Figure 1

Conceptualization of the causality in inbreeding and heterozygosity–fitness correlations/regressions. Arrowheads represent the causal direction (see also Szulkin et al., 2010). We are generally interested in estimating GWIBD because it is most directly related to the homozygous mutational load and inbreeding depression. The heterogeneous distribution of recessive deleterious mutations, the environment and other genetic factors like epistatic interactions are introducing noise into that relation. Mating patterns as represented by pedigrees are one way to quantify GWIBD (Pedigree F), but Mendelian segregation is adding noise to this estimate of GWIBD. Background inbreeding resulting from relatedness between pedigree founders introduces both random noise and bias into the relationship between GWIBD and Pedigree F. If Background F is absent and the relation between fitness and GWIBD is linear, both Pedigree F and GWIBD are error-free predictors in fitness–inbreeding regressions and consequently the regression slopes are unbiased. Berkson (1950) explains this in terms of a ‘controlled’ experiment, in which case both an underlying variable measured accurately (GWIBD) and its expected value (Pedigree F) give unbiased linear regression slopes (see also Muff et al., 2015). Frequently, molecular markers are used as predictors of GWIBD. Here, the direction of causality is reversed, because GWIBD causes Marker IBD that in turn affects Marker IBS. Both dependencies are affected by noise components that will introduce random error in the predictors (Marker IBD or Marker IBS) used in heterozygosity–fitness regressions. Consequently, the regression slopes will be biased downward. Colors and dashed lines represent the different estimates depicted in Figure 4 and Supplementary Figures S6 and S7.