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University of Edinburgh School of Mathematics and BioSS Date: Friday 24th November, 15:05, Location: JCMB 5323 Speaker: Maria Xosé Rodríguez Álvarez, Basque Center for Applied Mathematics, Spain Title: A penalised spline approach for the correction for spatial heterogeneity in plant breeding experiments Abstract: An important aim of the analysis of agricultural field experiments is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This work explores the use of two-dimensional smooth surfaces to model random spatial variation. We propose the use of anisotropic tensor product penalised splines to explicitly model large-scale (global trend) and small-scale (local trend) spatial dependence. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. Each component in the model is shown to have an effective dimension. They are closely related to variance estimation, and helpful for characterising the importance of model components. An important result of this work is the formal proof of the relation between several definitions of heritability and the effective dimension associated with the genetic component. The practical value of our approach is illustrated by simulations and analyses of large-scale plant breeding experiments. An R-package, SpATS, implementing the approach, is also briefly described. This is joint work with Paul H.C. Eilers (Erasmus University Medical Centre, Rotterdam, the Netherlands), Martin P. Boer and Fred A. van Eeuwijk (Biometris, Wageningen University & Research, the Netherlands). This seminar is a part of Maxwell Institute seminar series. You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank.