Leaf density-based modelling of phototropic crown dynamics and long-term predictive application to European beech

- Spatial leaf area density allows efficient simulations of tree crown dynamics.
- Based on this notion, we develop a teleonomic functional-structural growth model.
- The calibrated model predicts a wide range of high-quality empirical data.
- Among numerous emergent properties, the model generates the allometric 3/4 rule.

The landscape of functional-structural tree growth models is divided into small-scale models with a topological architecture, and large-scale models based on a description of crown shape in terms of rigid structures such as empirical crown envelopes. Due to their computational heaviness, the former meet their limits in the simulation of old and large trees, whereas the latter are unable to allow for unrestricted spatial variability and plasticity. This article presents a mechanistic, spatially explicit tree growth model based on the characterisation of the spatial distribution of foliage in terms of the 3D leaf area density. This allows efficient and robust simulations while avoiding the complexity of branch topology and any a priori shape constraints. A key element of our model is the spatial expansion of the crown along the local light gradient or, in an equivalent teleonomic interpretation, in the optimal direction with respect to future biomass production. The calibrated model accurately predicts long-term growth dynamics for 16 stands of European beech (Fagus sylvatica L.), a species known to be particularly plastic. It generates complex properties in conjunction with crown shape, response to stand density, height dynamics and, in particular, the emergence of the allometric 3/4-rule. Simulation results motivate hypotheses on the weight of phototropism as one driver of the spatial growth of European beech in early and late stages as well as in and off competition.