Bone growth in ducks through mathematical models with special reference to the Janoschek growth curve.

The Janoschek growth curve was reviewed and a reparameterized form was presented which includes 4 biologically interpretable parameters: the weight at hatching/birth (W0), asymptotic (adult) weight (A), the time to grow to half of the final weight (t50) and a shape parameter (p) adjusting the degree of maturity when growth rate peaks. The model obtained was compared to the Richards, Bertalanffy, Gompertz and Logistic growth curve using bone weight data in White Pekin ducks. The Janoschek yielded least residual sums of squares for humerus mass and the Richards model for femur mass with only minor differences between both equations. All 3-parameter models failed to give reasonable estimations of the weight at hatching; in some cases further growth curve characteristics were unrealistic. The femur showed a higher degree of maturity at hatching, an earlier growth rate peak and its development preceded that of the humerus. This differential growth is an evolutionary feature first seen in birds.