COMPUTER PROGRAMS: onesamp: a program to estimate effective population size using approximate Bayesian computation

The estimation of effective population size from one sample of genotypes has been problematic because most estimators have been proven imprecise or biased. We developed a web-based program, onesamp that uses approximate Bayesian computation to estimate effective population size from a sample of microsatellite genotypes. onesamp requires an input file of sampled individuals' microsatellite genotypes along with information about several sampling and biological parameters. onesamp provides an estimate of effective population size, along with 95% credible limits. We illustrate the use of onesamp with an example data set from a re-introduced population of ibex Capra ibex.     

Unbiased estimator for genetic drift and effective population size

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

Efficient computation of approximate gene clusters based on reference occurrences

Whole genome comparison based on the analysis of gene cluster conservation has become a popular approach in comparative genomics. While gene order and gene content as a whole randomize over time, it is observed that certain groups of genes which are often functionally related remain co-located across species. However, the conservation is usually not perfect which turns the identification of these structures, often referred to as approximate gene clusters, into a challenging task. In this article, we present an efficient set distance based approach that computes approximate gene clusters by means of reference occurrences. We show that it yields highly comparable results to the corresponding non-reference based approach, while its polynomial runtime allows for approximate gene cluster detection in parameter ranges that used to be feasible only with simpler, e.g., max-gap based, gene cluster models. To illustrate further the performance and predictive power of our algorithm, we compare it to a state-of-the art approach for max-gap gene cluster computation.     

Note on the computation of critical effective population sizes.

This work extends the work of Whitlock in examining the critical effective population sizes from the fixation of both deleterious and beneficial mutations under drift and selection to prevent mutation breakdown of the population. The validity of approximations for the probability of fixation depends on the nature of the assumed distribution for the fitness effect of both types of mutations. Using no approximation for the probability of fixation and assuming a heavy tailed fitness effect distribution, the current model indicates that the coefficients of variation for the fitness effect distributions of both types of mutations and the fitness effect distribution mean for the beneficial mutations are important predictors of the critical effective population size. The current model further predicts that very small populations can be sustained if the fitness effect variances for both types of mutations and the mean for beneficial mutations are large.     

Monitoring the effective population size of a brown bear (Ursus arctos) population using new single-sample approaches

The effective population size (N(e) ) could be the ideal parameter for monitoring populations of conservation concern as it conveniently summarizes both the evolutionary potential of the population and its sensitivity to genetic stochasticity. However, tracing its change through time is difficult in natural populations. We applied four new methods for estimating N(e) from a single sample of genotypes to trace temporal change in N(e) for bears in the Northern Dinaric Mountains. We genotyped 510 bears using 20 microsatellite loci and determined their age. The samples were organized into cohorts with regard to the year when the animals were born and yearly samples with age categories for every year when they were alive. We used the Estimator by Parentage Assignment (EPA) to directly estimate both N(e) and generation interval for each yearly sample. For cohorts, we estimated the effective number of breeders (N(b) ) using linkage disequilibrium, sibship assignment and approximate Bayesian computation methods and extrapolated these estimates to N(e) using the generation interval. The N(e) estimate by EPA is 276 (183-350 95% CI), meeting the inbreeding-avoidance criterion of N(e) > 50 but short of the long-term minimum viable population goal of N(e) > 500. The results obtained by the other methods are highly consistent with this result, and all indicate a rapid increase in N(e) probably in the late 1990s and early 2000s. The new single-sample approaches to the estimation of N(e) provide efficient means for including N(e) in monitoring frameworks and will be of great importance for future management and conservation.     

The effective population size of an age-structured population with a sex-linked locus

Let a population have the same age distribution and age-specific sex ratios at times 0, 1, 2,..., and let M, F, and L, respectively, be the numbers of males and females in the youngest age group and the generation interval. It can then be shown that if there is a sex-linked locus the fixation probabilities of a neutral allele are respectively 1/3LM or 1/3LF if the allele first appears in one newborn male or in one newborn female. The effective population size can then be derived. It is the same as for a population with discrete generations having the same means, variances, and covariances of male and female progeny during a lifetime and the same number of individuals entering the population per generation.     

