Growth Equations in Forest Research: Mathematical Basis and Model Similarities

Growth equations have been widely used in forest research, commonly to assess ecosystem-level behavior and forest management. Nevertheless, the large number of growth equations has obscured the growth-rate behavior of each of these equations and several different terms for referring to common phenomena. This review presents a unified mathematical treatment of growth-rates besides several well-known growth equations by giving their mathematical basis and representing their behavior using tree growth data as an example. We highlight the mathematical differences among several growth equations that can be better understood by using their differential equations forms rather than their integrated forms. Moreover, the assumed-and-claimed biological basis of these growth-rate models has been taken too seriously in forest research. The focus should be on using a plausible equation for the organism being modelled. We point out that more attention should be drawn to parameter estimation strategies and behavior analysis of the proposed models. Thus, it is difficult for a single model to capture all possible shapes and rates that such a complex biological process as tree growth can depict in nature. We pointed out misleading concepts attributed to some growth equations; however, the differences come from their mathematical properties rather than pure biological reasoning. Using the tree growth data, we depict those differences. Thus, comparisons of some functional forms (at least simple ones) must be carried out before selecting a function for drawing scientific findings.