Evaluating the utility of identity-by-descent segment numbers for relatedness inference via information theory and classification

Despite decades of methods development for classifying relatives in genetic studies, pairwise relatedness methods' recalls are above 90% only for first through third degree relatives. The top-performing approaches, which leverage identity-by-descent (IBD) segments, often use only kinship coefficients, while others, including ERSA, use the number of segments relatives share. To quantify the potential for using segment numbers in relatedness inference, we leveraged information theory measures to analyze exact (i.e., produced by a simulator) IBD segments from simulated relatives. Over a range of settings, we found that the mutual information between the relatives' degree of relatedness and a tuple of their kinship coefficient and segment number is on average 4.6% larger than between the degree and the kinship coefficient alone. We further evaluated IBD segment number utility by building a Bayes classifier to predict first through sixth degree relationships using different feature sets. When trained and tested with exact segments, the inclusion of segment numbers improves the recall by between 0.0028 and 0.030 for second through sixth degree relatives. However, the recalls improve by less than 0.018 per degree when using inferred segments, suggesting limitations due to IBD detection accuracy. Lastly, we compared our Bayes classifier that includes segment numbers with ERSA and IBIS and found comparable results, with the Bayes classifier and ERSA slightly outperforming each other across different degrees. Overall, this study shows that IBD segment numbers can improve relatedness inference but that errors from current SNP array-based detection methods yield dampened signals in practice.

Correcting statistical bias in correlation-based kinship estimators

Accurate estimate of relatedness is important for genetic data analyses, such as association mapping and heritability estimation based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to spurious associations and biased heritability estimations. Individual-level genotype data are often used to estimate kinship coefficient between individuals. The commonly used sample correlation-based genomic relationship matrix (scGRM) method estimates kinship coefficient by calculating the average sample correlation coefficient among all single nucleotide polymorphisms (SNPs), where the observed allele frequencies are used to calculate both the expectations and variances of genotypes. Although this method is widely used, a substantial proportion of estimated kinship coefficients are negative, which are difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists bias in the estimated kinship coefficient using the scGRM method when the observed allele frequencies are regarded as true frequencies. This leads to negative bias for the average estimate of kinship among all individuals, which explains the estimated negative kinship coefficients. Based on this observation, we propose an unbiased estimation method, UKin, which can reduce the bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to demonstrate that both bias and root mean square error in kinship coefficient estimation can be reduced by using UKin. Further simulations indicate that the power in association mapping can also be improved by using our unbiased kinship estimates to adjust for cryptic relatedness.

Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population

Recent modeling studies interested in runs of homozygosity (ROH) and identity by descent (IBD) have sought to connect these properties of genomic sharing to pairwise coalescence times. Here, we examine a variety of features of pairwise coalescence times in models that consider consanguinity. In particular, we extend a recent diploid analysis of mean coalescence times for lineage pairs within and between individuals in a consanguineous population to derive the variance of coalescence times, studying its dependence on the frequency of consanguinity and the kinship coefficient of consanguineous relationships. We also introduce a separation-of-time-scales approach that treats consanguinity models analogously to mathematically similar phenomena such as partial selfing, using this approach to obtain coalescence-time distributions. This approach shows that the consanguinity model behaves similarly to a standard coalescent, scaling population size by a factor 1 − 3c, where c represents the kinship coefficient of a randomly chosen mating pair. It provides the explanation for an earlier result describing mean coalescence time in the consanguinity model in terms of c. The results extend the potential to make predictions about ROH and IBD in relation to demographic parameters of diploid populations.

Heterosis and genetic distance in rapeseed (Brassica napus L.): use of kinship coefficient

Different agronomic characters have been measured on F1 rapeseeds from inbred lines that are more or less related and on their parents, in Rennes (France). Two different experiments were conducted over a 2-year period. A study of the relationship between heterosis and genetic distance, measured here by a function of kinship coefficient (1–ψ), was carried out in two steps. First, four classes of increasing 1–ψ values were defined and related to heterosis value and F1 performance. The results point out a significant effect of the class, whatever the character and the year. Moreover, the best heterotic hybrids were always obtained with lines unrelated and coming from two different geographic pools. Then, the efficiency of 1–ψ for predicting heterosis or cross values was tested: it varies with year and character. For example, in the first experiment average relationship between lines was high, about 50% of seed yield variation owing to mean parent heterosis was explained with the 1–ψ distance. Key words: heterosis, cross prediction, genetic distance, kinship coefficient, Brassica napus L.