Computational strategies for the preconditioned conjugate gradient method applied to ssSNPBLUP, with an application to a multivariate maternal model

Jeremie Vandenplas,Mario P L Calus,Maarten Bosmans,Herwin Eding

doi:10.1186/s12711-020-00543-9

Jeremie Vandenplas, Mario P L Calus + Show 2 more

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https://doi.org/10.1186/s12711-020-00543-9

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Abstract

BackgroundThe single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is one of the single-step evaluations that enable a simultaneous analysis of phenotypic and pedigree information of genotyped and non-genotyped animals with a large number of genotypes. The aim of this study was to develop and illustrate several computational strategies to efficiently solve different ssSNPBLUP systems with a large number of genotypes on current computers.ResultsThe different developed strategies were based on simplified computations of some terms of the preconditioner, and on splitting the coefficient matrix of the different ssSNPBLUP systems into multiple parts to perform its multiplication by a vector more efficiently. Some matrices were computed explicitly and stored in memory (e.g. the inverse of the pedigree relationship matrix), or were stored using a compressed form (e.g. the Plink 1 binary form for the genotype matrix), to permit the use of efficient parallel procedures while limiting the required amount of memory. The developed strategies were tested on a bivariate genetic evaluation for livability of calves for the Netherlands and the Flemish region in Belgium. There were 29,885,286 animals in the pedigree, 25,184,654 calf records, and 131,189 genotyped animals. The ssSNPBLUP system required around 18 GB Random Access Memory and 12 h to be solved with the most performing implementation.ConclusionsBased on our proposed approaches and results, we showed that ssSNPBLUP provides a feasible approach in terms of memory and time requirements to estimate genomic breeding values using current computers.

Highlights

The single-step single nucleotide polymorphism best linear unbiased prediction is one of the single-step evaluations that enable a simultaneous analysis of phenotypic and pedigree information of genotyped and non-genotyped animals with a large number of genotypes
In Vandenplas et al [10], we proposed a preconditioned conjugate gradient (PCG) method with a second-level preconditioner that is easy to implement, and that substantially improves the convergence issues associated with two ssSNPBLUP systems
The two ssSNPBLUP systems are equivalent and both systems of equations can be summarized as: Cixi = bi, where i refers to the linear system proposed by Mantysaari and Stranden [11] (i = MS) or to the linear system proposed by Liu et al [9] (i = Liu), Ci is a symmetricdefinite coefficient matrix, xi is the vector of solutions, and bi is the right-hand side of the linear system

Summary

Introduction

The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is one of the single-step evaluations that enable a simultaneous analysis of phenotypic and pedigree information of genotyped and non-genotyped animals with a large number of genotypes. Equivalent models that directly estimate SNP effects and that do not rely on G , hereafter called ssSNPBLUP, were proposed [7,8,9] These models have not yet been implemented and tested on a large scale due to several reasons, such as the lack of breeding value estimation software that is flexible enough to perform ssSNPBLUP, more complicated modeling compared to ssGBLUP, and convergence issues [1]. The objective of this paper is to present several computational strategies that improve the efficiency of solving two different ssSNPBLUP systems efficiently with a PCG method. These strategies aim at taking advantage of existing shared-memory parallel libraries while limiting the amount of required random access memory β

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