The estimates of effective population size based on linkage disequilibrium are virtually unaffected by natural selection

The effective population size (N_e) is a key parameter to quantify the magnitude of genetic drift and inbreeding, with important implications in human evolution. The increasing availability of high-density genetic markers allows the estimation of historical changes in N_e across time using measures of genome diversity or linkage disequilibrium between markers. Directional selection is expected to reduce diversity and N_e, and this reduction is modulated by the heterogeneity of the genome in terms of recombination rate. Here we investigate by computer simulations the consequences of selection (both positive and negative) and recombination rate heterogeneity in the estimation of historical N_e. We also investigate the relationship between diversity parameters and N_e across the different regions of the genome using human marker data. We show that the estimates of historical N_e obtained from linkage disequilibrium between markers (N_eLD) are virtually unaffected by selection. In contrast, those estimates obtained by coalescence mutation-recombination-based methods can be strongly affected by it, which could have important consequences for the estimation of human demography. The simulation results are supported by the analysis of human data. The estimates of N_eLD obtained for particular genomic regions do not correlate, or they do it very weakly, with recombination rate, nucleotide diversity, proportion of polymorphic sites, background selection statistic, minor allele frequency of SNPs, loss of function and missense variants and gene density. This suggests that N_eLD measures mainly reflect demographic changes in population size across generations.     

Evaluating methods for estimating local effective population size with and without migration

Effective population size is a fundamental parameter in population genetics, evolutionary biology, and conservation biology, yet its estimation can be fraught with difficulties. Several methods to estimate N_e from genetic data have been developed that take advantage of various approaches for inferring N_e. The ability of these methods to accurately estimate N_e, however, has not been comprehensively examined. In this study, we employ seven of the most cited methods for estimating N_e from genetic data (Colony2, CoNe, Estim, MLNe, ONeSAMP, TMVP, and NeEstimator including LDNe) across simulated datasets with populations experiencing migration or no migration. The simulated population demographies are an isolated population with no immigration, an island model metapopulation with a sink population receiving immigrants, and an isolation by distance stepping stone model of populations. We find considerable variance in performance of these methods, both within and across demographic scenarios, with some methods performing very poorly. The most accurate estimates of N_e can be obtained by using LDNe, MLNe, or TMVP; however each of these approaches is outperformed by another in a differing demographic scenario. Knowledge of the approximate demography of population as well as the availability of temporal data largely improves N_e estimates.     

Reconciling Genetic and Demographic Estimators of Effective Population Size in the Anuran Amphibian Bufo Calamita

We used genetic and demographic methods to estimate the variance effective population sizes (N _e) of three populations of natterjack toads Bufo calamita in Britain. This amphibian breeds in temporary pools where survival rates can vary among families. Census population sizes (N) were derived from spawn string counts. Point and coalescent-based maximum likelihood estimates of N _e based on microsatellite allele distributions were similar. N _e/N ratios based on genetic estimates of N _e ranged between 0.02 and 0.20. Mean demographic estimates of N _e were consistently higher (2.7–8.0-fold) than genetic estimates for all three populations when variance in breeding success was evaluated at the point where females no longer influence their progeny. However, discrepancies between genetic and demographic estimators could be removed by using a model that included extra variance in survivorship (above to Poisson expectations) among families. The implications of these results for the estimation of N _e in wild populations are discussed.     

Biases in Demographic Modeling Affect Our Understanding of Recent Divergence

Testing among competing demographic models of divergence has become an important component of evolutionary research in model and non-model organisms. However, the effect of unaccounted demographic events on model choice and parameter estimation remains largely unexplored. Using extensive simulations, we demonstrate that under realistic divergence scenarios, failure to account for population size (N_e) changes in daughter and ancestral populations leads to strong biases in divergence time estimates as well as model choice. We illustrate these issues reconstructing the recent demographic history of North Sea and Baltic Sea turbots (Scophthalmus maximus) by testing 16 isolation with migration (IM) and 16 secondary contact (SC) scenarios, modeling changes in N_e as well as the effects of linked selection and barrier loci. Failure to account for changes in N_e resulted in selecting SC models with long periods of strict isolation and divergence times preceding the formation of the Baltic Sea. In contrast, models accounting for N_e changes suggest recent (<6 kya) divergence with constant gene flow. We further show how interpreting genomic landscapes of differentiation can help discerning among competing models. For example, in the turbot data, islands of differentiation show signatures of recent selective sweeps, rather than old divergence resisting secondary introgression. The results have broad implications for the study of population divergence by highlighting the potential effects of unmodeled changes in N_e on demographic inference. Tested models should aim at representing realistic divergence scenarios for the target taxa, and extreme caution should always be exercised when interpreting results of demographic modeling.     

