Comparing heritability estimators under alternative structures of linkage disequilibrium

The single nucleotide polymorphism heritability of a trait is the proportion of its variance explained by the additive effects of the genome-wide single nucleotide polymorphisms. The existing approaches to estimate single nucleotide polymorphism heritability can be broadly classified into 2 categories. One set of approaches models the single nucleotide polymorphism effects as fixed effects and the other treats the single nucleotide polymorphism effects as random effects. These methods make certain assumptions about the dependency among individuals (familial relationship) as well as the dependency among markers (linkage disequilibrium) to provide consistent estimates of single nucleotide polymorphism heritability as the number of individuals increases. While various approaches have been proposed to account for such dependencies, it remains unclear which estimates reported in the literature are more robust against various model misspecifications. Here, we investigate the impact of different structures of linkage disequilibrium and familial relatedness on heritability estimation. We show that the performance of different methods for heritability estimation depends heavily on the structure of the underlying pattern of linkage disequilibrium and the degree of relatedness among sampled individuals. Moreover, we establish the equivalence between the 2 method-of-moments estimators, one using a fixed-single nucleotide polymorphism-effects approach, and another using a random-single nucleotide polymorphism-effects approach.