[Allometry and the original and generalized Gompertz function (author's transl)].
After a review of the traditional Gompertz function of organic growth the mathematical consequences in applying the allometry principle are studied. In graphs examples are presented showing the relation between the Gompertz function proper and several cases of allometry having the same functional structure. Moreover the investigations are extended to a generalized form of the Gompertz function resulting from changing the increase function from dW/dt = kWe-rt to dW/dt = kWme-rt thus allowing for one more parameter. This form has recently been developed by the author (SAGER 1979a), giving more flexibility to the growth curve and providing the inflexion point with a broad range of ordinate values thus being superior to the rigidity of the original behaviour. After giving a graphical impression of the effect of the additional parameter allometry relations are considered once more and applied to an example already used when treating interrelations of allometry and the Bertalanffy growth functions (SAGER 1980b).
D001699:Biometry; D006128:Growth; D008433:Mathematics
Allometrie und die Original- sowie generalisierte Form der Gompertz-Funktion.