A new likelihood estimator and its comparison with moment estimators of individual genome-wide diversity

A comparison of marker-based estimators of inbreeding and inbreeding depression

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_LH1 and F_LH2), VanRaden (F_VR1 and F_VR2), Yang and colleagues (F_YA1 and F_YA2), 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_LH1 and the best estimator of ΔID is F_YA2. The estimators F_VR2 and F_LH2 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_LH1 is the marker frequency-based estimator that is most correlated with F_IBD, and F_YA2 provides the most accurate estimates of ΔID. Estimates from F_ROH are also very precise in most scenarios. The estimators F_VR2 and F_LH2 have the poorest performances.

Multi-targeted management of upland game birds at the agroecosystem interface in midwestern North America

Despite its imperative, biodiversity conservation is chronically underfunded, a deficiency that often forces management agencies to prioritize. Single-species recovery thus becomes a focus (often with socio-political implications), whereas a more economical approach would be the transition to multi-targeted management (= MTM). This challenge is best represented in Midwestern North America where biodiversity has been impacted by 300+ years of chronic anthropogenic disturbance such that native tall-grass prairie is now supplanted by an agroecosystem. Here, we develop an MTM with a population genetic metric to collaboratively manage three Illinois upland gamebirds: common pheasant (Phasianus colchicus; pheasant), northern bobwhite quail (Colinus virginianus; quail), and threatened-endangered (T&E) greater prairie chicken (Tympanuchus cupido pinnatus; prairie chicken). We first genotyped our study pheasant at 19 microsatellite DNA loci and identified three captive breeding stocks (N = 143; IL Department of Natural Resources) as being significantly bottlenecked, with relatedness >1st-cousin (μR = 0.158). 'Wild' (non-stocked) pheasant [N = 543; 14 Pheasant-Habitat-Areas (PHAs)] were also bottlenecked, significantly interrelated (μR = 0.150) and differentiated (μFST = 0.047), yet distinct from propagation stock. PHAs that encompassed significantly with larger areas also reflected greater effective population sizes (μNE = 43; P<0.007). We juxtaposed these data against previously published results for prairie chicken and quail, and found population genetic structure driven by drift, habitat/climate impacts, and gender-biased selection via hunter-harvest. Each species (hunter-harvested or T&E) is independently managed, yet their composite population genetic baseline provides the quantitative criteria needed for an upland game bird MTM. Its implementation would require agricultural plots to be rehabilitated/reclaimed using a land-sharing/sparing portfolio that differs markedly from the Conservation Reserve Program (CRP), where sequestered land decreases as agricultural prices escalate. Cost-savings for an MTM would accrue by synchronizing single-species management with a dwindling hunter-harvest program, and by eliminating propagation/stocking programs. This would sustain not only native grasslands and their resident species, but also accelerate conservation at the wildlife-agroecosystem interface.

Genetic rescue, the greater prairie chicken and the problem of conservation reliance in the Anthropocene

A central question in conservation is how best to manage biodiversity, despite human domination of global processes (= Anthropocene). Common responses (i.e. translocations, genetic rescue) forestall potential extirpations, yet have an uncertain duration. A textbook example is the greater prairie chicken (GRPC: Tympanuchus cupido pinnatus), where translocations (1992-1998) seemingly rescued genetically depauperate Illinois populations. We re-evaluated this situation after two decades by genotyping 21 microsatellite loci from 1831 shed feathers across six leks in two counties over 4 years (2010-2013). Low migration rates (less than 1%) established each county as demographically independent, but with declining-population estimates (4 year average N = 79). Leks were genetically similar and significantly bottlenecked, with low effective population sizes (average N_e = 13.1; 4 year N_e/N = 0.166). Genetic structure was defined by 12 significantly different family groups, with relatedness r = 0.31 > half-sib r = 0.25. Average heterozygosity, indicating short-term survival, did not differ among contemporary, pre- and post-translocated populations, whereas allelic diversity did. Our results, the natural history of GRPC (i.e. few leks, male dominance hierarchies) and its controlled immigration suggest demographic expansion rather than genetic rescue. Legal protection under the endangered species act (ESA) may enhance recovery, but could exacerbate political-economic concerns on how best to manage 'conservation-reliant' species, for which GRPC is now an exemplar.

