A size-structured integro-differential model of forest stand dynamics

Overview & Synopsis

The challenges of modern forest management, exacerbated by climate change and the need for diverse ecosystem services, require a shift from purely empirical, stand-level models–commonly used in operational decision support for forest production–to models that explicitly account for internal stand dynamics. In this paper, we propose a new mathematical framework for forest stand dynamics using a size-structured integro-differential model. The state of the forest is described by a density function depending on time, tree height, and diameter. The core novelty lies in incorporating a nonlocal status function that captures the competitive dominance of trees within the stand, influencing both growth (transport) and mortality. We establish the well-posedness of the model, proving the existence, uniqueness, non-negativity, and L ∞ bounds of the weak solutions using the Banach fixed-point theorem and the theory of parabolic partial differential equations. Finally, we design a finite difference scheme, combining an upwind approach for the convective flux and an implicit treatment for diffusion, and present numerical simulations that illustrate the qualitative behavior of the model in a young, dense stand.