A proximal LAVA method for genome-wide association and prediction of traits with mixed inheritance patterns

Patrik Waldmann

doi:10.1186/s12859-021-04436-6

Abstract

BackgroundThe genetic basis of phenotypic traits is highly variable and usually divided into mono-, oligo- and polygenic inheritance classes. Relatively few traits are known to be monogenic or oligogeneic. The majority of traits are considered to have a polygenic background. To what extent there are mixtures between these classes is unknown. The rapid advancement of genomic techniques makes it possible to directly map large amounts of genomic markers (GWAS) and predict unknown phenotypes (GWP). Most of the multi-marker methods for GWAS and GWP falls into one of two regularization frameworks. The first framework is based on ell _1-norm regularization (e.g. the LASSO) and is suitable for mono- and oligogenic traits, whereas the second framework regularize with the ell _2-norm (e.g. ridge regression; RR) and thereby is favourable for polygenic traits. A general framework for mixed inheritance is lacking.ResultsWe have developed a proximal operator algorithm based on the recent LAVA regularization method that jointly performs ell _1- and ell _2-norm regularization. The algorithm is built on the alternating direction method of multipliers and proximal translation mapping (LAVA ADMM). When evaluated on the simulated QTLMAS2010 data, it is shown that the LAVA ADMM together with Bayesian optimization of the regularization parameters provides an efficient approach with lower test prediction mean-squared-error (65.89) than the LASSO (66.11), Ridge regression (83.41) and Elastic net (66.11). For the real pig data the test MSE of the LAVA ADMM is 0.850 compared to the LASSO, RR and EN with 0.875, 0.853 and 0.853, respectively.ConclusionsThis study presents the LAVA ADMM that is capable of joint modelling of monogenic major genetic effects and polygenic minor genetic effects which can be used for both genome-wide assoiciation and prediction purposes. The statistical evaluations based on both simulated and real pig data set shows that the LAVA ADMM has better prediction properies than the LASSO, RR and EN. Julia code for the LAVA ADMM is available at: https://github.com/patwa67/LAVAADMM.

Highlights

The genetic basis of phenotypic traits is highly variable and usually divided into mono, oligo- and polygenic inheritance classes
Simulated data After some initial runs with each of the regularizers, it was found that Bayesian optimization (BO) converged faster for the methods with one regularization parameter (i.e. RR and LASSO) when using the upper confidence bound (UCB) acquisition function, and for the methods with two regularization parameters (i.e. EN and LAVA) the mutual information (MI) acquisition function worked better
BO was run for 250 iterations for all methods with 4 Gaussian process (GP) function evaluations per iteration

Summary

Introduction

The genetic basis of phenotypic traits is highly variable and usually divided into mono-, oligo- and polygenic inheritance classes. The rapid advancement of genomic techniques makes it possible to directly map large amounts of genomic markers (GWAS) and predict unknown phenotypes (GWP). A mutation in a single gene can cause a disease, or another phenotypic alteration, that is inherited according to Mendel’s principles. Those traits are referred to as monogenic [1]. Quantitative genetics is generally defined as the study of characters that are influenced by a large number of genes where the effect of each gene is considered to be relatively small [5]. Oligogenic inheritance refers to an intermediate between monogenic and polygenic inheritance where a trait that is considered to be determined by a small number of genes. The advent of highthroughput sequencing techniques makes it possible to assess the direct effects of markers that cover large parts of the genome [9]

Objectives

Methods

Results

Discussion

Conclusion