Evaluating the role of inbreeding depression in heterozygosity-fitness correlations: how useful are tests for identity disequilibrium?

Heterozygosity-fitness correlations (HFCs) have been observed for several decades, but their causes are often elusive. Tests for identity disequilibrium (ID, correlated heterozygosity between loci) are commonly used to determine if inbreeding depression is a possible cause of HFCs. We used computer simulations to determine how often ID is detected when HFCs are caused by inbreeding depression. We also used ID in conjunction with HFCs to estimate the proportion of variation (r(2)) in fitness explained by the individual inbreeding coefficient (F). ID was not detected in a large proportion of populations with statistically significant HFCs (sample size = 120 individuals) unless the variance of F was high (σ(2)(F) ≥ 0.005) or many loci were used (100 microsatellites or 1000 SNPs). For example, with 25 microsatellites, ID was not detected in 49% of populations when HFCs were caused by six lethal equivalents and σ(2)(F) was typical of vertebrate populations (σ(2)(F) ≈ 0.002). Estimates of r(2) between survival and F based on ID and HFCs were imprecise unless ID was strong and highly statistically significant (P ≈ 0.01). These results suggest that failing to detect ID in HFC studies should not be taken as evidence that inbreeding depression is absent. The number of markers necessary to simultaneously detect HFC and ID depends strongly on σ(2)(F). Thus the mating system and demography of populations, which influence σ(2) (F), should be considered when designing HFC studies. ID should be used in conjunction with HFCs to estimate the correlation between fitness and F, because HFCs alone reveal little about the strength of inbreeding depression.