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.

Fig. 1. Allele sharing estimates for 283 non-founders in simulated pedigree.

Left: Pedigree f vs Pedigree F; Center: Gold f vs Pedigree f; Right: Pedigree coancestry vs Pedigree f.

Fig. 2. Values of ROH estimates of F and allele-sharing estimates of f for 283 non-founders in simulated pedigree.

Left: ${\widehat{F}}_{\mathrm{ROH}}$ vs F_Gold; Center: ${\widehat{f}}_{\mathrm{AS}}$ vs ${\widehat{F}}_{\mathrm{ROH}}$; Right: ${\widehat{f}}_{\mathrm{AS}}$ vs f_Gold.

Fig. 3. Values of UNI and STD estimates for 283 non-founders in simulated pedigree.

Top left: ${\widehat{f}}_{\mathrm{UNI}}^w$ vs $f_{{\mathrm{Gold}}_j}$; Top right: ${\widehat{f}}_{\mathrm{STD}}^w$ vs $f_{{\mathrm{Gold}}_j}$; Bottom left: ${\widehat{f}}_{\mathrm{UNI}}^u$ vs $f_{{\mathrm{Gold}}_j}$; Bottom right: ${\widehat{f}}_{\mathrm{STD}}^u$ vs $f_{{\mathrm{Gold}}_j}$.

Fig. 4. Individual inbreeding coefficient estimates for 1000 Genomes data.

Left panel: ${\widehat{f}}_{\mathrm{AS}}$; Right panel: ${\widehat{f}}_{\mathrm{UNI}}^u$. Green: Population as reference; Blue: Continental group as reference; Red: World as reference. Populations, left to right: (AFR) ACB, ASW, ESN, GWD, LWK, MSL, YRI; (AMR) CLM, PEL, PUR, MXL; (EAS) CHB, CHS, CDX, JPT, KHV; (EUR) CEU, FIN, GBR, IBS, TSI; (SAS) BEB, GIH, ITU, PJL, STU.

Fig. 5. Estimates of within-population individual-specific average kinships vs estimates of within-population individual-specific inbreeding coefficients for 1000 Genomes data.

Y-axis: ${\widehat{\psi }}_{{\mathrm{AS}}_j}$; X-axis: ${\widehat{f}}_{{\mathrm{AS}}_j}$. Top: Population as reference set; Center: Continent as reference set; Bottom: World as reference set. Left: All populations; Right: Excluding AMR populations in top and center rows. Excluding AMR and AFR in bottom row. Gold: AFR (not ACB or ASW); Orange: AFR (ACB and ASW); Red: AMR; Purple: SAS; Blue: EUR; Green: EAS.

Fig. 6. ROH/PLINK estimates vs SNP by SNP estimates for 1000 Genomes data, with the World as a reference set.

Left: ${\widehat{F}}_{\mathrm{ROH}}$ vs ${\widehat{f}}_{\mathrm{AS}}$; Right: F_ROH vs ${\widehat{f}}_{\mathrm{UNI}}^u$. Solid line X = Y. Gold: AFR (not ACB or ASW); Orange: AFR (ACB and ASW); Red: AMR; Purple: SAS; Blue: EUR; Green: EAS.