Modelling tree growth taking into account carbon source and sink limitations

Increasing CO2 concentrations are strongly controlled by the behaviour of undisturbed forests, which are believed to be a major current sink of atmospheric CO2. There are many models which predict forest responses to environmental changes but they are almost exclusively carbon source (i.e. photosynthesis) driven. Here we present a model for an individual tree that takes into account also the intrinsic limits of meristems and cellular growth rates, as well as control mechanisms within the tree that influence its diameter and height growth over time. This new framework is built on process-based understanding combined with differential equations solved by the Runge-Kutta-Fehlberg (RKF45) numerical method. It was successfully tested for stands of beech trees in two different sites representing part of a long-term forest yield experiment in Germany. This model provides new insights into tree growth and limits to tree height, and addresses limitations of previous models with respect to sink-limited growth.\n\nAuthor SummaryGreenhouse gas emissions, in particular of CO2, have emerged as one of the most important global concerns, and it is therefore important to understand the behaviour of forests as they absorb and store a very large quantity of carbon. Most models treat forests as boxes with growth only driven by photosynthesis, while their actual growth depends also on many other important processes such as the maximal rate at which individual cells can grow, the influences of temperature and soil moisture on these cells, and the control that the tree has on itself through endogenous signalling pathways. Therefore, and with inspiration from process-based understanding of the biological functioning of trees, we have developed a model which takes into account these different factors. We first use this knowledge and additional basic assumptions to derive a system of several equations which, when solved, enable us to predict the height and the radius of an individual tree at a given time, provided that we have enough information about its initial state and its surroundings. We use the Runge-Kutta-Fehlberg mathematical method to obtain a numerical solution and thus predict the development of the height and radius of an individual tree over time under specified conditions.