Modelling crown width–diameter relationship for Scots pine in the central Europe

Abstract

Crown width–diameter relationship, which is significantly influenced by various characteristics, was modelled using tree and stand measures, and plot-level random effect parameters. A proposed model precisely predicts crown width of Scots pine. Crown size is significantly correlated with growth and biomass of other parts of a tree, and therefore crown measures are used as predictors to develop tree growth and biomass models. We modelled crown width–diameter at breast height (DBH) allometry using data from permanent sample plots located in both monospecific and mixed species stands of Scots pine (Pinus sylvestris L.) in various parts of the Czech Republic. Among various predictors evaluated, dominant height (HDOM), height-to-DBH ratio (HDR—also known as a tree slenderness coefficient), height to live crown base (HCB), relative spacing index (RS), and basal area proportion of a species of interest (BAPOR) significantly contributed to the variations in the crown width–DBH allometry. The sample plot-level random effect parameters, which account for stand heterogeneity and randomness caused by various stochastic factors, were included through the mixed-effects modelling approach. Heteroskedasticity in the residuals was reduced through the integration of a power variance function with DBH as an independent variable. Both mixed-effects model and ordinary least square (OLS) model described more than two-thirds of the total variations in the crown width–DBH allometry with no significant trend in the residuals. The model showed that crown width increased with increasing site quality (increasing HDOM) and relative spacing index (increasing RS), and decreasing species mixture per sample plot (increasing BAPOR). However, crown width decreased with increasing tree slenderness coefficient (increasing HDR) and height to live crown base (increasing HCB). Model validation by splitting data also confirmed a high precision of the model, because it described most of the variations in the crown width–DBH allometry with no significant trend in the prediction errors. Because of more attractive fit statistics and higher prediction accuracy than that of the OLS model, the mixed-effects model with the random effect parameters estimated from crown width measurements of a sub-sample of four randomly selected Scots pine trees per sample plot is suggested for application. Application of the crown width model may have various implications that are briefly mentioned in the article.