Can Genetic Estimators Provide Robust Estimates of the Effective Number of Breeders in Small Populations?

The effective population size (N_e) is proportional to the loss of genetic diversity and the rate of inbreeding, and its accurate estimation is crucial for the monitoring of small populations. Here, we integrate temporal studies of the gecko Oedura reticulata, to compare genetic and demographic estimators of N_e. Because geckos have overlapping generations, our goal was to demographically estimate N_bI, the inbreeding effective number of breeders and to calculate the N_bI/N_a ratio (N_a = number of adults) for four populations. Demographically estimated N_bI ranged from 1 to 65 individuals. The mean reduction in the effective number of breeders relative to census size (N_bI/N_a) was 0.1 to 1.1. We identified the variance in reproductive success as the most important variable contributing to reduction of this ratio. We used four methods to estimate the genetic based inbreeding effective number of breeders N_bI(gen) and the variance effective populations size N_eV(gen) estimates from the genotype data. Two of these methods - a temporal moment-based (MBT) and a likelihood-based approach (TM3) require at least two samples in time, while the other two were single-sample estimators - the linkage disequilibrium method with bias correction LDNe and the program ONeSAMP. The genetic based estimates were fairly similar across methods and also similar to the demographic estimates excluding those estimates, in which upper confidence interval boundaries were uninformative. For example, LDNe and ONeSAMP estimates ranged from 14–55 and 24–48 individuals, respectively. However, temporal methods suffered from a large variation in confidence intervals and concerns about the prior information. We conclude that the single-sample estimators are an acceptable short-cut to estimate N_bI for species such as geckos and will be of great importance for the monitoring of species in fragmented landscapes.     

Effective/census population size ratio estimation: a compendium and appraisal

With an ecological-evolutionary perspective increasingly applied toward the conservation and management of endangered or exploited species, the genetic estimation of effective population size (N_e) has proliferated. Based on a comprehensive analysis of empirical literature from the past two decades, we asked: (i) how often do studies link N_e to the adult census population size (N)? (ii) To what extent is N_e correctly linked to N? (iii) How readily is uncertainty accounted for in both N_e and N when quantifying N_e/N ratios? and (iv) how frequently and to what degree might errors in the estimation of N_e or N affect inferences of N_e/N ratios? We found that only 20% of available N_e estimates (508 of 2617; 233 studies) explicitly attempted to link N_e and N; of these, only 31% (160 of 508) correctly linked N_e and N. Moreover, only 7% (41 of 508) of N_e/N ratios (correctly linked or not) reported confidence intervals for both N_e and N; for those cases where confidence intervals were reported for N_e only, 31% of N_e/N ratios overlapped with 1, of which more than half also reached below N_e/N = 0.01. Uncertainty in N_e/N ratios thus sometimes spanned at least two orders of magnitude. We conclude that the estimation of N_e/N ratios in natural populations could be significantly improved, discuss several options for doing so, and briefly outline some future research directions.     

Variance in Female Reproductive Success Differentially Impacts Effective Population Size in the Short-Nosed Fruit Bat, <Emphasis Type="Italic">Cynopterus sphinx</Emphasis>

Effective population size (N _e) quantifies the effects of micro-evolutionary processes and the rate of loss of genetic diversity in a population. Several demographic and mating parameters reduce N _e. Theoretical studies elucidate the impacts of various demographic and mating system parameters on N _e, while empirical studies illustrate realized N _e for species with differing life histories and mating systems. However, effect of intra-specific variation in mating system on effective size remains largely unexplored. In this paper we investigated the effect of promiscuous and polygynous mating on N _e in two wild populations of the short-nosed fruit bat, Cynopterus sphinx. N _e/N (ratio of effective population size to census size) was lower than unity in both populations, and much lower for the polygynous population compared to promiscuous population. Elasticity analyses reveal that N _e/N was sensitive to deviations in the sex ratio. Variance in female reproductive success had a higher impact on N _e compared to variance in male reproductive success in the promiscuous population. However, for the polygynous population, impact of variance in male reproductive success on N _e was higher than that of variance in female reproductive success. Our results suggest that depending on mating system, different populations of the same species could have alternate evolutionary trajectories. The rate of loss of genetic diversity would be lower for the promiscuous population compared to the polygynous population. Our study is the first to highlight which parameters would most significantly impact population specific N _e under different mating systems.     

