Czech J. Anim. Sci., 2026, 71(8):380-395 | DOI: 10.17221/56/2026-CJAS

Gompertz – Pütter – Gompertz: Resolving two centuries of debate on laws of biological growthOriginal Paper

Gerald Charles Emmans ORCID...¹, Robert Gous ORCID...²

¹ Animal Breeding and Genomics, Scotland’s Rural College (SRUC), Edinburgh, UK

² School of Agricultural, Earth and Environmental Sciences, University of KwaZulu-Natal, Scottsville, South Africa

The function of Gompertz (1825) can be derived from the growth equation of Pütter (1920), using the modified form proposed by Kühleitner et al. (2019). The genetic relative growth rate is derived as R_G = dlnW/dt = B_G.ln(A_G/W). The genetic characteristics are A_G, mature weight, and B_G, the rate parameter; the state variable is weight, W. The integrated form is W = A_G.exp[–exp–(G₀ + B_G.t)], where G₀ = –ln[–ln(W₀/A_G)] and W = W₀ when t = 0. The phenotypic equation is R_P = q_E.R_G, where q_E ≤ 1 is a measure of the quality of the environment. This function is consistent with data, collected where q_E 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 A_G^0.27, 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.

Keywords: birds, Dynamic Energy Budget; mammals; ontogenetic growth; von Bertalanffy

Received: April 21, 2026; Accepted: June 22, 2026; Published: August 26, 2026  Show citation