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

The rhizosphere: Molecular interactions between microorganisms and roots.

The rhizosphere has a large impact on plant performance in several ways. A stand-specific, more or less high diversity of microorganisms not only supports the plant in the acquisition of water and nutrients, but also modulates its ability to cope with pathogens. This diversity, however, has to be maintained and thus causes a considerable drain of photoassimilates, which are then not available for shoot development. In this chapter, we try to explain why the considerable allocation of carbon to the root system is a “wise” decision by the plant. We thus focus on the function of root-associated bacteria and their relevance for plant growth and development of disease resistance, and deliver data on the molecular basis of the root–fungus symbiosis (mycorrhiza)