Simple life-history traits explain key effective population size ratios across diverse taxa

Effective population size (N_e) controls both the rate of random genetic drift and the effectiveness of selection and migration, but it is difficult to estimate in nature. In particular, for species with overlapping generations, it is easier to estimate the effective number of breeders in one reproductive cycle (N_b) than N_e per generation. We empirically evaluated the relationship between life history and ratios of N_e, N_b and adult census size (N) using a recently developed model (agene) and published vital rates for 63 iteroparous animals and plants. N_b/N_e varied a surprising sixfold across species and, contrary to expectations, N_b was larger than N_e in over half the species. Up to two-thirds of the variance in N_b/N_e and up to half the variance in N_e/N was explained by just two life-history traits (age at maturity and adult lifespan) that have long interested both ecologists and evolutionary biologists. These results provide novel insights into, and demonstrate a close general linkage between, demographic and evolutionary processes across diverse taxa. For the first time, our results also make it possible to interpret rapidly accumulating estimates of N_b in the context of the rich body of evolutionary theory based on N_e per generation.     

PSMC analysis of effective population sizes in molecular ecology and its application to black‐and‐white Ficedula flycatchers

Climatic fluctuations during the Quaternary period governed the demography of species and contributed to population differentiation and ultimately speciation. Studies of these past processes have previously been hindered by a lack of means and genetic data to model changes in effective population size (N_e) through time. However, based on diploid genome sequences of high quality, the recently developed pairwise sequentially Markovian coalescent (PSMC) can estimate trajectories of changes in N_e over considerable time periods. We applied this approach to resequencing data from nearly 200 genomes of four species and several populations of the Ficedula species complex of black‐and‐white flycatchers. N_e curves of Atlas, collared, pied and semicollared flycatcher converged 1–2 million years ago (Ma) at an N_e of ≈ 200 000, likely reflecting the time when all four species last shared a common ancestor. Subsequent separate N_e trajectories are consistent with lineage splitting and speciation. All species showed evidence of population growth up until 100–200 thousand years ago (kya), followed by decline and then start of a new phase of population expansion. However, timing and amplitude of changes in N_e differed among species, and for pied flycatcher, the temporal dynamics of N_e differed between Spanish birds and central/northern European populations. This cautions against extrapolation of demographic inference between lineages and calls for adequate sampling to provide representative pictures of the coalescence process in different species or populations. We also empirically evaluate criteria for proper inference of demographic histories using PSMC and arrive at recommendations of using sequencing data with a mean genome coverage of ≥18X, a per‐site filter of ≥10 reads and no more than 25% of missing data.     

A century-long genetic record reveals that protist effective population sizes are comparable to those of macroscopic species

Effective population size (N_e) determines the rate of genetic drift and the relative influence of selection over random genetic changes. While free-living protist populations characteristically consist of huge numbers of cells (N), the absence of any estimates of contemporary N_e raises the question whether protist effective population sizes are comparably large. Using microsatellite genotype data of strains derived from revived cysts of the marine dinoflagellate Pentapharsodinium dalei from sections of a sediment record that spanned some 100 years, we present the first estimates of contemporary N_e for a local population in a free-living protist. The estimates of N_e are relatively small, of the order of a few 100 individuals, and thus are similar in magnitude to values of N_e reported for multicellular animals: the implications are that N_e of P. dalei is of many orders of magnitude lower than the number of cells present (N_e/N ∼ 10⁻¹²) and that stochastic genetic processes may be more prevalent in protist populations than previously anticipated.     

