Adapting a growth equation to model tree regeneration in mountain forests

Management and risk analysis of protection forests depend on a reliable estimation of regeneration processes and tree growth under different site conditions. While the growth of forest stands and thus the average growth of larger trees is well studied and published in yield tables as well as embodied in numerous simulation models, there is still a lack of information about the crucial initial stages of tree growth. Thus, we evaluated juvenile tree growth for different site conditions in the Swiss Alps and developed an approach to model both the early and later stages of growth based on the Bertalanffy equation. This equation is physiologically well founded and requires only two parameter estimates: a maximum tree height and a growth parameter. Data for the parameter estimation were available from studies of tree regeneration at a range of sites in Switzerland: growth patterns of larch (Larix decidua) were available from a high-elevation afforestation experiment. For spruce (Picea abies), data were obtained from a blowdown area in the Alps. The growth equation was fitted to the observed data and we found a good correlation of the fitted curves with the observed data. The parameter estimates were validated with independent data sets. The extrapolated growth curves, calculated with the estimated growth rates, correspond well to the validation data. Thus, it is possible to use the Bertalanffy equation to model both the early and later stages of growth. With this approach, we provide a basis for modelling the growth of juvenile and mature trees of different tree species in mountain forests of the European Alps.