Adjusting for Spatial Effects in Genomic Prediction
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Adjusting for Spatial Effects in Genomic Prediction Xiaojun Mao, Somak Dutta , Raymond K. W. Wong, and Dan Nettleton This paper investigates the problem of adjusting for spatial effects in genomic prediction. Despite being seldomly considered in genomic prediction, spatial effects often affect phenotypic measurements of plants. We consider a Gaussian random field model with an additive covariance structure that incorporates genotype effects, spatial effects and subpopulation effects. An empirical study shows the existence of spatial effects and heterogeneity across different subpopulation families, while simulations illustrate the improvement in selecting genotypically superior plants by adjusting for spatial effects in genomic prediction. Key Words: Gaussian random field; Genomic prediction; Spatial effects; Subpopulation effects.
1. INTRODUCTION In plant breeding, predicting the genetic value of plant genotypes plays an important role in determining which genotypes to include in subsequent generations. Recently, several powerful statistical methods have been developed that use high-dimensional single-nucleotide polymorphism (SNP) genotypes for genomic prediction. Most of the methods based on mixed linear models (MLM) are quite flexible due to the consideration of fixed and random effects. For instance, population structure (discussed in Pritchard et al 2000) is often accounted for by modeling the fixed effects of principal components (PCs) derived from the SNPs (Price et al. 2006; Reich et al. 2008; McVean 2009). For unified MLM approaches (Yu et al. 2006), SNP data are used to determine a kinship matrix that is assumed to be proportional to the variance of a vector of random effects that accounts for dependencies due to relatedness among individuals. For a more computationally efficient compressed MLM (CMLM) approach (Zhang et al. 2010), data from many individuals are compressed into a
X. Mao, School of Data Science, Fudan University, Shanghai 200433, China. S. Dutta (B) · D. Nettleton, Department of Statistics, Iowa State University, Ames, IA 50011, USA (E-mail: [email protected]). R. K. W. Wong, Department of Statistics, Texas A&M University, College Station, TX 77843, USA. © 2020 International Biometric Society Journal of Agricultural, Biological, and Environmental Statistics https://doi.org/10.1007/s13253-020-00396-1
X. Mao et al.
smaller number of groups, and the interindividual kinship matrix is replaced by a lowerdimensional matrix that characterizes correlations among group random effects induced by genetic similarities among groups. Aside from correlations due to relatedness among individuals or groups, phenotypes measured on plants grown in fields can be spatially correlated (Stroup 2002). Such correlation can arise because plants growing near each other may share a common microenvironment that differs from the microenvironment experienced by plants in other parts of the field. This microenvironmental variation can induce phenotypic similarity among neighboring plants. When such spatial effects e
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