The Gompertz is one of a family of growth functions that, when the environment (e.g. food, housing) is non-limiting, provides a useful description of growth as a comparatively simple, single equation. It has three parameters of which the important ones are mature size, A, and the rate parameter, B. Estimates of A and B, however, are highly correlated and defining their separate values for individual animals is problematic. This problem was explored using five methods for estimating the parameters, or transformations of them, to describe the growth of two genotypes of Suffolk sheep kept under non-limiting conditions. One genotype was under selection for high lean growth rate and the other was its control. Live-weights that were collected at least fortnightly from near birth to 150 days of age over a 9-year period on 1934 lambs were used. The Gompertz form adequately described the growth of the great majority of the lambs evaluated. When considering A and B as a lumped parameter, Z = A·B, and fitting Z, B and an initial condition (a transformed birth weight) as the parameters, the problems in estimation were substantially overcome as shown by a low correlation of Z with estimates of B both within and across animals. Usefully Z has a biological interpretation in that Z/e is the maximum daily growth rate. Since the Gompertz form adequately described growth in these sheep, the extent of genetic co-variation for the growth parameters values (A, B, Z) was estimated to determine if they were amenable to selection. A weighted univariate animal model was fitted. Mature size, A, and the rate parameter, B, were moderately heritable (0.37 (s.e. 0.04) and 0.38 (s.e. 0.05), respectively) as was live weight at 150 days of age (0.31 (s.e. 0.06)). However there was a substantial negative genetic relationship between A and B (-0.48). Z was highly heritable (0.72 (s.e. 0.05)). After 9 years of selection, the genotype selected for high lean growth rate was heavier (P < 0.001) at 150 days of age (5.2 kg) and at maturity (6.6 kg), with a maximum growth rate (Z/e) that was 1.12 times that of the control. Our lumped parameter Z, in effect a rate parameter scaled for mature size, avoided problems in estimating A and B and, in so doing, offers a general and robust description of lamb growth amenable to selection.
- Genetic parameters
- Gompertz function