An individual-tree linear mixed-effects model for predicting the basal area increment of major forest species in Southern Europe


Aims of the study. Assessment of growth is essential to support sustainability of forest management and forest policies. The objective of the study was to develop a species-specific model to predict the annual increment of tree basal area through variables recorded by forest surveys, to assess forest growth directly or in the context of more complex forest growth and yield simulation models.

Area of the study. Italy.

Material and methods. Data on 34638 trees of 31 different forest species collected in 5162 plots of the Italian National Forest Inventory were used; the data were recorded between 2004 and 2006. To account for the hierarchical structure of the data due to trees nested within plots, a two-level mixed-effects modelling approach was used.

Main results. The final result is an individual-tree linear mixed-effects model with species as dummy variables. Tree size is the main predictor, but the model also integrates geographical and topographic predictors and includes competition. The model fitting is good (McFadden’s Pseudo-R2 0.536), and the variance of the random effect at the plot level is significant (intra-class correlation coefficient 0.512). Compared to the ordinary least squares regression, the mixed-effects model allowed reducing the mean absolute error of estimates in the plots by 64.5% in average.

Research highlights. A single tree-level model for predicting the basal area increment of different species was developed using forest inventory data. The data used for the modelling cover 31 species and a great variety of growing conditions, and the model seems suitable to be applied in the wider context of Southern Europe.   

Keywords: Tree growth; forest growth modelling; forest inventory; hierarchical data structure; Italy.

Abbreviations used: BA - basal area; BAI – five-year periodic basal area increment; BALT - basal area of trees larger than the subject tree; BASPratio - ratio of subject tree species basal area to stand basal area; BASTratio - ratio of subject tree basal area to stand basal area; CRATIO - crown ratio; DBH – diameter at breast height ; DBH0– diameter at breast height corresponding to five years before the survey year; DBHt– diameter at breast height measured in the survey year; DI5 - five-year, inside bark, DBH increment; HDOM - dominant height; LULUCF - Land Use, Land Use Changes and Forestry; ME - mean error; MAE - mean absolute error; MPD - mean percent deviation; MPSE - mean percent standard error; NFI(s) - National Forest Inventory/ies; OLS - ordinary least squares regression; RMSE - root mean squared error; UNFCCC - United Nation Framework Convention on Climate Change.


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Author Biographies

Lucio Di Cosmo, CREA - Consiglio per la ricerca in agricoltura e l'analisi dell'economia agraria
Research Centre for Forestry and Wood, piazza Nicolini 6, Trento, 38123, Italy
Diego Giuliani, University of Trento
Department of Economic and Management, via Inama 5, 38122 Trento, Italy
Maria Michela Dickson, University of Trento
Department of Economic and Management, via Inama 5, 38122 Trento, Italy
Patrizia Gasparini, CREA - Consiglio per la ricerca in agricoltura e l'analisi dell'economia agraria
Research Centre for Forestry and Wood, piazza Nicolini 6, Trento, 38123, Italy


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How to Cite
Di Cosmo, L., Giuliani, D., Dickson, M. M., & Gasparini, P. (2021). An individual-tree linear mixed-effects model for predicting the basal area increment of major forest species in Southern Europe. Forest Systems, 29(3), e019.
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