Carbon-based models of individual tree growth: a critical appraisal

Twenty-seven individual tree growth models are reviewed. The models take into account the same main physiological processes involved in carbon metabolism (photosynthate production, respiration, reserve dynamics, allocation of assimilates and growth) and share common rationales that are discussed. It is shown that the spatial resolution and representation of tree architecture used mainly depend on model objectives. Beyond common rationales, the models reviewed exhibit very different treatments of each process involved in carbon metabolism. The treatments of all these processes are presented and discussed in terms of formulation simplicity, ability to account for response to environment, and explanatory or predictive capacities. Representation of photosynthetic carbon gain ranges from merely empirical relationships that provide annual photosynthate production, to mechanistic models of instantaneous leaf photosynthesis that explicitly account for the effects of the major environmental variables. Respiration is often described empirically as the sum of two functional components (maintenance and growth). Maintenance demand is described by using temperature-dependent coefficients, while growth efficiency is described by using temperature-independent conversion coefficients. Carbohydrate reserve pools are generally represented as black boxes and their dynamics is rarely addressed. Storage and reserve mobilisation are often treated as passive phenomena, and reserve pools are assumed to behave like buffers that absorb the residual, excessive carbohydrate on a daily or seasonal basis. Various approaches to modelling carbon allocation have been applied, such as the use of empirical partitioning coefficients, balanced growth considerations and optimality principles, resistance mass-flow models, or the source-sink approach. The outputs of carbon-based models of individual tree growth are reviewed, and their implications for forestry and ecology are discussed. Three critical issues for these models to date are identified: (i) the representation of carbon allocation and of the effects of architecture on tree growth is Achilles' heel of most of tree growth models; (ii) reserve dynamics is always poorly accounted for; (iii) the representation of below ground processes and tree nutrient economy is lacking in most of the models reviewed. Addressing these critical issues could greatly enhance the reliability and predictive capacity of individual tree growth models in the near future.