Modeling age-related leaf biomass changes in forest stands under the assumptions of the self-thinning lawModeling age-related leaf biomass changes in forest stands under the assumptions of the self-thinning law
Kira and Shidei (Jpn J Ecol 17:70–87, 1967) and Odum (Science 164:262–270, 1969) proposed a classical hypothetical trend that leaf biomass of a forest stand shows a more or less constant level after the initial peak maximum, with the result of constant GPP after canopy closure. On the contrary, Ryan et al. (Adv Ecol Res 27:213–262, 1997; Ecol Monogr 74:393–414, 2004) proposed a hypothetical trend that stand leaf biomass shows a singular peak maximum of leaf biomass, coinciding with canopy closure, with the result of singular peak of GPP. However, neither the hypothesis of leaf biomass constancy nor the hypothesis of a leaf biomass maximum explicitly states why leaf biomass should remain constant or decline after canopy closure from the mathematical or theoretical models. Therefore, age-related change in leaf biomass was modeled on the basis of the following three assumptions after canopy closure: (1) self-thinning law, (2) allometric scaling between mean individual leaf mass and mean individual total mass, and (3) formulation of a logistic function in stand density change. In the present modeling, both hypotheses can exist theoretically, but hypothesis by Kira and Shidei (Jpn J Ecol 17:70–87, 1967) and Odum (Science 164:262–270, 1969) holds only in a case limited mathematically. Using the reliable data on leaf biomass, leaf biomass constancy was also discussed by fitting mathematical model. From the empirical and theoretical viewpoints, possibility of leaf biomass constancy in forest stands is not so high, and it is reasonable that the forest stand leaf biomass declines after the canopy closure.