Applicability of the pipe-model theory to seedlings of hinoki cypress (Chamaecyparis obtusa)

Abstract

Abstract According to the pipe-model theory, the relationship between the cumulative mass of leaves [F(z)] and the density of non-photosynthetic organs [C(z)] at depth z from the crown surface is linear for adult trees. However, the present study of seedlings of Chamaecyparis obtusa demonstrates that the F(z)–C(z) relationship can be approximated as a non-rectangular hyperbola with convexity (θ) between 0 and 1. For θ=1, the F(z)–C(z) relationship is linear, in accordance with adult trees. Therefore, the basic concept of pipe-model theory regarding the F(z)–C(z) relationship can be generalized as a non-rectangular hyperbola for both growth stages (i.e., seedlings and adult trees). The difference between linearity (θ = 1) and curvilinearity \(\left(\theta \ne 1\right)\)in the F(z)–C(z) relationship corresponds to the difference in proportional area of sapwood in the studied seedlings. Thus, the proportional sapwood area is larger for seedlings with a linear F(z)–C(z) relationship than for seedlings with a curvilinear F(z)–C(z) relationship. The relationship between convexity and the square of stem diameter at the crown base showed scatter in terms of both season and seedling size, indicating that the size dependence of the degree of curvature in the F(z)–C(z) relationship for seedlings remains unclear. The allometric relationship between leaf mass and the square of stem diameter at crown base tended to separate seedlings from adult trees. Seedlings have more leaves per stem cross-sectional area at crown base than adult trees, as seedling stems are mostly composed of sapwood, which functions as an assemblage of living pipes connected to the leaves. Greater scattering of data for seedlings than adult trees in the allometry between leaf mass and the square of stem diameter at crown base could be explained by the non-rectangular hyperbola of the F(z)–C(z) relationship.