Comparing growth patterns of three species: Similarities and differences

Abstract

Quantitative studies of the growth of dinosaurs have made comparisons with modern animals possible. Therefore, it is meaningful to ask, if extinct dinosaurs grew faster than modern animals, e.g. birds (modern dinosaurs) and reptiles. However, past studies relied on only a few growth models. If these models were false, what about the conclusions? This paper fits growth data to a more comprehensive class of models, defined by the von Bertalanffy-Pütter (BP) differential equation. Applied to data about Tenontosaurus tilletti, Alligator mississippiensis and the Athens Canadian Random Bred strain of Gallus gallus domesticus the best fitting growth curves did barely differ, if they were rescaled for size and lifespan. A difference could be discerned, if time was rescaled for the age at the inception point (maximal growth) or if the percentual growth was compared.

Fig 1

Named models (blue) and part of the search-region (yellow) for the exponent-pair of the best fitting growth model.

Fig 2

Growth data and best fitting growth curves in dimensionless coordinates (mass as a fraction of m_max, time as a fraction of t_infl) for chicken (red), alligators (green), and tenontosaurs (blue).

Fig 3

Growth rates relative to body mass for chicken (red), alligators (green) and tenontosaurs (blue) with time as a fraction of t_infl.

Fig 4

Optimal and near-optimal exponent-pairs for chicken (triangle and red area), alligators (upside triangle and green area) and tenontosaurs (circle and blue area). For better orientation, the exponent-pairs of three named models are plotted (blue).

Fig 5

Maximal growth rate, m´(t_infl), and mass at the inflection point, m_infl = m(t_infl), for near-optimal growth curves m(t) for chicken (red), alligators (green) and tenentosaurs (blue).