Modeling sapling distribution over time using a functional predictor in a generalized additive model

  • Daniel Moreno-Fernández
  • Nicole H. Augustin
  • Fernando Montes
  • Isabel Cañellas
  • Mariola Sánchez-González
Original Paper


Key message

The effect of adult trees on sapling density distribution during the regeneration fellings is determined in a Pinus sylvestris L. Mediterranean forest using generalized additive models.


Spatial pattern of adult trees determines the number of new individuals after regeneration fellings, which modify the light and air temperature under tree canopy.


We proposed a novel spatiotemporal model with a functional predictor in a generalized additive model framework to describe nonlinear relationships between the size of the adult trees and the number of saplings of P. sylvestris and to determine if the spatial pattern of the number of saplings remained constant or changed in time.


In 2001, two plots (0.5 ha) were set up in two phases of regeneration fellings under the group shelterwood method. We mapped the trees and saplings and measured their diameter and height. The inventories were repeated in 2006, 2010, and 2014.


We found a negative association between the diameter of adult trees and number of saplings up to 7–8 m. Beyond these distances, the diameter of adult trees was not associated with the number of saplings. Our results indicate that the spatial pattern of the number of saplings remained quite constant in time.


The generalized additive models are a flexible tool to determine the distance range of inhibition of saplings by adult trees.


Edge effect Intra-specific competition Mountain forest Shade tolerance Mediterranean areas 



We wish to thank everybody who participated in the field work, especially Ángel Bachiller, Estrella Viscasillas, and Enrique Garriga. We appreciate the comments made by the referees and the editors of Annals of Forest Science during the revision process. We also thank Adam Collins for revising the English writing.


DMF has been funded by Spanish Ministry of Education, Culture and Sport thorough the FPU program (FPU13/02113) and by the short-term visiting program (EST15/00242). This work has been funded by AGL2013-46028-R and BOSSANOVA-CM (S2013/MAE-2760).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.


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Copyright information

© INRA and Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  1. 1.INIA-CIFORMadridSpain
  2. 2.MONTES (School of Forest Engineering and Natural Resources)Universidad Politécnica de MadridMadridSpain
  3. 3.Department of Mathematical SciencesUniversity of BathBathUK

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