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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 e LD ) 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 e LD 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 e LD measures mainly reflect demographic changes in population size across generations.

Inferring changes in effective population size (Ne) in the recent past is of special interest for conservation of endangered species and for human history research. Current methods for estimating the very recent historical Ne are unable to detect complex demographic trajectories involving multiple episodes of bottlenecks, drops, and expansions. We develop a theoretical and computational framework to infer the demographic history of a population within the past 100 generations from the observed spectrum of linkage disequilibrium (LD) of pairs of loci over a wide range of recombination rates in a sample of contemporary individuals. The cumulative contributions of all of the previous generations to the observed LD are included in our model, and a genetic algorithm is used to search for the sequence of historical Ne values that best explains the observed LD spectrum. The method can be applied from large samples to samples of fewer than ten individuals using a variety of genotyping and DNA sequencing data: haploid, diploid with phased or unphased genotypes and pseudohaploid data from low-coverage sequencing. The method was tested by computer simulation for sensitivity to genotyping errors, temporal heterogeneity of samples, population admixture, and structural division into subpopulations, showing high tolerance to deviations from the assumptions of the model. Computer simulations also show that the proposed method outperforms other leading approaches when the inference concerns recent timeframes. Analysis of data from a variety of human and animal populations gave results in agreement with previous estimations by other methods or with records of historical events.

Linkage disequilibrium methods for demographic inference usually rely on panmictic population models. However, the structure of natural populations is generally complex and the quality of the genotyping data is often suboptimal. We present two software tools that implement theoretical developments to estimate the effective population size ( N e ): GONE2 , for inferring recent changes in N e when a genetic map is available, and currentNe2 , which estimates contemporary N e even in the absence of genetic maps. These tools operate on SNP data from a single sample of individuals, and provide insights into population structure, including the F ST index, migration rate, and subpopulation number. GONE2 can also handle haploid data, genotyping errors, and low sequencing depth data. Results from simulations and laboratory populations of Drosophila melanogaster validated the tools in different demographic scenarios, and analysis were extended to populations of several species. These results highlight that ignoring population subdivision often leads to N e underestimation. Accurate estimation of effective population size is critical for understanding population history but is often confounded by structure and data quality. Here, the authors show that GONE2 and currentNe2 infer this from SNP data while accounting for structure and suboptimal genotyping.

The inbreeding coefficient (F) of individuals can be estimated from molecular marker data, such as SNPs, using measures of homozygosity of individual markers or runs of homozygosity (ROH) across the genome. These different measures of F can then be used to estimate the rate of inbreeding depression (ID) for quantitative traits. Some recent simulation studies have investigated the accuracy of this estimation with contradictory results. Whereas some studies suggest that estimates of inbreeding from ROH account more accurately for ID, others suggest that inbreeding measures from SNP‐by‐SNP homozygosity giving a large weight to rare alleles are more accurate. Here, we try to give more light on this issue by carrying out a set of computer simulations considering a range of population genetic parameters and population sizes. Our results show that the previous studies are indeed not contradictory. In populations with low effective size, where relationships are more tight and selection is relatively less intense, F measures based on ROH provide very accurate estimates of ID whereas SNP‐by‐SNP‐based F measures with high weight to rare alleles can show substantial upwardly biased estimates of ID. However, in populations of large effective size, with more intense selection and trait allele frequencies expected to be low if they are deleterious for fitness because of purifying selection, average estimates of ID from SNP‐by‐SNP‐based F values become unbiased or slightly downwardly biased and those from ROH‐based F values become slightly downwardly biased. The noise attached to all these estimates, nevertheless, can be very high in large‐sized populations. We also investigate the relationship between the different F measures and the homozygous mutation load, which has been suggested as a proxy of inbreeding depression.

