Tree growth as affected by stem and crown structure
Authors: Pretzsch Hans 
Published: March 2021

Abstract
Key message
Prediction of tree growth based on size or mass as proposed by the Metabolic Scaling Theory is an over-simplification and can be significantly improved by consideration of stem and crown morphology.
Tree growth and metabolic scaling theory, as well as corresponding growth equations, use tree volume or mass as predictors for growth. However, this may be an over-simplification, as the future growth of a tree may, in addition to volume or mass, also depend on its past development and aspects of the current inner structure and outer morphology. The objective of this evaluation was to analyse the effect of selected structural and morphological tree characteristics on the growth of common tree species in Europe. Here, we used eight long-term experiments with a total of 24 plots and extensive individual measurements of 1596 trees in monospecific stands of European beech (Fagus sylvatica L.), Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and sessile oak (Quercus petraea (Matt.) Liebl.). Some of the experiments have been systematically surveyed since 1870. The selected plots represent a broad range of stand density, from fully to thinly stocked stands. We applied linear mixed models with random effects for analysing and modelling how tree growth and productivity are affected by stem and crown structure. We used the species-overarching relationship $$\mathrm{iv}={{a}_{0}\times v}$$

iv
=

a
0

×
v

between stem volume growth, $$\mathrm{iv}$$
iv
and stem volume, $$v,$$

v
,

as the baseline model. In this model $${a}_{0}$$

a
0

represents the allometric factor and α the allometric exponent. Then we included tree age, mean stem volume of the stand and structural and morphological tree variables in the model. This significantly reduced the AIC; RMSE was reduced by up to 43%. Interestingly, the full model estimating $$\mathrm{iv}$$
iv
as a function of $$v$$
v
and mean tree volume, crown projection area, crown ratio and mean tree ring width, revealed a $$\alpha \cong 3/4$$

α
≅
3
/
4

scaling for the relationship between $$\mathrm{iv}\propto {v}^{\alpha }$$

iv
∝

v

α

. This scaling corresponded with Kleiber’s rule and the West-Brown-Enquist model of the metabolic scaling theory. Simplified approaches based on stem diameter or tree mass as predictors may be useful for a rough estimation of stem growth in uniform stands and in cases where more detailed predictors are not available. However, they neglect other stem and crown characteristics that can have a strong additional effect on the growth behaviour. This becomes of considerable importance in the heterogeneous mixed-species stands that in many countries of the world are designed for forest restoration. Heterogeneous stand structures increase the structural variability of the individual trees and thereby cause a stronger variation of growth compared with monocultures. Stem and crown characteristics, which may improve the analysis and projection of tree and stand dynamics in the future forest, are becoming more easily accessible by Terrestrial laser scanning.