Effective Population Size,Genetic Variation,and Their Relevance for Conservation: The Bighorn Sheep in Tiburon Island and Comparisons with Managed Artiodactyls

The amount of genetic diversity in a finite biological population mostly depends on the interactions among evolutionary forces and the effective population size (N _e) as well as the time since population establishment. Because the N _e estimation helps to explore population demographic history, and allows one to predict the behavior of genetic diversity through time, N _e is a key parameter for the genetic management of small and isolated populations. Here, we explored an N _e-based approach using a bighorn sheep population on Tiburon Island, Mexico (TI) as a model. We estimated the current (N _crnt) and ancestral stable (N _stbl) inbreeding effective population sizes as well as summary statistics to assess genetic diversity and the demographic scenarios that could explain such diversity. Then, we evaluated the feasibility of using TI as a source population for reintroduction programs. We also included data from other bighorn sheep and artiodactyl populations in the analysis to compare their inbreeding effective size estimates. The TI population showed high levels of genetic diversity with respect to other managed populations. However, our analysis suggested that TI has been under a genetic bottleneck, indicating that using individuals from this population as the only source for reintroduction could lead to a severe genetic diversity reduction. Analyses of the published data did not show a strict correlation between H _E and N _crnt estimates. Moreover, we detected that ancient anthropogenic and climatic pressures affected all studied populations. We conclude that the estimation of N _crnt and N _stbl are informative genetic diversity estimators and should be used in addition to summary statistics for conservation and population management planning.     

Did Genetic Drift Drive Increases in Genome Complexity?

Mechanisms underlying the dramatic patterns of genome size variation across the tree of life remain mysterious. Effective population size (N_e) has been proposed as a major driver of genome size: selection is expected to efficiently weed out deleterious mutations increasing genome size in lineages with large (but not small) N_e. Strong support for this model was claimed from a comparative analysis of N_eu and genome size for ≈30 phylogenetically diverse species ranging from bacteria to vertebrates, but analyses at that scale have so far failed to account for phylogenetic nonindependence of species. In our reanalysis, accounting for phylogenetic history substantially altered the perceived strength of the relationship between N_eu and genomic attributes: there were no statistically significant associations between N_eu and gene number, intron size, intron number, the half-life of gene duplicates, transposon number, transposons as a fraction of the genome, or overall genome size. We conclude that current datasets do not support the hypothesis of a mechanistic connection between N_e and these genomic attributes, and we suggest that further progress requires larger datasets, phylogenetic comparative methods, more robust estimators of genetic drift, and a multivariate approach that accounts for correlations between putative explanatory variables.     

Effects of population characteristics and structure on estimates of effective population size in a house sparrow metapopulation

Effective population size (N_e) is a key parameter to understand evolutionary processes and the viability of endangered populations as it determines the rate of genetic drift and inbreeding. Low N_e can lead to inbreeding depression and reduced population adaptability. In this study, we estimated contemporary N_e using genetic estimators (LDNE, ONeSAMP, MLNE and CoNe) as well as a demographic estimator in a natural insular house sparrow metapopulation. We investigated whether population characteristics (population size, sex ratio, immigration rate, variance in population size and population growth rate) explained variation within and among populations in the ratio of effective to census population size (N_e/N_c). In general, N_e/N_c ratios increased with immigration rates. Genetic N_e was much larger than demographic N_e, probably due to a greater effect of immigration on genetic than demographic processes in local populations. Moreover, although estimates of genetic N_e seemed to track N_c quite well, the genetic N_e‐estimates were often larger than N_c within populations. Estimates of genetic N_e for the metapopulation were however within the expected range (<N_c). Our results suggest that in fragmented populations, even low levels of gene flow may have important consequences for the interpretation of genetic estimates of N_e. Consequently, further studies are needed to understand how N_e estimated in local populations or the total metapopulation relates to actual rates of genetic drift and inbreeding.     