Low incidence of inbreeding in a long-lived primate population isolated for 75 years

ABSTRACT

When close relatives mate, offspring are expected to suffer fitness consequences due to inbreeding depression. Inbreeding has previously been quantified in two ways: using a sufficiently large panel of markers or deep and complete pedigrees over several generations. However, the application of both approaches is still limited by the challenge of compiling such data for species with long generation times, such as primates. Here, we assess inbreeding in rhesus macaques living on Cayo Santiago (Puerto Rico), a population genetically isolated since 1938, but descendant of a large set of presumably unrelated founders. Using comprehensive genetic data, we calculated inbreeding coefficients (F) for 2669 individuals with complete three generation pedigrees and 609 individuals with complete four generation pedigrees. We found that 0.79 and 7.39% of individuals had an F > 0 when using data from three and four generation pedigrees, respectively. No evidence of an increase in inbreeding over the study period (up to 23 years) was found. Furthermore, the observed mean relatedness of breeding pairs differed significantly from the distribution of parental relatedness expected as simulated based on previous reproductive data, suggesting that kin generally avoid breeding with each other. Finally, inbreeding was not a predictor of early mortality measured as survival until weaning and sexual maturation, respectively. Our results remain consistent with three estimators of inbreeding (standardized heterozygosity, internal relatedness, and homozygosity by loci) using up to 42 highly polymorphic microsatellites for the same set of individuals. Together, our results demonstrate that close inbreeding may not be prevalent even in populations isolated over long periods when mechanisms of inbreeding avoidance can operate.

SIGNIFICANCE STATEMENT

When close relatives mate, offspring may suffer from such inbreeding, e.g., via lower survival and/or fertility. Using (i) a large panel of genetic markers and (ii) complete three or four generation pedigrees, respectively, we show that incidences of inbreeding in a long-lived primate population are rare, even after genetic isolation for 75 years. Moreover, our simulations suggest that kin in our population generally avoid breeding with each other. Finally, the few inbred individuals detected in our large sample did not suffer from lower survival. Given that many animal species face dramatic habitat loss combined with critical population declines, our study provides important implications for conservation biology in general and for population management in particular.

Observed and expected frequencies of structural hemoglobin variants in newborn screening surveys in Africa and the Middle East: deviations from Hardy-Weinberg equilibrium

PURPOSE

Our objective was to compare observed and expected genotype proportions from newborn screening surveys of structural hemoglobin variants.

METHODS

We conducted a systematic review of newborn screening surveys of hemoglobins S and C in Africa and the Middle East. We compared observed frequencies to those expected assuming Hardy-Weinberg equilibrium (HWE). Significant deviations were identified by an exact test. The fixation index FIS was calculated to assess excess homozygosity. We compared newborn estimates corrected and uncorrected for HWE deviations using demographic data.

RESULTS

Sixty samples reported genotype counts for hemoglobin variants in Africa and the Middle East. Observed and expected counts matched in 27%. The observed number of sickle cell anemia (SCA) individuals was higher than expected in 42 samples, reaching significance (P < 0.05) in 24. High FIS values were common across the study regions. The estimated total number of newborns with SCA, corrected based on FIS, was 33,261 annual births instead of 24,958 for the 38 samples across sub-Saharan Africa and 1,109 annual births instead of 578 for 12 samples from the Middle East.

CONCLUSION

Differences between observed and expected genotype frequencies are common in surveys of hemoglobin variants in the study regions. Further research is required to identify and quantify factors responsible for such deviations. Estimates based on HWE might substantially underestimate the annual number of SCA-affected newborns (up to one-third in sub-Saharan Africa and one-half in the Middle East).

Pedigrees or markers: Which are better in estimating relatedness and inbreeding coefficient?

