Modelling spatial variation in agricultural field trials with INLA

Abstract

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. Here 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 geostatistical model using the stochastic partial differential equation (SPDE) approach. The SPDE approach models a Gaussian random field, which can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding program 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. We evaluate predictive performance by correlation between true and estimated breeding values, the continuous rank probability score and how often the best individuals rank at the top. The results show best predictive performance with the AR1⊗AR1 and the SPDE. We also present an example of fitting the models to real wheat breeding data and simulated tree breeding data with the Nelder wheel design.