The rules by REINEKE, YODA and the law of spatial allometry.

In his attempt to find an adequate expression for stand density independent of site quality and age REINEKE (1933) developed the following equation fo r even-aged and fully stocked stands in the Norwest of the USA: In N = a -1 ,605 In dg, based on the relationship between the average diameter dg and t he number of trees per acre N. With no knowledge of these results KIRA et a l. (1953) and YODA et al. (1963) found the border line In m = b -3/2 In N i n their study of herbaceous plants. This self-thinning rule - also called - 3/2-power rule or YODA's rule - describes the relationship between the ave rage weight of a plant m and the density N in even-aged plant populations g rowing under natural development conditions. It is possible to make a trans ition from YODA's rule to REINEKE'S Stand density rule if mass m in the for mer rule is substituted by the diameter dg. From biomass analyses for the t ree species spruce and beech allometric relationships between biomass m and diameter d are derived. By using the latter in the equation In m = b -3/2 In N allometric coefficients are obtained for spruce and beech, that come v ery 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 allome tric law governing the volume of a sphere v and its surface of projection s : v = c(1).s(3/2). If the surface of projection s is substituted by the rec iprocal value of the number of stems s = 1/N and the isometric relationship between volume v and biomass m is considered v = c(2) . m(1.0) we come to YODA's rule m = c(3).N-3/2 or in the logarithmic version ln m = c(3)-3/2.ln N.