Comparing growth patterns of three species: Similarities and differences.

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.

Best fitting tumor growth models of the von Bertalanffy-PütterType.

Background: Longitudinal studies of tumor volume have used certain named mathematical growth models. The Bertalanffy-Pütter differential equation unifies them: It uses five parameters, amongst them two exponents related to tumor metabolism and morphology. Each exponent-pair defines a unique three-parameter model of the Bertalanffy-Pütter type, and the above-mentioned named models correspond to specific exponent-pairs.

Best-fitting growth curves of the von Bertalanffy-Pütter type.

Introduction: A large body of literature aims at identifying growth models that fit best to given mass-at-age data. The von Bertalanffy-Pütter differential equation is a unifying framework for the study of growth models.

Problem: The most common growth models used in poultry science literature fit into this framework, as these models correspond to different exponent-pairs (e.

Optimal and near-optimal exponent-pairs for the Bertalanffy-Pütter growth model.

The Bertalanffy-Pütter growth model describes mass at age by means of the differential equation d/d = * m  -  * . The special case using the von Bertalanffy exponent-pair = 2/3 and = 1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). Fitting VBGF to size-at-age data requires the optimization of three model parameters (the constants , , and an initial value for the differential equation).

On the exponent in the Von Bertalanffy growth model.

Von Bertalanffy proposed the differential equation '() =  × ()  -  × () for the description of the mass growth of animals as a function () of time . He suggested that the solution using the metabolic scaling exponent = 2/3 (Von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit.