Performance of marker-based relatedness estimators in natural populations of outbred vertebrates

Knowledge of relatedness between pairs of individuals plays an important role in many research areas including evolutionary biology, quantitative genetics, and conservation. Pairwise relatedness estimation methods based on genetic data from highly variable molecular markers are now used extensively as a substitute for pedigrees. Although the sampling variance of the estimators has been intensively studied for the most common simple genetic relationships, such as unrelated, half- and full-sib, or parent-offspring, little attention has been paid to the average performance of the estimators, by which we mean the performance across all pairs of individuals in a sample. Here we apply two measures to quantify the average performance: first, misclassification rates between pairs of genetic relationships and, second, the proportion of variance explained in the pairwise relatedness estimates by the true population relatedness composition (i.e., the frequencies of different relationships in the population). Using simulated data derived from exceptionally good quality marker and pedigree data from five long-term projects of natural populations, we demonstrate that the average performance depends mainly on the population relatedness composition and may be improved by the marker data quality only within the limits of the population relatedness composition. Our five examples of vertebrate breeding systems suggest that due to the remarkably low variance in relatedness across the population, marker-based estimates may often have low power to address research questions of interest.     

Estimating the correlation of pairwise relatedness along chromosomes

The 'spatial' pattern of the correlation of pairwise relatedness among loci within a chromosome is an important aspect for an insight into genomic evolution in natural populations. In this article, a statistical genetic method is presented for estimating the correlation of pairwise relatedness among linked loci. The probabilities of identity-in-state (IIS) are related to the probabilities of identity-by-descent (IBS) for the two- and three-loci cases. By decomposing the joint probabilities of two- or three-loci IBD, the probability of pairwise relatedness at a single locus and its correlation among linked loci can be simultaneously estimated. To provide effective statistical methods for estimation, weighted least square (LS) and maximum likelihood (ML) methods are evaluated through extensive Monte Carlo simulations. Results show that the ML method gives a better performance than the weighted LS method with haploid genotypic data. However, there are no significant differences between the two methods when two- or three-loci diploid genotypic data are employed. Compared with the optimal size for haploid genotypic data, a smaller optimal sample size is predicted with diploid genotypic data.     

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.     

A comparison of approaches to estimate the inbreeding coefficient and pairwise relatedness using genomic and pedigree data in a sheep population

Genome-wide SNP data provide a powerful tool to estimate pairwise relatedness among individuals and individual inbreeding coefficient. The aim of this study was to compare methods for estimating the two parameters in a Finnsheep population based on genome-wide SNPs and genealogies, separately. This study included ninety-nine Finnsheep in Finland that differed in coat colours (white, black, brown, grey, and black/white spotted) and were from a large pedigree comprising 319 119 animals. All the individuals were genotyped with the Illumina Ovine SNP50K BeadChip by the International Sheep Genomics Consortium. We identified three genetic subpopulations that corresponded approximately with the coat colours (grey, white, and black and brown) of the sheep. We detected a significant subdivision among the colour types (F _ST = 5.4%, P<0.05). We applied robust algorithms for the genomic estimation of individual inbreeding (F _SNP) and pairwise relatedness (Φ _SNP) as implemented in the programs KING and PLINK, respectively. Estimates of the two parameters from pedigrees (F _PED and Φ _PED) were computed using the RelaX2 program. Values of the two parameters estimated from genomic and genealogical data were mostly consistent, in particular for the highly inbred animals (e.g. inbreeding coefficient F>0.0625) and pairs of closely related animals (e.g. the full- or half-sibs). Nevertheless, we also detected differences in the two parameters between the approaches, particularly with respect to the grey Finnsheep. This could be due to the smaller sample size and relative incompleteness of the pedigree for them.We conclude that the genome-wide genomic data will provide useful information on a per sample or pairwise-samples basis in cases of complex genealogies or in the absence of genealogical data.     

Informativeness of genetic markers for pairwise relationship and relatedness inference

Measuring the information content of markers in relationship/relatedness inferences is important in selecting highly informative markers to attain a given statistical power with the minimal genotyping effort. Using information-theoretic principles, I introduce the informativeness for relationship (I(R)) and the informativeness for relatedness (I(r)) to measure the amount of information provided by markers in inferring pairwise relationships (R) and relatedness (r), respectively. I also propose a fast and accurate algorithm to calculate the power (PW(R)) of a set of markers in differentiating two candidate relationships, and the reciprocal of the mean squared deviations of relatedness estimates (RMSD) to measure the amount of information of markers actually used by an estimator in estimating relatedness. All of the four measurements (I(R), I(r), PW(R), RMSD) apply to dominant and codominant markers, haploid and diploid individuals, and take into account of mutations and typing errors in data. The statistical properties of the four measurements and their relationships are investigated analytically and are examined by applying these methods to simulated and empirical data.     

PERMANENT GENETIC RESOURCES: Identification of nuclear microsatellite loci for Ipomopsis aggregata and the distribution of pairwise relatedness in a natural population

Nine microsatellite loci were developed from enriched libraries of scarlet gilia (Ipomopsis aggregata). A screen of 160 individuals from a population identified reduced levels of heterozygosity, low levels of relatedness, and weak spatial genetic patterns. The population inbreeding coefficient was calculated to be 0.19 (SE = 0.04). These patterns are consistent with those expected from low levels of biparental inbreeding in an obligate outcrosser and extensive seed and pollen dispersal. These preliminary data confirm the usefulness of microsatellite markers for breeding system studies of I. aggregata.     

On the use of large marker panels to estimate inbreeding and relatedness: empirical and simulation studies of a pedigreed zebra finch population typed at 771 SNPs

In recent years there has been a dramatic increase in the availability of high density genetic marker data for both model and non‐model organisms. A potential application of these data is to infer relatedness in the absence of a complete pedigree. Using a marker panel of 771 SNPs genotyped in three generations of an extensive zebra finch pedigree, correlations between pedigree relatedness and seven marker‐based estimates of relatedness were examined, as was the relationship between heterozygosity and inbreeding. Although marker‐based and pedigree relatedness were highly correlated, the variance in estimated relatedness was high. Further, the correlation between heterozygosity and inbreeding was weak, even though mean inbreeding coefficient is typical of that seen in wild vertebrate pedigrees; the weak relationship was in part due to the small variance in inbreeding in the pedigree. Our data suggest that using marker information to reconstruct the pedigree, and then calculating relatedness from the pedigree, is likely to give more accurate relatedness estimates than using marker‐based estimators directly.     

A maximum-likelihood method for the estimation of pairwise relatedness in structured populations

A maximum-likelihood estimator for pairwise relatedness is presented for the situation in which the individuals under consideration come from a large outbred subpopulation of the population for which allele frequencies are known. We demonstrate via simulations that a variety of commonly used estimators that do not take this kind of misspecification of allele frequencies into account will systematically overestimate the degree of relatedness between two individuals from a subpopulation. A maximum-likelihood estimator that includes F(ST) as a parameter is introduced with the goal of producing the relatedness estimates that would have been obtained if the subpopulation allele frequencies had been known. This estimator is shown to work quite well, even when the value of F(ST) is misspecified. Bootstrap confidence intervals are also examined and shown to exhibit close to nominal coverage when F(ST) is correctly specified.     

Spatial relatedness and brood parasitism in a female-philopatric bird population

The spatial structure of relatedness between individuals ina population can be crucial for social selection and evolution.Here we analyze a female alternative reproductive tactic, conspecificbrood parasitism, in relation to spatial relatedness among femalesin a Baltic Sea population of the common eider Somateria mollissima.The role of relatedness in brood parasitism is debated: somemodels predict parasite avoidance of related hosts, others predicthost–parasite relatedness. We estimate pairwise relatednessfrom protein fingerprinting of egg albumen in 156 nests, withpairwise nest distances ranging from 1 to 6 km. Relatednessincreases significantly from the longest distances to an averageof r 0.09 below 20 m. Brood parasitism is common, and averagepairwise relatedness between host and parasite is estimatedat 0.18–0.21. Parasites thus do not avoid relatives, andcombined with the findings of a similar study in another eiderpopulation, the results show that mean host–parasite relatednessis higher than that among close neighbors. High host–parasiterelatedness is therefore not an effect of natal philopatry alone;some other form of kin bias is also involved. Recognition andassociation between birth nest mates is a candidate mechanismfor further study.     

