MATHEMATICAL-MODELS FOR GROWTH IN ALLIGATOR (ALLIGATOR-MISSISSIPPIENSIS) EMBRYOS DEVELOPING AT DIFFERENT INCUBATION TEMPERATURES

A variety of model-based (growth models) and model-free (cubic splines , exponentials) equations were fitted using weighted-nonlinear least s quares regression to embryonic growth data from Alligator mississippie nsis eggs incubated at 30 and 33 degrees C. Goodness of fit was estima ted using a chi(2) on the sum of squared, weighted residuals, and run and sign tests on the residuals. One of the growth models used (Preece & Baines, 1978) was found to be superior to the classical growth mode ls (exponential, monomolecular, logistic, Gompertz, von Bertalanffy) a nd gave an adequate fit to all longitudinal measures taken from the em bryonic body and embryonic mass. However, measurements taken from the head could not be fitted by growth models but were adequately fitted b y weighted least squares cubic splines. Data for the stage of developm ent were best fitted by a sum of 2 exponentials with a transition poin t. Comparison of the maximum growth rates and parameter values, indica ted that the growth data at 30 degrees C could be scaled to 33 degrees C to multiplying the time by a scaling factor of 1.2. This is equival ent to a Q(10) of about 1.86 or, after solving the Arrhenius equation, an E double dagger of 46.9 kJmol(-1). This may be interpreted as indi cating a common rate-limiting step in development at the 2 temperature s.