Using the Pareto principle in genome-wide breeding value estimation.

Genome-wide breeding value (GWEBV) estimation methods can be classified based on the prior distribution assumptions of marker effects. Genome-wide BLUP methods assume a normal prior distribution for all markers with a constant variance, and are computationally fast. In Bayesian methods, more flexible prior distributions of SNP effects are applied that allow for very large SNP effects although most are small or even zero, but these prior distributions are often also computationally demanding as they rely on Monte Carlo Markov chain sampling. In this study, we adopted the Pareto principle to weight available marker loci, i.e., we consider that x% of the loci explain (100 - x)% of the total genetic variance. Assuming this principle, it is also possible to define the variances of the prior distribution of the 'big' and 'small' SNP. The relatively few large SNP explain a large proportion of the genetic variance and the majority of the SNP show small effects and explain a minor proportion of the genetic variance. We name this method MixP, where the prior distribution is a mixture of two normal distributions, i.e. one with a big variance and one with a small variance. Simulation results, using a real Norwegian Red cattle pedigree, show that MixP is at least as accurate as the other methods in all studied cases. This method also reduces the hyper-parameters of the prior distribution from 2 (proportion and variance of SNP with big effects) to 1 (proportion of SNP with big effects), assuming the overall genetic variance is known. The mixture of normal distribution prior made it possible to solve the equations iteratively, which greatly reduced computation loads by two orders of magnitude. In the era of marker density reaching million(s) and whole-genome sequence data, MixP provides a computationally feasible Bayesian method of analysis.