Selection dramatically reduces effective population size in HIV-1 infection

Background  

In HIV-1 evolution, a 100–100,000 fold discrepancy between census size and effective population size (N _e ) has been noted. Although it is well known that selection can reduce N _e , high in vivo mutation and recombination rates complicate attempts to quantify the effects of selection on HIV-1 effective size.     

Quantifying the variation in the effective population size within a genome

The effective population size (N(e)) is one of the most fundamental parameters in population genetics. It is thought to vary across the genome as a consequence of differences in the rate of recombination and the density of selected sites due to the processes of genetic hitchhiking and background selection. Although it is known that there is intragenomic variation in the effective population size in some species, it is not known whether this is widespread or how much variation in the effective population size there is. Here, we test whether the effective population size varies across the genome, between protein-coding genes, in 10 eukaryotic species by considering whether there is significant variation in neutral diversity, taking into account differences in the mutation rate between loci by using the divergence between species. In most species we find significant evidence of variation. We investigate whether the variation in N(e) is correlated to recombination rate and the density of selected sites in four species, for which these data are available. We find that N(e) is positively correlated to recombination rate in one species, Drosophila melanogaster, and negatively correlated to a measure of the density of selected sites in two others, humans and Arabidopsis thaliana. However, much of the variation remains unexplained. We use a hierarchical Bayesian analysis to quantify the amount of variation in the effective population size and show that it is quite modest in all species-most genes have an N(e) that is within a few fold of all other genes. Nonetheless we show that this modest variation in N(e) is sufficient to cause significant differences in the efficiency of natural selection across the genome, by demonstrating that the ratio of the number of nonsynonymous to synonymous polymorphisms is significantly correlated to synonymous diversity and estimates of N(e), even taking into account the obvious nonindependence between these measures.     

Estimation of effective population size in continuously distributed populations: there goes the neighborhood

Use of genetic methods to estimate effective population size (N_e) is rapidly increasing, but all approaches make simplifying assumptions unlikely to be met in real populations. In particular, all assume a single, unstructured population, and none has been evaluated for use with continuously distributed species. We simulated continuous populations with local mating structure, as envisioned by Wright''s concept of neighborhood size (NS), and evaluated performance of a single-sample estimator based on linkage disequilibrium (LD), which provides an estimate of the effective number of parents that produced the sample (N_b). Results illustrate the interacting effects of two phenomena, drift and mixture, that contribute to LD. Samples from areas equal to or smaller than a breeding window produced estimates close to the NS. As the sampling window increased in size to encompass multiple genetic neighborhoods, mixture LD from a two-locus Wahlund effect overwhelmed the reduction in drift LD from incorporating offspring from more parents. As a consequence, never approached the global N_e, even when the geographic scale of sampling was large. Results indicate that caution is needed in applying standard methods for estimating effective size to continuously distributed populations.     

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.     

Estimation of effective population size for the long-lived darkblotched rockfish Sebastes crameri

We report the variance effective population size (Ne) in darkblotched rockfish (Sebastes crameri) utilizing the temporal method for overlapping generations, which requires a combination of age-specific demography and genetic information from cohorts. Following calculations of age-specific survival and reproductive success from fishery data, we genotyped a sample (n = 1087) comprised by 6 cohorts (from 1995 to 2000) across 7 microsatellite loci. Our Ne estimate (Ne) plus 95% confidence interval was (Ne) = 9157 [6495-12 215], showing that the breeding population number could be 3-4 orders of magnitude smaller than the census population size (N) = 24 376 210). Our estimates resemble closely those found for fishes with similar life history, suggesting that the small (Ne)/(N) ratio for S. crameri is most likely explained by a combination of high variance in reproductive success among individuals, genetic structure, and demographic perturbations such as historical fishing. Because small (Ne)/(N) ratios have been commonly associated with potential loss of genetic variation, our estimates need careful consideration in rockfish management and conservation.     

Estimation of effective population size and detection of a recent population decline coinciding with habitat fragmentation in a ground beetle

We assess the impact of habitat fragmentation on the effective size (N(e)) of local populations of the flightless ground beetle Carabus violaceus in a small (<25 ha) and a large (>80 ha) forest fragment separated by a highway. N(e) was estimated based on the temporal variation of allele frequencies at 13 microsatellite loci using two different methods. In the smaller fragment, N(e) estimates ranged between 59 and a few hundred, whereas values between 190 and positive infinity were estimated for the larger fragment. In both samples, we detected a signal of population decline, which was stronger in the small fragment. The estimated time of onset of this N(e) reduction was consistent with the hypothesis that recent road constructions have divided a continuous population into several isolated subpopulations. In the small fragment, N(e) of the local population may be so small that its long-term persistence is endangered.     

