Using the Pareto principle in genome-wide breeding value estimation

Abstract

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.

Whole-Genome Regression and Prediction Methods Applied to Plant and Animal Breeding

“…Another possibility is to link the proportion of effects coming from the “small-variance” component with the proportion of variance accounted for. For instance, following Yu and Meuwissen (2011), one could assume that $\tilde{\pi }\%$ of the markers account for $(100-\tilde{\pi })\%$ of genetic variance. The so-called Pareto principle represents a specific case of the more general principle with $\tilde{\pi }=20$.…”

“…The abbreviations used for the methods are given in Table 2. The following references were used: (Meuwissen et al 2001; Habier et al 2007; Piyasatian et al 2007; González-Recio et al 2008; Lee et al 2008; Bennewitz et al 2009; de los Campos et al 2009; Gonzalez-Recio et al 2009; Hayes et al 2009a,b; Lorenzana and Bernardo 2009; Luan et al 2009; Lund et al 2009; Meuwissen 2009; Meuwissen et al 2009; Moser et al 2009; Solberg et al 2009; Usai et al 2009; Verbyla et al 2009; Zhong et al 2009; Andreescu et al 2010; Bastiaansen et al 2010; Coster et al 2010; Crossa et al 2010; Daetwyler et al 2010a,b; de los Campos et al 2010a,b; Gonzalez-Recio et al 2010; Gredler et al 2010; Guo et al 2010; Habier et al 2010; Konstantinov and Hayes 2010; Meuwissen and Goddard 2010; Mrode et al 2010; Pérez et al 2010; Shepherd et al 2010; Zhang et al 2010; Calus and Veerkamp 2011; Clark et al 2011; Croiseau et al 2011; de Roos et al 2011; Gonzalez-Recio and Forni 2011; Habier et al 2011; Heffner et al 2011; Iwata and Jannink 2011; Legarra et al 2011; Long et al 2011a,b; Makowsky et al 2011; Mujibi et al 2011; Ober et al 2011; Ostersen et al 2011; Pryce et al 2011; Pszczola et al 2011; Wiggans et al 2011; Wittenburg et al 2011; Wolc et al 2011a,b; Yu and Meuwissen 2011; Bastiaansen et al 2012; Heslot et al 2012). …”

Prioritizing animals for dense genotyping in order to impute missing genotypes of sparsely genotyped animals

“…When N e increases, the effective number of segregating segments increases [ 19 ] and the accuracy of GEBV is expected to decrease, which was observed. The genetic architecture of the design used in this study had relatively few QTL, so MixP was expected to have an advantage over GBLUP in terms of accuracy [ 17 ]. When using only loci with a MAF ≥ 0.05 instead of all loci, the difference in accuracy between MixP and GBLUP decreased; since the QTL were selected independently of their MAF, increasing the MAF threshold excluded more QTL and increased the reliance on LD with marker loci.…”

“…Two genomic selection methods were used for GEBV estimation, MixP [ 17 ] and GBLUP (Genomic best linear unbiased prediction) [ 13 ]. GBLUP is reported to be robust in real data analyses, but it benefits less from an increase in the marker density and is indifferent to QTL architecture.…”

Optimization of a Saccharomyces cerevisiae fermentation process for production of a therapeutic recombinant protein using a multivariate bayesian approach

“…The controllable parameters showing impact on the CQA(s) were considered as CPPs. The Pareto principle (80:20 tool)19, 20 was applied to assign the RPN scores; scores ≥ 7 were determined to be high risk. Only the CPPs for the production bioreactor were optimized and discussed in this study.…”