Accuracy of genotypic value predictions for marker-based selection in biparental plant populations

The availability of cheap and abundant molecular markers has led to plant-breeding methods that rely on the prediction of genotypic value from marker data, but published information is lacking on the accuracy of genotypic value predictions with empirical data in plants. Our objectives were to (1) determine the accuracy of genotypic value predictions from multiple linear regression (MLR) and genomewide selection via best linear unbiased prediction (BLUP) in biparental plant populations; (2) assess the accuracy of predictions for different numbers of markers (N _M) and progenies (N _P) used in estimation; and (3) determine if an empirical Bayes approach for modeling of the variances of individual markers and of epistatic effects leads to more accurate predictions in empirical data. We divided each of four maize (Zea mays L.) datasets, one Arabidopsis dataset, and two barley (Hordeum vulgare L.) datasets into an estimation set, where marker effects were calculated, and a test set, where genotypic values were predicted based on markers. Predictions were more accurate with BLUP than with MLR. Predictions became more accurate as N _P and N _M increased, until sufficient genome coverage was reached. Modeling marker variances with the empirical Bayes method sometimes led to slightly better predictions, but the accuracy with different variants of the empirical Bayes method was often inconsistent. In nearly all cases, the accuracy with BLUP was not significantly different from the highest accuracy across all methods. Accounting for epistasis in the empirical Bayes procedure led to poorer predictions. We concluded that among the methods considered, the quick and simple BLUP approach is the method of choice for predicting genotypic value in biparental plant populations.     

Performance of nonparametric species richness estimators in a high diversity plant community

Abstract. The efficiency of four nonparametric species richness estimators — first‐order Jackknife, second‐order Jackknife, Chao2 and Bootstrap — was tested using simulated quadrat sampling of two field data sets (a sandy ‘Dune’ and adjacent ‘Swale’) in high diversity shrublands (kwongan) in south‐western Australia. The data sets each comprised > 100 perennial plant species and > 10 000 individuals, and the explicit (x‐y co‐ordinate) location of every individual. We applied two simulated sampling strategies to these data sets based on sampling quadrats of unit sizes 1/400th and 1/100th of total plot area. For each site and sampling strategy we obtained 250 independent sample curves, of 250 quadrats each, and compared the estimators’ performances by using three indices of bias and precision: MRE (mean relative error), MSRE (mean squared relative error) and OVER (percentage overestimation). The analysis presented here is unique in providing sample estimates derived from a complete, field‐based population census for a high diversity plant community. In general the true reference value was approached faster for a comparable area sampled for the smaller quadrat size and for the swale field data set, which was characterized by smaller plant size and higher plant density. Nevertheless, at least 15–30% of the total area needed to be sampled before reasonable estimates of S_t (total species richness) were obtained. In most field surveys, typically less than 1% of the total study domain is likely to be sampled, and at this sampling intensity underestimation is a problem. Results showed that the second‐order Jackknife approached the actual value of S_t more quickly than the other estimators. All four estimators were better than S_obs (observed number of species). However, the behaviour of the tested estimators was not as good as expected, and even with large sample size (number of quadrats sampled) all of them failed to provide reliable estimates. First‐ and second‐order Jackknives were positively biased whereas Chao2 and Bootstrap were negatively biased. The observed limitations in the estimators’ performance suggests that there is still scope for new tools to be developed by statisticians to assist in the estimation of species richness from sample data, especially in communities with high species richness.     

Assortative mating for relatedness in a large naturally occurring population of Drosophila melanogaster

New theoretical work on kin selection and inclusive fitness benefits predicts that individuals will sometimes choose close or intermediate relatives as mates to maximize their fitness. However, empirical examples supporting such predictions are rare. In this study, we look for such evidence in a natural population of Drosophila melanogaster. We compared mating and nonmating individuals to test whether mating was nonrandom with respect to relatedness. Consistent with optimal inbreeding, males were more closely related to their mate than to randomly sampled females. However, all individuals collected mating showed higher relatedness and males were not significantly more related to their mate than to other mating females. We also found a negative relationship between relatedness and fecundity. Our results are consistent with the hypothesis that inclusive fitness benefits may drive inbreeding tolerance despite direct costs to fitness; however, an experimental approach is needed to investigate the link between mate preference and relatedness.     

identix,a software to test for relatedness in a population using permutation methods

The computer program identix estimates relatedness in natural populations using multilocus genotypic data. Queller & Goodnight's (1989) and Lynch & Ritland's (1999) estimators of pairwise relatedness are implemented, as well as the identity index of Mathieu et al. (1990). Estimates of the confidence intervals around these pairwise values are also provided. The null hypothesis of no relatedness (multilocus genotypes are independent draws from a panmictic population) is tested using a permutation method that compares the observed distribution of the moments of pairwise relatedness coefficients to that expected in unstructured population.     

