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Training set construction is an important prerequisite to Genomic Prediction (GP), and while this has been studied in diploids, polyploids have not received the same attention. Polyploidy is a common feature in many crop plants, like for example banana and blueberry, but also potato which is the third most important crop in the world in terms of food consumption, after rice and wheat. The aim of this study was to investigate the impact of different training set construction methods using a publicly available diversity panel of tetraploid potatoes. Four methods of training set construction were compared: simple random sampling, stratified random sampling, genetic distance sampling and sampling based on the coefficient of determination (CDmean). For stratified random sampling, population structure analyses were carried out in order to define sub-populations, but since sub-populations accounted for only 16.6% of genetic variation, there were negligible differences between stratified and simple random sampling. For genetic distance sampling, four genetic distance measures were compared and though they performed similarly, Euclidean distance was the most consistent. In the majority of cases the CDmean method was the best sampling method, and compared to simple random sampling gave improvements of 4–14% in cross-validation scenarios, and 2–8% in scenarios with an independent test set, while genetic distance sampling gave improvements of 5.5–10.5% and 0.4–4.5%. No interaction was found between sampling method and the statistical model for the traits analyzed.

Use of genomic prediction (GP) in tetraploid is becoming more common. Therefore, we think it is the right time for a comparison of GP models for tetraploid potato. GP models were compared that contrasted shrinkage with variable selection, parametric vs. non-parametric models and different ways of accounting for non-additive genetic effects. As a complement to GP, association studies were carried out in an attempt to understand the differences in prediction accuracy. We compared our GP models on a data set consisting of 147 cultivars, representing worldwide diversity, with over 39 k GBS markers and measurements on four tuber traits collected in six trials at three locations during 2 years. GP accuracies ranged from 0.32 for tuber count to 0.77 for dry matter content. For all traits, differences between GP models that utilised shrinkage penalties and those that performed variable selection were negligible. This was surprising for dry matter, as only a few additive markers explained over 50% of phenotypic variation. Accuracy for tuber count increased from 0.35 to 0.41, when dominance was included in the model. This result is supported by Genome Wide Association Study (GWAS) that found additive and dominance effects accounted for 37% of phenotypic variation, while significant additive effects alone accounted for 14%. For tuber weight, the Reproducing Kernel Hilbert Space (RKHS) model gave a larger improvement in prediction accuracy than explicitly modelling epistatic effects. This is an indication that capturing the between locus epistatic effects of tuber weight can be done more effectively using the semi-parametric RKHS model. Our results show good opportunities for GP in 4x potato.