Individual inbreeding coefficient (F) and pairwise relatedness (r) are fundamental parameters in population genetics and have important applications in diverse fields such as human medicine, forensics, plant and animal breeding, conservation and evolutionary biology. Traditionally, both parameters are calculated from pedigrees, but are now increasingly estimated from genetic marker data. Conceptually, a pedigree gives the expected F and r values, FP and rP, with the expectations being taken (hypothetically) over an infinite number of individuals with the same pedigree. In contrast, markers give the realised (actual) F and r values at the particular marker loci of the particular individuals, FM and rM. Both pedigree (FP, rP) and marker (FM, rM) estimates can be used as inferences of genomic inbreeding coefficients FG and genomic relatedness rG, which are the underlying quantities relevant to most applications (such as estimating inbreeding depression and heritability) of F and r. In the pre-genomic era, it was widely accepted that pedigrees are much better than markers in delineating FG and rG, and markers should better be used to validate, amend and construct pedigrees rather than to replace them. Is this still true in the genomic era when genome-wide dense SNPs are available? In this simulation study, I showed that genomic markers can yield much better estimates of FG and rG than pedigrees when they are numerous (say, 10(4) SNPs) under realistic situations (e.g. genome and population sizes). Pedigree estimates are especially poor for species with a small genome, where FG and rG are determined to a large extent by Mendelian segregations and may thus deviate substantially from their expectations (FP and rP). Simulations also confirmed that FM, when estimated from many SNPs, can be much more powerful than FP for detecting inbreeding depression in viability. However, I argue that pedigrees cannot be replaced completely by genomic SNPs, because the former allows for the calculation of more complicated IBD coefficients (involving more than 2 individuals, more than one locus, and more than 2 genes at a locus) for which the latter may have reduced capacity or limited power, and because the former has social and other significance for remote relationships which have little genetic significance and cannot be inferred reliably from markers.

Estimating relatedness and inbreeding using molecular markers and pedigrees: the effect of demographic history

Estimates of inbreeding and relatedness are commonly calculated using molecular markers, although the accuracy of such estimates has been questioned. As a further complication, in many situations, such estimates are required in populations with reduced genetic diversity, which is likely to affect their accuracy. We investigated the correlation between microsatellite- and pedigree-based coefficients of inbreeding and relatedness in laboratory populations of Drosophila melanogaster that had passed through bottlenecks to manipulate their genetic diversity. We also used simulations to predict expected correlations between marker- and pedigree-based estimates and to investigate the influence of linkage between loci and null alleles. Our empirical data showed lower correlations between marker- and pedigree-based estimates in our control (nonbottleneck) population than were predicted by our simulations or those found in similar studies. Correlations were weaker in bottleneck populations, confirming that extreme reductions in diversity can compromise the ability of molecular estimates to detect recent inbreeding events. However, this result was highly dependent on the strength of the bottleneck and we did not observe or predict any reduction in correlations in our population that went through a relatively severe bottleneck of N = 10 for one generation. Our results are therefore encouraging, as molecular estimates appeared robust to quite severe reductions in genetic diversity. It should also be remembered that pedigree-based estimates may not capture realized identity-by-decent and that marker-based estimates may actually be more useful in certain situations.

Reconstructing paternal genotypes to infer patterns of sperm storage and sexual selection in the hawksbill turtle

Postcopulatory sperm storage can serve a range of functions, including ensuring fertility, allowing delayed fertilization and facilitating sexual selection. Sperm storage is likely to be particularly important in wide-ranging animals with low population densities, but its prevalence and importance in such taxa, and its role in promoting sexual selection, are poorly known. Here, we use a powerful microsatellite array and paternal genotype reconstruction to assess the prevalence of sperm storage and test sexual selection hypotheses of genetic biases to paternity in one such species, the critically endangered hawksbill turtle, Eretmochelys imbricata. In the majority of females (90.7%, N = 43), all offspring were sired by a single male. In the few cases of multiple paternity (9.3%), two males fertilized each female. Importantly, the identity and proportional fertilization success of males were consistent across all sequential nests laid by individual females over the breeding season (up to five nests over 75 days). No males were identified as having fertilized more than one female, suggesting that a large number of males are available to females. No evidence for biases to paternity based on heterozygosity or relatedness was found. These results indicate that female hawksbill turtles are predominantly monogamous within a season, store sperm for the duration of the nesting season and do not re-mate between nests. Furthermore, females do not appear to be using sperm storage to facilitate sexual selection. Consequently, the primary value of storing sperm in marine turtles may be to uncouple mating and fertilization in time and avoid costly re-mating.

Maximum likelihood estimation of individual inbreeding coefficients and null allele frequencies

In this paper, we developed and compared several expectation-maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).