Robust Genomic Prediction and Heritability Estimation using Density Power Divergence

Abstract

This manuscript delves into the intersection of genomics and phenotypic prediction, focusing on the statistical innovation required to navigate the complexities introduced by noisy covariates and confounders. The primary emphasis is on the development of advanced robust statistical models tailored for genomic prediction from single nucleotide polymorphism data in plant and animal breeding and multi-field trials. The manuscript highlights the significance of incorporating all estimated effects of marker loci into the statistical framework and aiming to reduce the high dimensionality of data while preserving critical information. This paper introduces a new robust statistical framework for genomic prediction, employing one-stage and two-stage linear mixed model analyses along with utilizing the popular robust minimum density power divergence estimator (MDPDE) to estimate genetic effects on phenotypic traits. The study illustrates the superior performance of the proposed MDPDE-based genomic prediction and associated heritability estimation procedures over existing competitors through extensive empirical experiments on artificial datasets and application to a real-life maize breeding dataset. The results showcase the robustness and accuracy of the proposed MDPDE-based approaches, especially in the presence of data contamination, emphasizing their potential applications in improving breeding programs and advancing genomic prediction of phenotyping traits.

• University of Maryland Baltimore County, USA [upamap1@umbc.edu]

• Indian Statistical Institute, Kolkata, India

• Indian Statistical Institute, Kolkata, India [https://orcid.org/0000-0001-8034-6877]

• Indian Statistical Institute, Kolkata, India [abhikghosh@isical.ac.in]

Keywords: Genomic Prediction, Field Trials, Robust Estimation, Minimum Density Power Divergence Estimator, Linear Mixed Models.

1 Tables, and Equations

Table 1: Prediction accuracy measures obtained from different existing methods and proposed method with different tunning parameters under the one-stage approach with artificial datasets (test data).

Methods	Pure Data		Random Contamination		Block Contamination
	$\widehat{\rho }$	MAD	$\widehat{\rho }$	MAD	$\widehat{\rho }$	MAD
RMLA	0.532	23.84	0.270	18.38	0.322	11.12
RMLV	0.587	16.77	0.387	16.69	0.470	18.38
Rob-RMLA	0.540	25.10	0.343	17.50	0.520	13.29
Rob-RMLV	0.712	7.23	0.430	8.18	0.550	6.48
Proposed MDPDE based approach
$\alpha =0.1$	0.667	6.02	0.620	7.34	0.667	6.34
$\alpha =0.3$	0.745	6.30	0.650	7.37	0.645	6.37
$\alpha =0.5$	0.737	6.67	0.537	6.67	0.537	5.67
$\alpha =0.7$	0.710	5.37	0.630	6.37	0.210	5.37
$\alpha =1$	0.823	4.37	0.670	5.30	0.440	5.13

Table 2: Prediction accuracy measures obtained from different methods under the two-stage approach with artificial datasets (test data).

Methods	Pure Data		Random Contamination		Block Contamination
	$\widehat{\rho }$	MAD	$\widehat{\rho }$	MAD	$\widehat{\rho }$	MAD
Rob1	0.754	4.10	0.740	5.5	0.710	5.29
Rob2	0.793	4.23	0.730	4.18	0.740	4.48
Proposed MDPDE based approach
$\alpha =0.1$	0.820	4.02	0.760	4.14	0.747	4.34
$\alpha =0.3$	0.845	4.20	0.750	3.67	0.742	4.37
$\alpha =0.5$	0.837	3.67	0.737	3.39	0.733	4.67
$\alpha =0.7$	0.810	2.37	0.820	3.08	0.758	3.37
$\alpha =1$	0.860	2.37	0.832	2.93	0.800	3.34

Here, $\widehat{\rho }$ is the Pearsonian corelation coefficient and MAD is the median absolute deviation, which we used as a precision measure.

2 Data analysis

In addition, there is a real world data analysis on the breeding data set of life collected by the International Center for the Improvement of Maize and Wheat (CIMMYT). The data contains 300 tropical maize lines in 10 blocks and the genotyping was conducted using 1135 SNP markers and the target phenotypic trait was grain yield assessed under severe drought stress and well-watered conditions.