Background Effective population size ( N e ) is a crucial parameter in conservation genetics and animal breeding. A recent method, implemented by the software GONE, has been shown to be rather accurate in estimating recent historical changes in N e from a single sample of individuals. However, GONE estimations assume that the population being studied has remained isolated for a period of time, that is, without migration or confluence of other populations. If this occurs, the estimates of N e can be heavily biased. In this paper, we evaluate the impact of migration and admixture on the estimates of historical N e provided by GONE through a series of computer simulations considering several scenarios: (a) the mixture of two or more ancestral populations; (b) subpopulations that continuously exchange individuals through migration; (c) populations receiving migrants from a large source; and (d) populations with balanced systems of chromosomal inversions, which also generate genetic structure. Results Our results indicate that the estimates of historical N e provided by GONE may be substantially biased when there has been a recent mixture of populations that were previously separated for a long period of time. Similarly, biases may occur when the rate of continued migration between populations is low, or when chromosomal inversions are present at high frequencies. However, some biases due to population structuring can be eliminated by conducting population structure analyses and restricting the estimation to the differentiated groups. In addition, disregarding the genomic regions that are involved in inversions can also remove biases in the estimates of N e . Conclusions Different kinds of deviations from isolation and panmixia of the populations can generate biases in the recent historical estimates of N e . Therefore, estimation of past demography could benefit from performing population structure analyses beforehand, by mitigating the impact of these biases on historical N e estimates.

The estimation of the inbreeding coefficient (F) is essential for the study of inbreeding depression (ID) or for the management of populations under conservation. Several methods have been proposed to estimate the realized F using genetic markers, but it remains unclear which one should be used. Here we used whole-genome sequence data for 245 individuals from a Holstein cattle pedigree to empirically evaluate which estimators best capture homozygosity at variants causing ID, such as rare deleterious alleles or loci presenting heterozygote advantage and segregating at intermediate frequency. Estimators relying on the correlation between uniting gametes (FUNI) or on the genomic relationships (FGRM) presented the highest correlations with these variants. However, homozygosity at rare alleles remained poorly captured. A second group of estimators relying on excess homozygosity (FHOM), homozygous-by-descent segments (FHBD), runs-of-homozygosity (FROH) or on the known genealogy (FPED) was better at capturing whole-genome homozygosity, reflecting the consequences of inbreeding on all variants, and for young alleles with low to moderate frequencies (0.10 < . < 0.25). The results indicate that FUNI and FGRM might present a stronger association with ID. However, the situation might be different when recessive deleterious alleles reach higher frequencies, such as in populations with a small effective population size. For locus-specific inbreeding measures or at low marker density, the ranking of the methods can also change as FHBD makes better use of the information from neighboring markers. Finally, we confirmed that genomic measures are in general superior to pedigree-based estimates. In particular, FPED was uncorrelated with locus-specific homozygosity.

Background The availability of genome-wide marker data allows estimation of inbreeding coefficients ( F , the probability of identity-by-descent, IBD) and, in turn, estimation of the rate of inbreeding depression (ΔID). We investigated, by computer simulations, the accuracy of the most popular estimators of inbreeding based on molecular markers when computing F and ΔID in populations under random mating, equalization of parental contributions, and artificially selected populations. We assessed estimators described by Li and Horvitz ( F LH 1 and F LH 2 ), VanRaden ( F VR 1 and F VR 2 ), Yang and colleagues ( F YA 1 and F YA 2 ), marker homozygosity ( F HOM ), runs of homozygosity ( F ROH ) and estimates based on pedigree ( F PED ) in comparison with estimates obtained from IBD measures ( F IBD ). Results If the allele frequencies of a base population taken as a reference for the computation of inbreeding are known, all estimators based on marker allele frequencies are highly correlated with F IBD and provide accurate estimates of the mean ΔID. If base population allele frequencies are unknown and current frequencies are used in the estimations, the largest correlation with F IBD is generally obtained by F LH 1 and the best estimator of ΔID is F YA 2 . The estimators F VR 2 and F LH 2 have the poorest performance in most scenarios. The assumption that base population allele frequencies are equal to 0.5 results in very biased estimates of the average inbreeding coefficient but they are highly correlated with F IBD and give relatively good estimates of ΔID. Estimates obtained directly from marker homozygosity ( F HOM ) substantially overestimated ΔID. Estimates based on runs of homozygosity ( F ROH ) provide accurate estimates of inbreeding and ΔID. Finally, estimates based on pedigree ( F PED ) show a lower correlation with F IBD than molecular estimators but provide rather accurate estimates of ΔID. An analysis of data from a pig population supports the main findings of the simulations. Conclusions When base population allele frequencies are known, all marker-allele frequency-based estimators of inbreeding coefficients generally show a high correlation with F IBD and provide good estimates of ΔID. When base population allele frequencies are unknown, F LH 1 is the marker frequency-based estimator that is most correlated with F IBD , and F YA 2 provides the most accurate estimates of ΔID. Estimates from F ROH are also very precise in most scenarios. The estimators F VR 2 and F LH 2 have the poorest performances.

