Embryonic metabolism of the ornithischian dinosaurs Protoceratops andrewsi and Hypacrosaurus stebingeri and implications for calculations of dinosaur egg incubation times

Trends in embryonic and ontogenetic growth metabolisms in nonavian dinosaurs and extant birds, mammals, and crocodylians with implications for dinosaur egg incubation

The embryonic metabolism of the saurischian dinosaur Troodon formosus and the ornithischian dinosaurs Protoceratops andrewsi and Hypacrosaurus stebingeri have been determined by using a mass growth model based on conservation of energy and found to be very similar. Embryonic and ontogenetic growth metabolisms are also evaluated for extant altricial birds, precocial birds, mammals, and crocodylians to examine for trends in the different groups of animals and to provide a context for interpreting our results for nonavian dinosaurs. This analysis reveals that the embryonic metabolisms of these nonavian dinosaurs were closer to the range observed in extant crocodylians than extant birds. The embryonic metabolisms of nonavian dinosaurs were in the range observed for extant mammals of similar masses. The measured embryonic metabolic rates for these three nonavian dinosaurs are then used to calculate the incubation times for eggs of 22 nonavian dinosaurs from both Saurischia and Ornithischia. The calculated incubation times vary from about 50 days for Archaeopteryx lithographica to about 150 days for Alamosaurus sanjuanensis.

Theoretical modeling of pre and postnatal growth

A simultaneous analysis of the pre and postnatal growth data obtained for five exemplary animals (zebra, rat, guinea pig, chicken, tilapia) is performed. To this aim, the generalized von Bertalanffy (VB) model is employed in which one of the fitted parameters is related to the gestation or incubation period of the system under consideration. The results obtained reveal a descriptive power of the VB model in both the pre and postnatal stages for a wide range of the data analyzed using several goodness-of-fit metrics and biologically meaningful parameters fitted. It has been proved that generalized VB function with one parameter constrained to the experimental value of the gestation (incubation) period and other parameters fitted only to the postnatal data predicts with high accuracy the growth of animals in the developmental prenatal stages. Hence, the VB model features not only descriptive but also retro-predictive power to reproduce the prenatal growth patterns of the animals considered. Three main sources of the problems with the fit stability reported for the VB function are identified: nonlinear nature of the scaling n-exponent, its strong correlation with remaining parameters defining the model and n-value placed in the vicinity of the discontinuity point n = 1 or outside the standard range 0 ≤ n < 1 usually applied in the data analysis.