Mathematical analysis of age-related changes in leaf biomass in forest stands

Temporal changes in leaf biomass during forest stand development were theoretically analyzed on the basis of two mathematical models, both of which assume that changes in stand density with age follow a logistic equation. According to the pipe model theory, stem cross-sectional area at the crown base was used to determine the time course of leaf biomass change. In Model I, the growth curve of average leaf mass of a tree is expressed by a single logistic equation, with the result that stand leaf biomass shows a singular peak maximum of leaf biomass, coinciding with crown closure. Model I results correspond to the hypothetical trend proposed by Ryan et al. (1997. Adv. Ecol. Res. 27: 213-262). In Model II, the growth curve of average leaf mass of a tree is expressed by several logistic equations, representing a growth phase shift, with the result that the time trend of stand leaf biomass shows a more or less constant level after the intial peak maximum. Stand leaf biomass constancy is supported by the mathematical scaling-up model from shoot to stand level proposed by Ogawa (2008. J. Ecol. 96: 188-191). Model II corresponds to the hypothetical trend proposed by Kira and Shidei (1967. Jpn. J. Ecol. 17: 70-87) and Odum (1969. Science 164: 262-270).