animal groups in which dispersal differences can be characterized. In total, genetic data were obtained for 333 species of vertebrates and invertebrates from terrestrial, freshwater and marine habitats. Across these groups, dispersal ability was consistently related to population structure, with a mean rank correlation of -0.72 between ranked dispersal ability and FST. Gene flow estimates derived from private alleles were also correlated with dispersal ability, but were less widely available. Direct-count heterozygosity and average values of Nei's D showed moderate degrees of correlation with dispersal ability. Thus, despite regional, taxonomic and methodological differences among the groups of species surveyed, available data demonstrate that dispersal makes a measurable contribution to population genetic differentiation in the majority of animal species in nature, and that gene flow estimates are rarely so overwhelmed by population history, departures from equilibrium, or other microevolutionary forces as to be uninformative.     

Estimation of the number of individuals founding colonized populations

A method for estimating the number of founding chromosomes in an isolated population is introduced. The method assumes that n/2 diploid individuals are sampled from a population and that alleles are identified at L unlinked loci. The population is assumed to have been founded T generations in the past by individuals carrying c chromosomes drawn randomly from a known source population, which has also been sampled. If c is small and the population grew rapidly after it was founded, accurate estimates of c can be obtained and those estimates are not sensitive to details of the history of population sizes. If c is larger or the population remained small after it was founded, then estimates of c depend on the history of population sizes. We test the performance of our method on simulated data and demonstrate its use on data from a rainbow trout (Oncorhynchus mykiss) population.     

Loss of genetic variation and effective population size of Kirikuchi charr: implications for the management of small, isolated salmonid populations

Small, isolated populations may face extinction due to a combination of inbreeding depression and other threats. Effective population size ( N _e) is one comprehensive measure that allows us to evaluate the genetic status of a population, and to make management decisions regarding genetic viability. We simulated loss of genetic variation and estimated N _e for two small, isolated populations of Kirikuchi charr Salvelinus leucomaenis japonicus , the endangered, southernmost local populations of the genus Salvelinus in the world, using VORTEX, an individual-based stochastic PVA model. Approximately half of the genetic variation was lost over 200 years regardless of census population size and demographic parameters, and N _e estimates were roughly 50 in each of the two populations, suggesting the possibility of inbreeding depression. The target population size of N _e>500, by securing long-term viability, is several times that of the present size of each of the populations studied, and no local habitats maintaining such a target number are considered to exist. The results strongly indicate a need for recovering natural connections and potential gene flow among local populations. However, the impending threat to these populations from non-native charr widely distributed throughout the drainage has prevented the recovery of the connections. Given the small N _e of the two populations, it would be necessary to retain gene flow artificially within or across local populations. This will be true of many other salmonid populations that have been isolated or fragmented recently.     

Inferring Patterns of Migration from Gene Frequencies under Equilibrium Conditions

A new maximum likelihood method to simultaneously estimate the parameters of any migration pattern from gene frequencies in stochastic equilibrium is developed, based on a model of multivariate genetic drift in a subdivided population. Motivated by simulations of this process in the simplified case of two subpopulations, problems related to the nuisance parameter q, the equilibrium gene frequency, are eliminated by conditioning on the observed mean gene frequency. The covariance matrix of this conditional distribution is calculated by constructing an abstract process that mimics the behavior of the original process in the subspace of interest. The approximation holds as long as there is limited differentiation between subpopulations. The bias and variance of estimates of long-range and short-range migration in a finite stepping stone model are evaluated by fitting the model to simulated data with known values of the parameters. Possible ecological extensions of the model are discussed.