Background Genomic relationship matrices are used to obtain genomic inbreeding coefficients. However, there are several methodologies to compute these matrices and there is still an unresolved debate on which one provides the best estimate of inbreeding. In this study, we investigated measures of inbreeding obtained from five genomic matrices, including the Nejati-Javaremi allelic relationship matrix ( F NEJ ), the Li and Horvitz matrix based on excess of homozygosity ( F L&H ), and the VanRaden (methods 1, F VR 1 , and 2, F VR 2 ) and Yang ( F YAN ) genomic relationship matrices. We derived expectations for each inbreeding coefficient, assuming a single locus model, and used these expectations to explain the patterns of the coefficients that were computed from thousands of single nucleotide polymorphism genotypes in a population of Iberian pigs. Results Except for F NEJ , the evaluated measures of inbreeding do not match with the original definitions of inbreeding coefficient of Wright (correlation) or Malécot (probability). When inbreeding coefficients are interpreted as indicators of variability (heterozygosity) that was gained or lost relative to a base population, both F NEJ and F L&H led to sensible results but this was not the case for F VR 1 , F VR 2 and F YAN . When variability has increased relative to the base, F VR 1 , F VR 2 and F YAN can indicate that it decreased. In fact, based on F YAN , variability is not expected to increase. When variability has decreased, F VR 1 and F VR 2 can indicate that it has increased. Finally, these three coefficients can indicate that more variability than that present in the base population can be lost, which is also unreasonable. The patterns for these coefficients observed in the pig population were very different, following the derived expectations. As a consequence, the rate of inbreeding depression estimated based on these inbreeding coefficients differed not only in magnitude but also in sign. Conclusions Genomic inbreeding coefficients obtained from the diagonal elements of genomic matrices can lead to inconsistent results in terms of gain and loss of genetic variability and inbreeding depression estimates, and thus to misleading interpretations. Although these matrices have proven to be very efficient in increasing the accuracy of genomic predictions, they do not always provide a useful measure of inbreeding.

Inbreeding depression (ID), the reduction in fitness due to inbreeding, is typically measured by the regression of the phenotypic values of individuals for a particular trait on their corresponding inbreeding coefficients (F). While genealogical records can provide these coefficients, they may be unavailable or incomplete, making molecular markers a useful alternative. The power to detect ID and its accuracy depend on the variation of F values of individuals, the sample sizes available, and the accuracy in the estimation of individual fitness traits and F values. In this study, we used Drosophila melanogaster to evaluate the effectiveness of molecular markers in estimating ID under suboptimal conditions. We generated two sets of 100 pairs of unrelated individuals from a large panmictic population and mated them for two generations to produce non‐inbred and unrelated individuals (F = 0) and inbred individuals (full‐sib progeny; F = 0.25). Using these expected genealogical F values, we calculated inbreeding depression for two fitness‐related traits, pupae productivity and competitive fitness. We then sequenced the males from 17 non‐inbred pairs and 17 inbred pairs to obtain their genomic inbreeding coefficients and estimate ID for the two traits. The scenario assumed was rather restrictive in terms of estimation of ID because: (1) the individuals belonged to the same generation of a large panmictic population, leading to low variation in individual F coefficients; (2) the sample sizes were small; and (3) the traits measured depended on both males and females while only males were sequenced. Despite the challenging conditions of our study, we found that molecular markers provided estimates of ID that were comparable to those obtained from simple pedigree estimations with larger sample sizes. The results therefore suggest that genomic measures of inbreeding are useful to provide estimates of inbreeding depression even under very challenging scenarios.