EFFECTIVE POPULATION SIZE AND GENETIC DRIFT IN TRISTYLOUS EICHHORNIA PANICULATA (PONTEDERIACEAE)

Populations of the tristylous, annual Eichhornia paniculata are markedly differentiated with respect to frequency of mating types. This variation is associated with evolutionary changes in mating system, from predominant outcrossing to high self-fertilization. To assess the potential influence of genetic drift acting on this variation, we estimated effective population size in 10 populations from northeastern Brazil using genetic and demographic methods. Effective size (N_e) was inferred from temporal changes in allele frequency at two to eight isozyme loci and also calculated using five demographic variables: 1) the number of flowering individuals (N); 2) temporal fluctuations in N; 3) variance in flower number; 4) frequency of mating types; and 5) selfing rate. Average N_e based on isozyme data was 15.8, range 3.4–70.6, and represented a fraction (mean N_e/N = 0.106) of the census number of individuals (mean N = 762.8; range: 30.5–5,040). Temporal variation in N and variance in flower number each reduced N_e to about a half of N whereas mating type frequencies and selfing rate caused only small reductions in N_e relative to N. All estimates of N_e based on demographic variables were considerably larger than those obtained from genetic data. The two kinds of estimates were in general agreement, however, when all demographic variables were combined into a single measure. Monte Carlo simulations indicated that effective size must be fewer than about 40 for drift to overcome the frequency-dependent selection that maintains the polymorphism for mating type. Applying the average N_e/N value to 167 populations censused in northeastern Brazil indicated that 72% had effective sizes below this number. This suggests that genetic drift is likely to play a dominant role in natural populations of E. paniculata.     

The Effects of Demography and Long-Term Selection on the Accuracy of Genomic Prediction with Sequence Data

The use of dense SNPs to predict the genetic value of an individual for a complex trait is often referred to as “genomic selection” in livestock and crops, but is also relevant to human genetics to predict, for example, complex genetic disease risk. The accuracy of prediction depends on the strength of linkage disequilibrium (LD) between SNPs and causal mutations. If sequence data were used instead of dense SNPs, accuracy should increase because causal mutations are present, but demographic history and long-term negative selection also influence accuracy. We therefore evaluated genomic prediction, using simulated sequence in two contrasting populations: one reducing from an ancestrally large effective population size (N_e) to a small one, with high LD common in domestic livestock, while the second had a large constant-sized N_e with low LD similar to that in some human or outbred plant populations. There were two scenarios in each population; causal variants were either neutral or under long-term negative selection. For large N_e, sequence data led to a 22% increase in accuracy relative to ∼600K SNP chip data with a Bayesian analysis and a more modest advantage with a BLUP analysis. This advantage increased when causal variants were influenced by negative selection, and accuracy persisted when 10 generations separated reference and validation populations. However, in the reducing N_e population, there was little advantage for sequence even with negative selection. This study demonstrates the joint influence of demography and selection on accuracy of prediction and improves our understanding of how best to exploit sequence for genomic prediction.     

A comparative analysis between SNPs and SSRs to investigate genetic variation in a juniper species (<Emphasis Type="Italic">Juniperus phoenicea</Emphasis> ssp. <Emphasis Type="Italic">turbinata</Emphasis>)

Genomic resources are a valuable research tool for understanding and forecasting the response of forest trees to global change and for developing science-based management strategies. Yet, many ecologically relevant tree species still lack such resources. The conifer genus Juniperus contains >?70 species that are widely distributed through the Northern Hemisphere, including several keystone species that form extensive forests in arid landscapes. To date, single-nucleotide polymorphism (SNP) markers have not been described for this ecologically important tree genus and the few described simple sequence repeat (SSR) markers result insufficient for performing reliable population demographic inference. Here, we report on the successful development of 19 new SSR and 147 SNP markers for Phoenician juniper (Juniperus phoenicea ssp. turbinata), a species widely distributed along the coasts of the Mediterranean Basin. We calculate a series of population genetic diversity estimates for each set of markers independently and for both sets combined. Our comparison shows that the higher per-locus information content of SSRs makes them the marker of choice for parentage and assignment studies, whereas SNPs provide more reliable demographic inferences (N_e and detection of a recent bottleneck). We also test and confirm the transferability of the new set of SNP markers to the closely related tetraploid species J. thurifera. Finally, we perform an orthology analysis with two gymnosperm model species to search for SNPs linked with functional genes.     

