Efficient Estimation of Realized Kinship from Single Nucleotide Polymorphism Genotypes

Abstract

Realized kinship is a key statistic in analyses of genetic data involving relatedness of individuals or structure of populations. There are several estimators of kinship that make use of dense SNP genotypes. We introduce a class of estimators, of which some existing estimators are special cases. Within this class, we derive properties of the estimators and determine an optimal estimator. Additionally, we introduce an alternative marker weighting that takes allelic associations [linkage disequilibrium (LD)] into account, and apply this weighting to several estimators. In a simulation study, we show that improved estimators are obtained (1) by optimal weighting of markers, (2) by taking physical contiguity of genome into account, and (3) by weighting on the basis of LD.

New kinship andFSTestimates reveal higher levels of differentiation in the global human population

“…Kinship matrices are crucial for accurate inference under population structure in many important biomedical applications, including genome-wide association studies [6][7][8][9][10][11][12][13] and heritability estimation [14,15]. However, the most commonly-used standard kinship estimator [9,10,[13][14][15][16][17][18][19] is accurate only in the absence of population structure [2,20]. Likewise, current F ST estimators assume that individuals are partitioned into statistically-independent subpopulations [4,5,[21][22][23], which does not hold for human and other complex population structures.…”

“…ϕ jk is the mean kinship of individual j with all others andφ = 1 n 2 n j =1 n k =1 ϕ j k is the overall mean kinship in the data [2]. This estimator is widely-used in approaches for structured populations, including genetic association studies and heritability estimation [9,10,[13][14][15][16][17][18][19]. The original F ST measures inbreeding in a subpopulation relative to an ancestral population [4], excluding local inbreeding if present [5].…”

A unified characterization of population structure and relatedness

“…The new estimators we display in Equation 6 differ from the standard estimators (e.g., Ritland 1996;Yang et al 2011;Wang et al 2017). For biallelic loci these estimators arê…”

“…A more extensive discussion was given in the Appendix of WC84 for population structure, and by Ritland (1996) for inbreeding and relatedness. More recently, Ochoa and Storey (2016b) discussed weights for their estimates, and Wang et al (2017) discuss weighting in the context of known allele frequencies. Regardless of weighting scheme, the use of several loci allows us to use bootstrapping over loci (Weir 1996) to generate empirical sampling distributions for our estimates.…”

Correlations between relatives: From Mendelian theory to complete genome sequence

“…In an infinite idealized population, the expected value of is , so any weights in provide an unbiased estimate of relatedness relative to the current population. While the most usual form has for all , other forms have been used for robustness against extreme ‐values (van Raden, ), for greater statistical efficiency, and/or to accommodate LD (Speed, Hemani, Johnson, & Balding, ; Wang, Sverdlov, & Thompson, ). Methods to estimate location‐specific IBD probabilities between individuals from population data have also been established (Brown, Glazner, Zheng, & Thompson, ).…”