Conservation rule of stem surface area: a hypothesis

Abstract

The relationship between stem surface area and stand density was analyzed using a large data set collected from 14 districts for Japanese cedar (Cryptomeria japonica D. Don) and 11 districts for Japanese cypress (Chamaecyparis obtusa Endl.) stands across Japan. The results demonstrated that the mean stem surface area in overcrowded stands was inversely proportional to the stand density for both species and all districts. The inverse relationship indicates that the total stem surface area in overcrowded stands becomes a maximum constant independent of stand density, which is termed the ‘conservation rule of stem surface area.’ Since the stem surface area is proportional to the amount of cambium cells in the stem, the conservation rule suggests that there is an upper limit to the total amount of cambium per unit area, i.e., conservation rule of cambium. The conservation rule of stem surface area was linked to the 3/2 power law of self-thinning by an allometric power exponent between stem surface area and volume. Since the allometric power exponent was approximately equal to 3/2, the self-thinning exponent would vary within a relatively narrow band around −3/2. In conclusion, we hypothesized that the conservation rule of stem surface area, or the conservation rule of cambium, may be an alternative starting point for understanding self-thinning in overcrowded tree populations.