Rank-invariant estimation of inbreeding coefficients

Abstract

The two alleles an individual carries at a locus are identical by descent (ibd) if they have descended from a single ancestral allele in a reference population, and the probability of such identity is the inbreeding coefficient of the individual. Inbreeding coefficients can be predicted from pedigrees with founders constituting the reference population, but estimation from genetic data is not possible without data from the reference population. Most inbreeding estimators that make explicit use of sample allele frequencies as estimates of allele probabilities in the reference population are confounded by average kinships with other individuals. This means that the ranking of those estimates depends on the scope of the study sample and we show the variation in rankings for common estimators applied to different subdivisions of 1000 Genomes data. Allele-sharing estimators of within-population inbreeding relative to average kinship in a study sample, however, do have invariant rankings across all studies including those individuals. They are unbiased with a large number of SNPs. We discuss how allele sharing estimates are the relevant quantities for a range of empirical applications.

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

“…F VR 1 and F VR 2 : Estimators described by VanRaden [ 19 ]. F YA 1 and F YA 2 : Estimator proposed by Yang et al [ 20 ] and modified by Zhang et al [ 34 ]. F LH 1 and F LH 2 : Estimators derived by Li and Horvitz [ 16 ].…”

“… which is a coefficient based on the correlation between uniting gametes [ 20 ], such that homozygous genotypes are weighted by the inverse of their allele frequencies, and it is expected to show lower sampling variance than other estimators [ 36 ]. an analogous estimator to that of Yang et al [ 20 ] ( ) but considering the summation of terms separately in the numerator and denominator, as recommended by Zhang et al [ 34 ]. the metric that was initially proposed by Li and Horvitz [ 16 ], which gives the deviation of the observed frequency of homozygotes from the expected values under Hardy–Weinberg equilibrium when current allele frequencies are considered.…”

“…However, allele frequencies in the base population are usually not available and inferring them is difficult [ 33 ], thus frequencies in the current generation are often used instead. In that case, marker frequency-based measures of inbreeding provide deviations from Hardy–Weinberg proportions or correlations of allele frequencies of homologous genes relative to the current generation of the population rather than estimates of IBD [ 22 ], and the estimates are confounded by the average coancestry of individuals with other individuals in the sample taken for analysis [ 34 ].…”

“…The different measures of molecular inbreeding have been evaluated in multiple studies, both based on empirical data [13,14,24,[34][35][36][37][38][39][40][41][42][43][44], and based on simulated data or theoretical analyses [9,32,34,[45][46][47]. Some empirical studies have used inbreeding estimators based on known [12] or estimated [35] allele frequencies from a predefined base population.…”

Effect of reduced genomic representation on using runs of homozygosity for inbreeding characterization

“…With the advancements in high throughput sequencing technologies it became possible to estimate with sufficient accuracy genomic-based inbreeding coefficients, and several studies have shown molecular estimates to be more accurate than pedigree-based estimates (Alemu et al, 2020; Curik et al, 2014; Kardos et al, 2015; Keller et al, 2011; Wang, 2016). Many different genomic-based inbreeding coefficients have then been proposed, such as F HOM (Chang et al, 2015; Purcell et al, 2007), F AS (Weir & Goudet, 2017), F UNI and F GRM (both described in Yang et al, 2011) but there is still no consensus on which is the most accurate (Alemu et al, 2020; Caballero et al, 2020; Goudet et al, 2018; Nietlisbach et al, 2019; Yengo et al, 2017; Zhang et al, 2022). These estimates quantify average excess SNP homozygosity or correlation between uniting gametes and treat all SNPs independently.…”