Die Regeln von Reineke, Yoda und das Gesetz der räumlichen Allometrie

In his attempt to find an adequate expression for stand density independent of site quality and age REINEKE (1933) developed the following equation for even-aged and fully stocked stands in the Norwest of the USA: In N = a -1,605 · ln dg, based on the relationship between the average diameter dg and the number of trees per acre N. With no knowledge of these results KIRA et al. (1953) and YODA et al. (1963) found the border line ln m = b -3/2 · ln N in their study of herbaceous plants. This self-thinning rule - also called - -3/2-power rule or YODA'S rule - describes the relationship between the average weight of a plant m and the density N in even-aged plant populations growing under natural development conditions. It is possible to make a transition from YODA'S rule to REINEKE'S stand density rule if mass m in the former rule is substituted by the diameter dg. From biomass analyses for the tree species spruce and beech allometric relationships between biomass m and diameter d are derived. By using the latter in the equation 1n m = b -3/2 · ln N allometric coefficients are obtained for spruce and beech, that come very close to the REINEKE-coefficient. Thus REINEKE'S rule (1933) proves to be a special case of YODA'S rule. Both rules are based on the simple allometric law governing the volume of a sphere v and its surface of projection s: v = C₁ · s^3/2. If the surface of projection s is substituted by the reciprocal value of the number of stems s = 1/N and the isometric relationship between volume v and biomass m is considered v = C₂ · m^1.0 we come to YODA'S rule m = C₃ · N^-3/2 or in the logarithmic version 1n m = C₃ - 3/2 · ln N.