Data reconciliation in multi‐trait experiments with kinship ordination

Abstract A central aim in biology is understanding the heritability of traits and how trait interactions contribute to success in diverse environments. Experiments that record multiple traits from individuals of known pedigree or genetic relatedness in distinct environments are key to addressing this aim. Mixed modelling approaches have been proposed for analysing such multivariate trait data. The parameter space of these mixed models grows quadratically with the number of traits and environments considered, which increases computational demand and the risk of overfitting. Existing approaches can also be challenging to implement for datasets in which different traits were measured in different environments. We developed a latent variable model that incorporates genetic marker data for estimating heritability and improving predictions of traits. Our approach promotes model parsimony by estimating environmental associations and genetic variances for a reduced number of latent traits. The model can accommodate variation in genetic correlations across environments and can be applied in settings where only a subset of traits is observed in each environment, maximizing use of the data. We show that existing model‐based ordination methods can be viewed as simplifications of our approach. In a simulation study, we found that our approach improves sampling efficiency by an order of magnitude relative to standard multivariate mixed modelling approaches. Compared with existing ordination methods, our approach also improved inference for environmental associations and predictive performance. We applied our model to reconcile partially overlapping datasets collected from growth chamber and common garden experiments of Bromus tectorum , an annual grass invasive to the United States. Fitting mixed models independently to the data sources resulted in biologically unreasonable estimates of narrow‐sense heritability, and a joint analysis with our latent variable model improved inference. Drawing from the joint analysis, we present a holistic explanation for the strength of several clines in Bromus tectorum and discuss their relevance for invasion in the Intermountain West. The flexibility, tractability and performance of our approach make it appealing for joint inference and prediction in experiments of multiple traits. More broadly, we demonstrate the value of incorporating genetic marker data into latent variable models.