Improvement of Predictive Ability by Uniform Coverage of the Target Genetic Space

Abstract

Genome-enabled prediction provides breeders with the means to increase the number of genotypes that can be evaluated for selection. One of the major challenges in genome-enabled prediction is how to construct a training set of genotypes from a calibration set that represents the target population of genotypes, where the calibration set is composed of a training and validation set. A random sampling protocol of genotypes from the calibration set will lead to low quality coverage of the total genetic space by the training set when the calibration set contains population structure. As a consequence, predictive ability will be affected negatively, because some parts of the genotypic diversity in the target population will be under-represented in the training set, whereas other parts will be over-represented. Therefore, we propose a training set construction method that uniformly samples the genetic space spanned by the target population of genotypes, thereby increasing predictive ability. To evaluate our method, we constructed training sets alongside with the identification of corresponding genomic prediction models for four genotype panels that differed in the amount of population structure they contained (maize Flint, maize Dent, wheat, and rice). Training sets were constructed using uniform sampling, stratified-uniform sampling, stratified sampling and random sampling. We compared these methods with a method that maximizes the generalized coefficient of determination (CD). Several training set sizes were considered. We investigated four genomic prediction models: multi-locus QTL models, GBLUP models, combinations of QTL and GBLUPs, and Reproducing Kernel Hilbert Space (RKHS) models. For the maize and wheat panels, construction of the training set under uniform sampling led to a larger predictive ability than under stratified and random sampling. The results of our methods were similar to those of the CD method. For the rice panel, all training set construction methods led to similar predictive ability, a reflection of the very strong population structure in this panel.

Modelling of genotype by environment interaction and prediction of complex traits across multiple environments as a synthesis of crop growth modelling, genetics and statistics

“…These 199 genotypes are a sample of the Australian TPG constructed to represent the range in flowering time variation for Australian genotypes (Australian Wheat Flowering time Association Mapping panel, AWFAM). Most of the AWFAM genotypes have been used in previous research about phenotype prediction in Australian environments (Zheng et al, 2013;Bustos-Korts et al, 2016a). To characterise AWFAM population structure, a relationship matrix was calculated from the SNPs following…”

“…Prediction accuracy was calculated as the Pearson correlation coefficient between the APSIM phenotypes (genotypic value) and the predicted phenotypes (Meuwissen et al, 2001), considering a training set of 130 genotypes and a validation set of 69 genotypes. 50 training sets were constructed with the uniform sampling method described by (Jansen & van Hintum, 2007;Bustos-Korts et al, 2016a). We calculated mean predictive ability and standard error across 50 training set realizations.…”

“…Those estimates are used to predict the phenotypes of the collection of genotypes for which no phenotypic information is available, the so called test set (Meuwissen, 2007). For predictions to be accurate, training and test sets must belong to the same target population of genotypes (TPG) (Albrecht et al, 2014;Bustos-Korts et al, 2016a). The TPG contains all possible genotypes that could be considered as selection candidates Schulz-Streeck et al, 2012;Albrecht et al, 2014).…”

Optimization of selective phenotyping and population design for genomic prediction

“…Mixed model based criteria [19] were proposed to optimize the choice of individuals to phenotype using as an input the expected trait heritability and markers or pedigree data [20]- [22]. Such optimization is a part of a broader class of so called "model-based design" also used to optimize field trials design [23]- [25].…”

“…[21] combined the approach of [20] with stratified sampling to improve the results in structured populations. [22] used an uniform sampling approach for the same objective and compared those methods along with a few simple others. Contrary to our results, differences between methods were smaller at small training set sizes than at larger training set sizes.…”