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

  • Eduardo Pablo CappaEmail author
  • Facundo Muñoz
  • Leopoldo Sanchez
Research Paper


Key message

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.


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.


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).


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.


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.


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 



The authors sincerely acknowledge Jean-Charles Bastien for his help in identifying trials and accessing data. Thanks go to the staff of INRA experimental units (UE GBFOR, INRA Val de Loire) who have established, maintained, and assessed the field trials.


Eduardo P Cappa, F. Muñoz, and L. Sánchez received funding from the European Union’s Seventh Framework Program for research, technological development, and demonstration under grant agreement no. 284181 (“Trees4Future”). F. Muñoz is partially funded by research grant MTM2016-77501-P from the Spanish Ministry of Economy and Competitiveness.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

13595_2019_836_MOESM1_ESM.docx (1.1 mb)
ESM 1 (DOCX 1174 kb)


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Copyright information

© INRA and Springer-Verlag France SAS, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Bosques Cultivados, Centro de Investigación en Recursos Naturales, Instituto Nacional de Tecnología Agropecuaria (INTA)Instituto de Recursos BiológicosBuenos AiresArgentina
  2. 2.Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)Buenos AiresArgentina
  3. 3.UMR BioForA, INRAArdonFrance

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