An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation

Existing growth equations have been derived by hypothesizing the growth rate as self-referencing. Although that hypothesis is appropriate for quantities with growth directly restricted to themselves, it requires the solution of differential equations that are difficult to be derived. However, for quantities of growth that are indirectly related to themselves, and for quantities that exhibit cumulative growth, such as growth of diameter or volume of trees with lignification, ordinary growth models with assumptions that include self-referencing or implied catabolism terms might not be appropriate. For such quantities, the author proposes an approach for derivation of growth models based on stochastic and microscopic interpretation. Results show that ordinary growth models can be interpreted from the perspective. The approach enables one to derive growth functions without solving differential equations. Based on that approach, growth functions are derived by integrating cumulative distribution functions. Three growth functions are generated using reasonable probability distributions. The fitness of the generated growth functions for real diameter growth data was compared with that of generalized ordinary growth models. Results show that the presented approach has high ability to generate growth models that fit data much better than ordinary growth models for a given number of parameters.