Likelihood-based estimation of the effective population size using temporal changes in allele frequencies: a genealogical approach

A new genetic estimator of the effective population size (N(e)) is introduced. This likelihood-based (LB) estimator uses two temporally spaced genetic samples of individuals from a population. We compared its performance to that of the classical F-statistic-based N(e) estimator (N(eFk)) by using data from simulated populations with known N(e) and real populations. The new likelihood-based estimator (N(eLB)) showed narrower credible intervals and greater accuracy than (N(eFk)) when genetic drift was strong, but performed only slightly better when genetic drift was relatively weak. When drift was strong (e.g., N(e) = 20 for five generations), as few as approximately 10 loci (heterozygosity of 0.6; samples of 30 individuals) are sufficient to consistently achieve credible intervals with an upper limit <50 using the LB method. In contrast, approximately 20 loci are required for the same precision when using the classical F-statistic approach. The N(eLB) estimator is much improved over the classical method when there are many rare alleles. It will be especially useful in conservation biology because it less often overestimates N(e) than does N(eLB) and thus is less likely to erroneously suggest that a population is large and has a low extinction risk.     

Estimation of effective population size and migration rate from one- and two-locus identity measures

Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.     

Estimation of the size of an open population using local estimating equations II: a partially parametric approach

Kernel smoothing methods are applied to extend a modification of the closed population approach of Lloyd and Yip (1991, in Estimating Equations, 65-88) to open populations with frequent capture occasions. The method complements previous nonparametric methods and, when the parametric assumptions are met, simulations show the new method has a smaller integrated mean squared error than the previous fully nonparametric method. The method is applied to capture-recapture data on short-tailed shearwaters collected annually for 48 years.     

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.     

cloncase: Estimation of sex frequency and effective population size by clonemate resampling in partially clonal organisms

Inferring reproductive and demographic parameters of populations is crucial to our understanding of species ecology and evolutionary potential but can be challenging, especially in partially clonal organisms. Here, we describe a new and accurate method, cloncase , for estimating both the rate of sexual vs. asexual reproduction and the effective population size, based on the frequency of clonemate resampling across generations. Simulations showed that our method provides reliable estimates of sex frequency and effective population size for a wide range of parameters. The cloncase method was applied to Puccinia striiformis f.sp. tritici, a fungal pathogen causing stripe/yellow rust, an important wheat disease. This fungus is highly clonal in Europe but has been suggested to recombine in Asia. Using two temporally spaced samples of P. striiformis f.sp. tritici in China, the estimated sex frequency was 75% (i.e. three‐quarter of individuals being sexually derived during the yearly sexual cycle), indicating strong contribution of sexual reproduction to the life cycle of the pathogen in this area. The inferred effective population size of this partially clonal organism (N_c = 998) was in good agreement with estimates obtained using methods based on temporal variations in allelic frequencies. The cloncase estimator presented herein is the first method allowing accurate inference of both sex frequency and effective population size from population data without knowledge of recombination or mutation rates. cloncase can be applied to population genetic data from any organism with cyclical parthenogenesis and should in particular be very useful for improving our understanding of pest and microbial population biology.     

A robust measure of HIV-1 population turnover within chronically infected individuals

A simple nonparameteric test for population structure was applied to temporally spaced samples of HIV-1 sequences from the gag-pol region within two chronically infected individuals. The results show that temporal structure can be detected for samples separated by about 22 months or more. The performance of the method, which was originally proposed to detect geographic structure, was tested for temporally spaced samples using neutral coalescent simulations. Simulations showed that the method is robust to variation in samples sizes and mutation rates, to the presence/absence of recombination, and that the power to detect temporal structure is high. By comparing levels of temporal structure in simulations to the levels observed in real data, we estimate the effective intra-individual population size of HIV-1 to be between 10(3) and 10(4) viruses, which is in agreement with some previous estimates. Using this estimate and a simple measure of sequence diversity, we estimate an effective neutral mutation rate of about 5 x 10(-6) per site per generation in the gag-pol region. The definition and interpretation of estimates of such "effective" population parameters 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.     

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.     

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.