How should we compare different genomic estimates of the strength of inbreeding depression?

Yengo et al. (1) evaluate the ability of genomic measures of inbreeding to quantify inbreeding depression. The authors conclude that a measure of inbreeding based on “runs of homozygosity” (F_ROH) had low power and upwardly biased estimates of the amount of inbreeding depression compared with F_HOM (a measure of homozygosity relative to Hardy–Weinberg proportions) and F_UNI (correlation between uniting gametes; similar to F_HOM but with strong weight given to homozygous rare alleles). However, differences among these measures of inbreeding, and how their simulations were parameterized, invalidate these conclusions.

Yengo et al. (1) assume that regressions of phenotype (y) against F_ROH are comparable to regressions of y against F_UNI or F_HOM. This is incorrect because of the different properties of these measures of inbreeding. F_ROH ranges from 0 to 1 (like the pedigree inbreeding coefficient F_P), and estimates the fraction of the genome in ROH, where identical-by-descent chromosome copies coalesce in a “recent” ancestor. F_ROH can be interpreted as a probability of identity-by-descent and used to estimate lethal equivalents (2). F_UNI and F_HOM include negative values and frequently have substantially higher variance than F_P and F_ROH (3–6).

Steeper slopes for F_ROH are expected, and incorrectly interpreted as upward bias, when F_ROH has a lower variance than F_UNI (7). For example, when the variance of F_UNI is twice the variance of F_ROH, regressions of y vs. F_ROH are expected to be 1.41 times steeper than regressions of y vs. F_UNI, assuming equal correlations of y with F_ROH and F_UNI. Measures of inbreeding with different variances should first be standardized (z-transformed) to equitably compare estimates of inbreeding depression by regression (7).

y was simulated as a function of F_QTL (1), which measures inbreeding relative to Hardy–Weinberg proportions at causal loci. F_QTL is thus expected to have a similar variance to F_UNI and F_HOM, depending on the simulated dominance effects. Simulating y as a function of F_QTL means that tests of inbreeding depression based on F_UNI and F_HOM are expected a priori to have lower bias and higher power than F_ROH when analyzing the simulated data.

Yengo et al. (1) detected inbreeding depression for more traits in humans with F_UNI than with F_ROH. This could be because F_UNI is more powerful than F_ROH, or because F_UNI captured variation in inbreeding due to distant ancestors, while F_ROH measured inbreeding due only to recent ancestors by excluding short ROH. F_ROH can incorporate short ROH arising from distant ancestors when millions of SNPs are analyzed (8, 9). Doing so would mean that F_ROH and F_UNI estimate similar parameters and would make for a more equitable comparison of the performance of these measures of inbreeding.

Comparisons of inbreeding metrics with different variances should focus on correlations or regressions of y versus standardized inbreeding coefficients. Correlation is a useful alternative measure of the strength of inbreeding depression, and is unaffected by differences in variance among measures of inbreeding. F_ROH was previously shown to be more strongly correlated with the homozygous mutation load (4), and F_ROH thus appears to be preferable for studies of inbreeding depression.