On the approximation of interaction effect models by Hadamard powers of the additive genomic relationship.

Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate the impact of this decreasing quality of approximation of the summands on the approximation of the weighted sum. Our results indicate that these approximations remain on a reliable level, but their quality reduces when the weights of interactions of higher degrees do not decrease quickly.