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.

The growth of domestic goats and sheep: A meta study with Bertalanffy-Pütter models

“…In recent papers, this difficulty was overcome (e.g. Brunner, Kühleitner, Nowak, Renner-Martin & Scheicher, 2019 ; Renner-Martin, Brunner, Kühleitner, Nowak & Scheicher, 2019 ) and the BP-model achieved an excellent fit to the data, resulting in significant improvements over previous studies (e.g. Brunner et al., 2019 ; Renner-Martin et al., 2019 ).…”

“…For each grid-point ( a, b ), the optimization of p, q , and c was done using a custom-made variant of the method of simulated annealing ( Vidal, 1993 ). The details and the Mathematica-code were outlined in other papers ( Brunner et al., 2019 ; Renner-Martin, Brunner, Kühleitner, Nowak & Scheicher, 2018 and 2019 ). Our strategy assured positive parameters ( p, q, c ) and therefore bounded growth functions.…”

Bertalanffy-Pütter models for avian growth

“…(For each bird, we optimized 37,454 to 98,903 grid-points, in the median 43,578.) We used Wolfram Mathematica 12 ( www.wolfram.com ) for our computations; for (explanations of) the Mathematica-code we refer to [ 27 , 28 ].…”

Bertalanffy-Pütter Models for the Growth of Tropical Trees and Stands

“…The data-fitting exercise for the BP-model is more challenging than for the Richards model, where standard optimization routines may run into difficulties [29]. In recent papers a method of data-fitting was developed for the BP-model [30] [31] [32] and [33]. This method was based on a grid-search, whereby we searched the best-fitting exponent-pairs (a, b) on a grid with step size 0.01 in both directions (Figure 1).…”