Modelling tree crown-to-bole diameter ratio for Norway spruce and European beech

摘要

Crown dimensions are correlated to growth of other parts of a tree and often used as predictors in growth models. The crown-to-bole diameter ratio (CDBDR), which is a ratio of maximum crown width to diameter at breast height (DBH), was modelled using data from permanent sample plots located on Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) stands in different parts of the Czech Republic. Among various tree and stand-level measures evaluated, DBH, height to crown base (HCB), dominant height (HDOM), basal area of trees larger in diameter than a subject tree (BAL), basal area proportion of the species of interest (BAPOR), and Hegyi's competition index (CI) were found to be significant predictors in the CDBDR model. Random effects were included using the mixed-effects modelling to describe sample plot-level variation. For each species, the mixed-effects model described a larger part of the variation of the CDBDR than nonlinear ordinary least squares model with no trend in the residuals. The spatially explicit mixed-effects model showed more attractive fit statistics [conditional R-2 approximate to 0.73 (spruce), 0.78 (beech)] than its spatially inexplicit counterpart [conditional R-2 approximate to 0.71 (spruce), 0.76 (beech)]. The model showed that CDBDR increased with increasing HDOM - a measure that combines the stand development stage and site quality - but decreased with increasing HCB and competition (increasing BAL and CI), and decreasing proportions of the species of interest (increasing BAPOR). For both species, the spatially explicit mixed-effects model should be a preferred choice for a precise prediction of the CDBDR. The CDBDR model will have various management implications such as determination of spacing, stand basal area, stocking, and planning of appropriate species mixture.