A stochastic height-diameter model for maritime pine ecoregions in Galicia (northwestern Spain)

A stochastic height-diameter model was developed for maritime pine (Pinus pinaster Ait.) in Galicia (northwestern Spain). Four well-known growth functions were initially considered in this work, however, only Schnute's function performed adequately. A set of 20 695 pairs of height-diameter measures, collected in thinned and unthinned pure and even-aged stands, were used to fit the model. These stands were located throughout Galicia Autonomous Region covering a wide range of forest stands and site conditions. Since unequal error variance occurs, the generalized non-linear least squares method was used to take into account the error structure. Different weighting factors were employed to remove the heterogeneous variance of the errors. Because the local model (including only tree dimensions as explanatory variables) did not provide adequate results, stand variables were tested and incorporated into the height-diameter model. Ecoregion differences in the height-diameter relationship were analysed using the non-linear extra sum of squares method and the Lakkis-Jones test. Both tests showed that model parameters were significantly different between the two ecoregions normally defined for this species: coast and interior. The effect of thinning was examined; however, no benefits were obtained by introducing an additional thinning response variable in the prediction model. Finally, since trees with the same diameter usually do not have the same height, even within the same stand, a stochastic component was added to the deterministic height function. This approach mimics the natural variability of heights and therefore provides more realistic height predictions. Un modèle stochastique de hauteur-diamètre pour le pin maritime en Galice (nord-ouest de l'Espagne). Un modèle stochastique hauteur-diamètre de pin maritime a été développé en Galice (nord-ouest de l'Espagne). Quatre fonctions bien connues de croissance ont été initialement prises en compte dans cette étude, et cependant seule la fonction de Schnute s'est comportée correctement. Un échantillon de 20 695 couples de mesures hauteur-diamètre recueilli sur des peuplements clairsemés et des peuplements denses y compris sur d'anciens peuplements, a été utilisé pour établir ce modèle. Ces peuplements étaient situées dans la région autonome de Galice, et constituent un large éventail de peuplements forestiers et de conditions de terrain. Comme une divergence de variabilité est apparue, la méthode généralisée des m