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

The 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 [Formula: see text]-norm regularization (e.g. the LASSO) and is suitable for mono- and oligogenic traits, whereas the second framework regularize with the [Formula: see text]-norm (e.g. ridge regression; RR) and thereby is favourable for polygenic traits. A general framework for mixed inheritance is lacking.

We have developed a proximal operator algorithm based on the recent LAVA regularization method that jointly performs [Formula: see text]- and [Formula: see text]-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.

This 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 .