Flexible modelling of spatial variation in agricultural field trials with the R package INLA

The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ( AR1⊗AR1 ) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the AR1⊗AR1 and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA

Genomic structural equation modelling provides a whole-system approach for the future crop breeding.

KEY MESSAGE: Using genomic structural equation modelling, this research demonstrates an efficient way to identify genetically correlating traits and provides an effective proxy for multi-trait selection to consider the joint genetic architecture of multiple interacting traits in crop breeding. Breeding crop cultivars with optimal value across multiple traits has been a challenge, as traits may negatively correlate due to pleiotropy or genetic linkage. For example, grain yield and grain protein content correlate negatively with each other in cereal crops. Future crop breeding needs to be based on practical yet accurate evaluation and effective selection of beneficial trait to retain genes with the best agronomic score for multiple traits. Here, we test the framework of whole-system-based approach using structural equation modelling (SEM) to investigate how one trait affects others to guide the optimal selection of a combination of agronomically important traits. Using ten traits and genome-wide SNP profiles from a worldwide barley panel and SEM analysis, we revealed a network of interacting traits, in which tiller number contributes positively to both grain yield and protein content; we further identified common genetic factors affecting multiple traits in the network of interaction. Our method demonstrates an efficient way to identify genetically correlating traits and underlying pleiotropic genetic factors and provides an effective proxy for multi-trait selection within a whole-system framework that considers the joint genetic architecture of multiple interacting traits in crop breeding. Our findings suggest the promise of a whole-system approach to overcome challenges such as the negative correlation of grain yield and protein content to facilitating quantitative and objective breeding decisions in future crop breeding