Mathematical consideration of the age-related decline in leaf biomass in forest stands under the self-thinning law

In addition to the hypothetical trends proposed by Kira and Shidei (1967), Odum (1969) and Ryan et al. (1997, 2004), Oshima et al. (1958) observed a complicated age-related change in stand leaf biomass in Abies forests. To explain this change in stand leaf biomass theoretically, the age-related change in leaf biomass was modeled based on the following three assumptions after canopy closure: (i) the self-thinning law; (ii) expanded allometric scaling between the mean individual leaf mass and mean individual total mass; and (iii) the formulation of a logistic function for stand density change. The model successfully explained these three trends in forest stand leaf biomass and introduced expanded allometric scaling including the properties of the model based on simple allometric scaling proposed by Ogawa (2017). Therefore, the model developed here can generalize age-related changes in forest stand biomass better than the model proposed by Ogawa (2017).