Performance of alternative spatial models in empirical Douglas-fir and simulated datasets

Based on an empirical dataset originating from the French Douglas-fir breeding program, we showed that the bidimensional autoregressive and the two-dimensional P-spline regression spatial models clearly outperformed the classical block model, in terms of both goodness of fit and predicting ability. In contrast, the differences between both spatial models were relatively small. In general, results from simulated data were well in agreement with those from empirical data.

Context Environmental (and/or non-environmental) global and local spatial trends can lead to biases in the estimation of genetic parameters and the prediction of individual additive genetic effects.
Aims The goal of the present research is to compare the performances of the classical a priori block design (block) and two different a posteriori spatial models: a bidimensional first-order autoregressive process (AR) and a bidimensional P-spline regression (splines).
Methods Data from eight trials of the French Douglas-fir breeding program were analyzed using the block, AR, and splines models, and data from 8640 simulated datasets corresponding to 180 different scenarios were also analyzed using the two a posteriori spatial models. For each real and simulated dataset, we compared the fitted models using several performance metrics.
Results There is a substantial gain in accuracy and precision in switching from classical a priori blocks design to any of the two alternative a posteriori spatial methodologies. However, the differences between AR and splines were relatively small. Simulations, covering a larger though oversimplified hypothetical setting, seemed to support previous empirical findings. Both spatial approaches yielded unbiased estimations of the variance components when they match with the respective simulation data.
Conclusion In practice, both spatial models (i.e., AR and splines) suitably capture spatial variation. It is usually safe to use any of them. The final choice could be driven solely by operational reasons.

Global and local spatial trends, Forest genetics trials, Autoregressive residual, Two-dimensional P-splines

Cappa, E.P., Muñoz, F. & Sanchez, L. Annals of Forest Science (2019) 76: 53.

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Data availability
The datasets generated and analyzed during the current study are available in the Zenodo repository (Cappa et al. 2019) at

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