Rank-invariant estimation of inbreeding coefficients

Qian S. Zhang,Bruce S. Weir,Jérôme Goudet

doi:10.1038/s41437-021-00471-4

Qian S. Zhang, Bruce S. Weir + Show 1 more

Open Access

https://doi.org/10.1038/s41437-021-00471-4

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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.

Highlights

Allelic dependence at a locus is usually quantified by inbreeding coefficients for individuals or populations, with these measures referring either to correlations of allelic state indicators (Wright, 1922) or to probabilities of identity by descent, ibd, (Malécot, 1948)
We provide more details elsewhere, but we note here that runs of homozygosity (ROH) methods offer a useful alternative to SNP-by-SNP methods even though they cannot completely compensate for lack of information on the ibd reference population
The zero-th generation was made of 50 founders, the first generation had 47 individuals and the second, third, fourth and fifth generations had 58, 56, 57, and 65 individuals respectively. This pedigree was fed to a custom R script to draw gametes from each parent at each reproductive event, allowing for recombination based on a 20 Morgan recombination map with a genetic marker every 0.1 cM, for a total of 20,000 markers

Summary

Introduction

Allelic dependence at a locus is usually quantified by inbreeding coefficients for individuals or populations, with these measures referring either to correlations of allelic state indicators (Wright, 1922) or to probabilities of identity by descent, ibd, (Malécot, 1948). We use ibd and we have advocated allele-sharing estimators ((Weir & Goudet, 2017), WG17 ; (Goudet et al, 2018)) that are unbiased for individual and population inbreeding coefficients relative to average kinships among specified pairs of individuals. There have been many published accounts of inbreeding estimation, including the recent evaluation of several methods by Alemu et al (2021) Among those that refer to allele sharing, Li & Horvitz (1953) discussed an inbreeding estimator based on observed homozygosity, i.e., within-individual sharing of maternal and paternal alleles. They compared observed sharing to the value expected without inbreeding. By not making explicit use of sample allele frequencies, we preserved the ranking of estimates across different samples and this is our central theme here

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