A Dual-Mode Single-Molecule Fluorescence Assay for the Detection of Expanded CGG Repeats in Fragile X Syndrome

Fragile X syndrome is the leading cause of inherited mental impairment and is associated with expansions of CGG repeats within the FMR1 gene. To detect expanded CGG repeats, we developed a dual-mode single-molecule fluorescence assay that allows acquisition of two parallel, independent measures of repeat number based on (1) the number of Cy3-labeled probes bound to the repeat region and (2) the physical length of the electric field-linearized repeat region, obtained from the relative position of a single Cy5 dye near the end of the repeat region. Using target strands derived from cell-line DNA with defined numbers of CGG repeats, we show that this assay can rapidly and simultaneously measure the repeats of a collection of individual sample strands within a single field of view. With a low occurrence of false positives, the assay differentiated normal CGG repeat lengths (CGG _N , N = 23) and expanded CGG repeat lengths (CGG _N , N = 118), representing a premutation disease state. Further, mixtures of these DNAs gave results that correlated with their relative populations. This strategy may be useful for identifying heterozygosity or for screening collections of individuals, and it is readily adaptable for screening other repeat disorders.     

Interval Estimation of the Effective Population Size from Heterozygote‐Excess in SNP Markers

The effective population size N_e is an important parameter in population genetics and conservation biology. In recent years, there has been great interest in the use of molecular markers to estimate N_e. Although the point estimates from molecular markers in general suffer from a low reliability, the use of single nucleotide polymorphism (SNP) markers over a wide range of genome is expected to remarkably improve the reliability. In this study, expressions were derived for interval estimates of N_e from one published method, the heterozygote‐excess method, when it is applied to SNP markers. The conditional variance theory is applied to the derivation of a confidence interval for N_e under random union of gametes, monogamy and polygyny. Stochastic simulation shows that the obtained confidence interval is slightly conservative, but fairly useful for practical applications. The result is illustrated with real data on SNP markers in a pig strain.     

The Evolution of Selfing Is Accompanied by Reduced Efficacy of Selection and Purging of Deleterious Mutations

The transition from outcrossing to selfing is predicted to reduce the genome-wide efficacy of selection because of the lower effective population size (N_e) that accompanies this change in mating system. However, strongly recessive deleterious mutations exposed in the homozygous backgrounds of selfers should be under strong purifying selection. Here, we examine estimates of the distribution of fitness effects (DFE) and changes in the magnitude of effective selection coefficients (N_es) acting on mutations during the transition from outcrossing to selfing. Using forward simulations, we investigated the ability of a DFE inference approach to detect the joint influence of mating system and the dominance of deleterious mutations on selection efficacy. We investigated predictions from our simulations in the annual plant Eichhornia paniculata, in which selfing has evolved from outcrossing on multiple occasions. We used range-wide sampling to generate population genomic datasets and identified nonsynonymous and synonymous polymorphisms segregating in outcrossing and selfing populations. We found that the transition to selfing was accompanied by a change in the DFE, with a larger fraction of effectively neutral sites (N_es < 1), a result consistent with the effects of reduced N_e in selfers. Moreover, an increased proportion of sites in selfers were under strong purifying selection (N_es > 100), and simulations suggest that this is due to the exposure of recessive deleterious mutations. We conclude that the transition to selfing has been accompanied by the genome-wide influences of reduced N_e and strong purifying selection against deleterious recessive mutations, an example of purging at the molecular level.     

Effective population size for culturally evolving traits

Population size has long been considered an important driver of cultural diversity and complexity. Results from population genetics, however, demonstrate that in populations with complex demographic structure or mode of inheritance, it is not the census population size, N, but the effective size of a population, N_e, that determines important evolutionary parameters. Here, we examine the concept of effective population size for traits that evolve culturally, through processes of innovation and social learning. We use mathematical and computational modeling approaches to investigate how cultural N_e and levels of diversity depend on (1) the way traits are learned, (2) population connectedness, and (3) social network structure. We show that one-to-many and frequency-dependent transmission can temporally or permanently lower effective population size compared to census numbers. We caution that migration and cultural exchange can have counter-intuitive effects on N_e. Network density in random networks leaves N_e unchanged, scale-free networks tend to decrease and small-world networks tend to increase N_e compared to census numbers. For one-to-many transmission and different network structures, larger effective sizes are closely associated with higher cultural diversity. For connectedness, however, even small amounts of migration and cultural exchange result in high diversity independently of N_e. Extending previous work, our results highlight the importance of carefully defining effective population size for cultural systems and show that inferring N_e requires detailed knowledge about underlying cultural and demographic processes.