Graph-based data selection for the construction

31 Efficient genomic selection in animals or crops requires the accurate prediction of 32 the agronomic performance of individuals from their high-density molecular marker 33 profiles. Using a training data set that contains the genotypic and phenotypic informa34 tion of a large number of individuals, each marker or marker allele is associated with 35 an estimated effect on the trait under study. These estimated marker effects are subse36 quently used for making predictions on individuals for which no phenotypic records are 37 available. As most plant and animal breeding programs are currently still phenotype38 driven, the continuously expanding collection of phenotypic records can only be used 39 to construct a genomic prediction model if a dense molecular marker fingerprint is 40 available for each phenotyped individual. However, as the genotyping budget is gen41 erally limited, the genomic prediction model can only be constructed using a subset of 42 the tested individuals and possibly a genome-covering subset of the molecular mark43 ers. In this paper, we demonstrate how an optimal selection of individuals can be made 44 with respect to the quality of their available phenotypic data. We also demonstrate how 45 the total number of molecular markers can be reduced while a maximum genome cov46 erage is ensured. The third selection problem we tackle is specific to the construction 47 of a genomic prediction model for a hybrid breeding program where only molecular 48 marker fingerprints of the homozygous parents are available. We show how to identify 49 the set of parental inbred lines of a predefined size which has produced the highest 50 number of progeny. These three selection approaches are put into practice in a simu51 lation study where we demonstrate how the trade-off between sample size and sample 52 quality affects the prediction accuracy of genomic prediction models for hybrid maize. 53