A Note on the Fundamental Equation of Self-Thinning in the Logistic Theory of Plant Growth
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概要
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The fundamental equation of self-thinning, which was proposed in the logistic theory ofplant growth for describing the density effect in self-thinning populations, is based onthe following two fundamental assumptions: one is that the growth of mean phytomass wfollows a general logistic equation; the other is that the final yield Y(t), which is prescribed as the product of the asymptote of mean phytomass W(t) and density P , becomesconstant irrespective of P , i.e. the law of constant final yield is assumed. In the lightof the basic principle of self-thinning that the relative growth rate of mean phytomass(l/u>) (dw/dt) is given by the sum of the relative growth rate of yield (1/y) (dy/dt) andthe relative mortality (-1/P) (dP/dt), the first assumption brings to the conclusion that thefinal yield Y(t) is not prescribed by W{t) P , but is prescribed by(l-tn/A (t))W(t) P(ro, relative mortality; A (f), coefficient of growth), whose value depends on density Pexcept for the special case where both Wit) P and m are independent of P. This inevitableconsequence is in conflict with the prescription referring to the final yield Y(t) in thesecond assumption of the logistic theory of plant growth. As a result, it is suggestedthat an alternative theory for the density effect in self-thinning populations should benewly constructed to harmonize the assumption referring to the growth of mean phytomasswith the assumption referring to the law of constant final yield.
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