title: Incorporating Genetic Heterogeneity in Whole-Genome Regressions Using Interactions.
abstract: Naturally and artificially selected populations usually exhibit some degree of stratification. In Genome-Wide Association Studies and in Whole-Genome Regressions (WGR) analyses, population stratification has been either ignored or dealt with as a potential confounder. However, systematic differences in allele frequency and in patterns of linkage disequilibrium can induce sub-population-specific effects. From this perspective, structure acts as an effect modifier rather than as a confounder. In this article, we extend WGR models commonly used in plant and animal breeding to allow for sub-population-specific effects. This is achieved by decomposing marker effects into main effects and interaction components that describe group-specific deviations. The model can be used both with variable selection and shrinkage methods and can be implemented using existing software for genomic selection. Using a wheat and a pig breeding data set, we compare parameter estimates and the prediction accuracy of the interaction WGR model with WGR analysis ignoring population stratification (across-group analysis) and with a stratified (i.e., within-sub-population) WGR analysis. The interaction model renders trait-specific estimates of the average correlation of effects between sub-populations; we find that such correlation not only depends on the extent of genetic differentiation in allele frequencies between groups but also varies among traits. The evaluation of prediction accuracy shows a modest superiority of the interaction model relative to the other two approaches. This superiority is the result of better stability in performance of the interaction models across data sets and traits; indeed, in almost all cases, the interaction model was either the best performing model or it performed close to the best performing model.
  
  
  BACKGROUND
  Supplementary materials for this article are available at 10.1007/s13253-015-0222-5.
authors.affiliation: Department of Epidemiology & Biostatistics, Michigan State University, 909 Fee Road, Room B601, East Lansing, MI 48824 USA ; Department of Statistics & Probability, Michigan State University, 619 Red Cedar Rd., East Lansing, MI 48824 USA.
authors.forename: Gustavo
authors.initials: G
authors.lastname: de Los Campos
authors.affiliation: University of Alabama at Birmingham, Ryals Public Health Bldg. 443, Birmingham, AL 35294 USA.
authors.forename: Yogasudha
authors.initials: Y
authors.lastname: Veturi
authors.affiliation: Department of Epidemiology & Biostatistics, Michigan State University, 909 Fee Road, Room B601, East Lansing, MI 48824 USA.
authors.forename: Ana I
authors.initials: AI
authors.lastname: Vazquez
authors.affiliation: Department of Plant Breeding, Technische Universität München, Liesel-Beckmann-Str. 2, 85354 Freising, Germany.
authors.forename: Christina
authors.initials: C
authors.lastname: Lehermeier
authors.affiliation: Colegio de Postgraduados, Km. 36.5, Carretera Mexico, Montecillo, 56230 Texcoco, Estado de México Mexico.
authors.forename: Paulino
authors.initials: P
authors.lastname: Pérez-Rodríguez
keywords: Bayesian; Genomic prediction; Genomic selection; Multi-breed analysis; Population structure