Relationships between mean shoot and root masses and density in an overcrowded population of hinoki (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.) seedlings

In an overcrowded population of seedlings of the tree hinoki (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.), an allometric power relationship was found to exist between mean root and shoot masses during the course of self-thinning. The allometric exponent was less than unity. The time trajectory of mean shoot mass and density was modeled mathematically. The value of the self-thinning exponent was 1.519 during the final phase of stand development. This value, which is close to 3/2, can be regarded as evidence in favor of the 3/2 power law of self-thinning. By combining the allometric power relationship and the time trajectory of mean shoot mass and density, it was possible to mathematically derive the time trajectory of mean root mass and density. The self-thinning exponent for root mass was estimated to be 1.368, and thus lower than 3/2, because the allometric coefficient was less than unity. The time trajectories of mean shoot and root masses and density allowed the time trajectory of the mean whole seedling mass and density to be derived. In this case, the value of the self-thinning exponent was close to 3/2. From the time trajectories of mean shoot and root masses and density, the relationship between the root/shoot ratio and density was mathematically modeled, and competition in relation to shoots and roots is discussed.