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. AVAILABILITY: The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc.     

Comparative analyses of effective population size within and among species: ranid frogs as a case study

It has recently become practicable to estimate the effective sizes (N(e) ) of multiple populations within species. Such efforts are valuable for estimating N(e) in evolutionary modeling and conservation planning. We used microsatellite loci to estimate N(e) of 90 populations of four ranid frog species (20-26 populations per species, mean n per population = 29). Our objectives were to determine typical values of N(e) for populations of each species, compare N(e) estimates among the species, and test for correlations between several geographic variables and N(e) within species. We used single-sample linkage disequilibrium (LD), approximate Bayesian computation (ABC), and sibship assignment (SA) methods to estimate contemporary N(e) for each population. Three of the species-Rana pretiosa, R. luteiventris, and R. cascadae- have consistently small effective population sizes (<50). N(e) in Lithobates pipiens spans a wider range, with some values in the hundreds or thousands. There is a strong east-to-west trend of decreasing N(e) in L. pipiens. The smaller effective sizes of western populations of this species may be related to habitat fragmentation and population bottlenecking.     

The effective size of a natural drosophila subobscura population.

The effective size of a natural Drosophila subobscura population has been computed by drawing together various pieces of ecological information. The value, for both variance and inbreeding effective numbers, is approximately 400. This is largely due to reductions caused by a winter bottleneck and non-random distributions of family sizes. Areas where such estimates might be refined further are pointed out, and the implications of the results are discussed.     

Volatility in the effective size of a freshwater gastropod population

Despite the utility of gastropod models for the study of evolutionary processes of great generality and importance, their effective population size has rarely been estimated in the field. Here, we report allele frequency variance at three allozyme‐encoding loci monitored over 7 years in a population of the invasive freshwater pulmonate snail Physa acuta (Draparnaud 1805), estimating effective population size with both single‐sample and two‐sample approaches. Estimated N_e declined from effectively infinite in 2009 to approximately 40–50 in 2012 and then rose back to infinity in 2015, corresponding to a striking fluctuation in the apparent census size of the population. Such volatility in N_e may reflect cryptic population subdivision.     

Testing demographic models of effective population size

Due to practical difficulties in obtaining direct genetic estimates of effective sizes, conservation biologists have to rely on so-called 'demographic models' which combine life-history and mating-system parameters with F-statistics in order to produce indirect estimates of effective sizes. However, for the same practical reasons that prevent direct genetic estimates, the accuracy of demographic models is difficult to evaluate. Here we use individual-based, genetically explicit computer simulations in order to investigate the accuracy of two such demographic models aimed at investigating the hierarchical structure of populations. We show that, by and large, these models provide good estimates under a wide range of mating systems and dispersal patterns. However, one of the models should be avoided whenever the focal species' breeding system approaches monogamy with no sex bias in dispersal or when a substructure within social groups is suspected because effective sizes may then be strongly overestimated. The timing during the life cycle at which F-statistics are evaluated is also of crucial importance and attention should be paid to it when designing field sampling since different demographic models assume different timings. Our study shows that individual-based, genetically explicit models provide a promising way of evaluating the accuracy of demographic models of effective size and delineate their field of applicability.     

Applications and extensions of Chao's moment estimator for the size of a closed population

This article revisits Chao's (1989, Biometrics45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model M(h)). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (M(th)) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for M(th). Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment.     

