Here we aim to overcome these limitations, using two novel approaches. So far, penalized selection indices have not been applied in a genomic prediction setting, and require plot-level data in order to reliably estimate genetic correlations. An alternative direction is to extend the classical selection indices using penalized regression. This approach is however infeasible when secondary traits are not measured on the test set, and cannot distinguish between genetic and non-genetic correlations. In this case, secondary traits are usually incorporated through additional relatedness matrices. Here we focus on the more challenging situation with a large number of secondary traits, which is increasingly common since the arrival of high-throughput phenotyping. With only a small number of secondary traits, this is known to be the case, given sufficiently high heritabilities and genetic correlations. This raises the important question whether these additional or “secondary” traits can be used to improve genomic prediction for the target trait. Given the current advances of high-throughput phenotyping and sequencing technologies, it is increasingly common to observe a large number of traits, in addition to the target trait of interest. In the past decades, genomic prediction has had a large impact on plant breeding.
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