Theoretical analysis of the interrelationships between self-thinning, biomass density, and plant form in dense populations of hinoki cypress (Chamaecyparis obtusa) seedlings

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Interrelationships between self-thinning, biomass density, and plant form were mathematically modeled in relation to stand development in which self-thinning is either not occurring or is occurring. The relationship between biomass density and mean shoot mass is derived as a simple power function at the stage when self-thinning does not occur. When self-thinning occurs, constant biomass density is attained when the 3/2 power law of self-thinning applies and the allometric coefficient is assumed to be 1/3 in the allometry between mean plant height and aboveground mass. The applicability of this mathematical model and the allometric reformulations of the self-thinning exponent were tested using experimental data for dense populations of Chamaecyparis obtusa seedlings during the first 2 years of growth. On the basis of the results of the present model and experimental data, the dependence on competition of the mean height:diameter ratio, mean stem diameter, and leaf biomass density are discussed. As a result, the mean height:diameter ratio was almost asymptotically constant at the latter growth stage in the second-year seedlings, so that the 3/2 power law of self-thinning was held in the present analysis. However, the value of height:diameter ratio will become smaller in older stands, because tree height is considered to be asymptotic with respect to tree age due to hydraulic and other limits. Therefore, the present modeling implies that one of the reasons why the 3/2 power law from a geometric basis has been recently rejected depends on whether or not the height:diamter ratio is constant in older trees.