Gompertz - Pütter - Gompertz: Resolving two centuries of debate on laws of biological growth

The function of Gompertz (1825) can be derived from the growth equation of Ptter (1920), using the modified form proposed by Khleitner et al. (2019). The genetic relative growth rate is derived as RG = dlnW/dt = BG.ln(AG/W). The genetic characteristics are AG, mature weight, and BG, the rate parameter; the state variable is weight, W. The integrated form is W = AG.exp[–exp–(G0 + BG.t)], where G0 = –ln[–ln(W0/AG)] and W = W0 when t = 0. The phenotypic equation is RP = qE.RG, where qE ≤ 1 is a measure of the quality of the environment. This function is consistent with data, collected where qE can reasonably be assumed to be 1, on the post-hatching growth of domestic and wild altricial birds, and with data from both the pre-natal and post-natal growth of domestic mammals. The mean value of the rate parameter, scaled to AG0.27, for mammals and precocial birds unselected by humans, is about 0.037, with considerable variation in avian species. Human selection for growth traits in poultry has nearly doubled the value. The mean value for seven altricial species was found to be nearly three times that for the average precocial species. The Gompertz function is consistent with data collected where the environment is not limiting. It follows logically that any function that is inconsistent with the Gompertz is inconsistent with relevant data, and therefore not a sufficient description of genetic growth. These results indicate that the Gompertz form is not merely a convenient empirical approximation, but a sufficient and biologically grounded description of genetic growth, against which alternative theoretical growth laws can be tested. It has the additional advantages of being simple and beautiful.