Molecular investigation on strain genetic relatedness and population structure of Beauveria bassiana

Triplicate molecular methods, i.e. polymerase chain reaction-restriction fragment length polymorphism of the pr1 gene, microsatellite markers and 28S rDNA haplotyping by detecting the presence or absence of group I introns, were used for population study of the entomopathogenic fungus, Beauveria bassiana. The findings showed that the average genetic diversity index of geographical populations was significantly smaller than that of populations derived from insect host orders, indicating that the genetic relatedness of B. bassiana strains was highly associated with geographical locality rather than insect host species. The reproductive style of all the B. bassiana populations was found to be non-clonal. Population structure analysis revealed that the average divergent coefficient among populations of B. bassiana was far below 1 (0.1112), which indicated that there was no significant genetic differentiation between populations, and that the overall genetic diversity mainly resulted from the genetic variations within geographical populations. Statistically, genetic distances between populations were positively correlated with geographical distances, suggesting that geographical separation poses an obstacle to the possibility and frequency of genetic exchanges between populations. On the other hand, gene flow was indirectly established to occur between B. bassiana populations.     

A spatial genetic structure and effects of relatedness on mate choice in a wild bird population

Inbreeding depression, as commonly found in natural populations, should favour the evolution of inbreeding avoidance mechanisms. If natal dispersal, the first and probably most effective mechanism, does not lead to a complete separation of males and females from a common origin, a small-scale genetic population structure may result and other mechanisms to avoid inbreeding may exist. We studied the genetic population structure and individual mating patterns in blue tits (Parus caeruleus). The population showed a local genetic structure in two out of four years: genetic relatedness between individuals (estimated from microsatellite markers) decreased with distance. This pattern was mainly caused by immigrants to the study area; these, if paired with fellow immigrants, were more related than expected by chance. Since blue tits did not avoid inbreeding with their social partner, we examined if individuals preferred less related partners at later stages of the mate choice process. We found no evidence that females or males avoided inbreeding through extra-pair copulations or through mate desertion and postbreeding dispersal. Although the small-scale genetic population structure suggests that blue tits could use a simple rule of thumb to select less related mates, females did not generally prefer more distantly breeding extra-pair partners. However, the proportion of young fathered by an extra-pair male in mixed paternity broods depended on the genetic relatedness with the female. This suggests that there is a fertilization bias towards less related copulation partners and that blue tits are able to reduce the costs of inbreeding through a postcopulatory process.     

A comparison of estimators of the population recombination rate

Three new estimators of the population recombination rate C = 4Nr are introduced. These estimators summarize the data using the number of distinct haplotypes and the estimated minimum number of recombination events, then calculate the value of C that maximizes the likelihood of obtaining the summarized data. They are compared with a number of previously proposed estimators of the recombination rate. One of the newly proposed estimators is generally better than the others for the parameter values considered here, while the three programs that calculate maximum-likelihood estimates give conflicting results.     

The role of relatedness in structuring the social network of a wild guppy population

Parasite avoidance is increasingly considered to be a potential driving factor in animal migrations. In many marine and freshwater benthic fish, migration into a pelagic environment by developing larvae is a common life history trait that could reduce exposure to parasites during a critical window of developmental susceptibility. We tested this hypothesis on congeneric fish (family Galaxiidae, genus Galaxias) belonging to a closely related species complex sampled from coastal streams in southeastern New Zealand. Migratory Galaxias have larvae that migrate to pelagic marine environments, whereas the larvae of non-migratory species rear close to adult habitats with no pelagic larval phase. Both migratory and non-migratory fish are hosts to two species of skin-penetrating trematodes that cause spinal malformations and high mortality in young fish. Using generalized linear models within an Akaike information criterion and model averaging framework, we compared infection levels between migratory and non-migratory fish while taking into account body size and several other local factors likely to influence infection levels. For one trematode species, we found a significant effect of migration: for any given body length, migratory fish harboured fewer parasites than non-migratory fish. Also, no parasites of any kind were found in juvenile migratory fish sampled in spring shortly after their return to stream habitats. Our results demonstrate that migration spares juvenile fish from the debilitating parasites to which they would be exposed in adult stream habitats. Therefore, either the historical adoption of a migratory strategy in some Galaxias was an adaptation against parasitism, or it evolved for other reasons and now provides protection from infection as a coincidental side-effect.