鸡SNP多样性的比较研究与群体有效规模的估算

以红色原鸡(Red Jungle Fowl, RJF)、丝羽乌骨鸡(Taihe silk Chicken, TS)、隐性白洛克鸡(White Recessive Rock, WRR)为资源群, 在鸡一号染色体的Contig.060226.1上选取了一个200 kb的区域, 比较研究了3个群体的SNP (single nucleotide polymorphism)多样性、估算了鸡的初始群体有效规模大小(effective size of population, Ne)。红色原鸡、丝羽乌骨鸡、隐性白洛克鸡3个群体的平均杂合度分别为0.28533±0.03475、0.32926±0.03919、0.30168±0.04038。显著性检验差异不显著(P=0.2368>0.05)。根据Latter 和Nei的方法对鸡的群体有效规模进行了估算, 鸡的初始群体有效规模大小为20 000～150 000。鸡在驯养的早期阶段经历过严厉的瓶颈效应, 但瓶颈效应对鸡各品种SNP的多样性并未产生显著影响。笔者认为, 鸡在驯养的早期阶段群体有效规模足够大, 品种分化过程中群体迅速扩张, 品种间的广泛杂交(特别是和红色原鸡之间)以及鸡基因组的高重组率等因素是导致家鸡和原鸡以及各家鸡品种间SNP多样性没有显著差别的重要原因。     

Parallel computation of a maximum-likelihood estimator of a physical map

Reconstructing a physical map of a chromosome from a genomic library presents a central computational problem in genetics. Physical map reconstruction in the presence of errors is a problem of high computational complexity that provides the motivation for parallel computing. Parallelization strategies for a maximum-likelihood estimation-based approach to physical map reconstruction are presented. The estimation procedure entails a gradient descent search for determining the optimal spacings between probes for a given probe ordering. The optimal probe ordering is determined using a stochastic optimization algorithm such as simulated annealing or microcanonical annealing. A two-level parallelization strategy is proposed wherein the gradient descent search is parallelized at the lower level and the stochastic optimization algorithm is simultaneously parallelized at the higher level. Implementation and experimental results on a distributed-memory multiprocessor cluster running the parallel virtual machine (PVM) environment are presented using simulated and real hybridization data.     

A note on effective population size with overlapping generations

A simple derivation is given for a formula obtained previously for the effective size of random-mating populations with overlapping generations. The effective population size is the same as that for a population with discrete generations having the same variance of lifetime family size and the same number of individuals entering the population per generation.     

Low effective population size and survivorship in a grassland grouse

Assessments of census size (N _c) and effective population size (N _e) are necessary for the conservation of species exhibiting population declines. We examined two populations (Oklahoma and New Mexico) of the lesser prairie-chicken (Tympanuchus pallidicinctus), a declining lek-breeding bird, in which one population (Oklahoma) has larger clutch size and more nesting attempts per year but lower survival caused by human changes to the landscape. We estimated demographic and genetic estimates of N _e for each population and found that both populations have low N _e estimates with a risk of inbreeding depression. Although Oklahoma females produce a larger number of offspring, the proportion of females successfully reproducing is not higher than in New Mexico. Higher reproductive effort has likely reached a physiological limit in Oklahoma prairie-chickens but has not led to a higher N _e or even a larger N _c than New Mexico. We propose that future conservation efforts focus on maximizing survivorship and decreasing the variance in reproductive success because these factors are more likely than increasing reproductive output alone to yield population persistence in lek-breeding species.     

The effect of multiple paternity on the genetically effective size of a population

With the availability of highly variable microsatellite loci, many previously elusive aspects of the lives of animals have been revealed. One important finding is that multiple paternity (MP) appears to be somewhat common throughout the metazoa. Frequently, along with the discovery of MP are assertions that it can increase the genetically effective size of the population (N_E). I argue that MP is not likely to have a positive effect on N_E because it increases the variance in male reproductive success. Published studies suggesting the contrary have implicitly or explicitly included other changes to the breeding system, and these additions are likely responsible for the presumed increase in N_E.     

A new method for estimating the effective population size from allele frequency changes

A new procedure is proposed for estimating the effective population size, given that information is available on changes in frequencies of the alleles at one or more independently segregating loci and the population is observed at two or more separate times. Approximate expressions are obtained for the variances of the new statistic, as well as others, also based on allele frequency changes, that have been discussed in the literature. This analysis indicates that the new statistic will generally have a smaller variance than the others. Estimates of effective population sizes and of the standard errors of the estimates are computed for data on two fly populations that have been discussed in earlier papers. In both cases, there is evidence that the effective population size is very much smaller than the minimum census size of the population.