Energy intake functions of ectotherms and endotherms derived from their body mass growth

TL;DR

This paper develops mathematical energy budget models for ectotherms and endotherms, deriving their energy intake functions from body mass growth, and validates these models against empirical data.

Contribution

It introduces a novel mathematical framework that explains energy allocation differences between ectothermic and endothermic vertebrates based on body mass growth.

Findings

Models produce energy intake patterns matching observed data.

Endotherms allocate more energy to heat production than growth.

Explains differences in energy intake between fish, reptiles, birds, and mammals.

Abstract

How animals allocate energy to different body functions is still not completely understood and a challenging topic until recently. Here, we investigate in more detail the allocation of energy intake to growth, reproduction or heat production by developing energy budget models for ectothermic and endothermic vertebrates using a mathematical approach. We calculated energy intake functions of ectotherms and endotherms derived from their body mass growth. We show that our energy budget model produces energy intake patterns and distributions as observed in ectothermic and endothermic species. Our results comply consistently with some empirical studies that in endothermic species, like birds and mammals, energy is used for heat production instead of growth. Our model additionally offers an explanation on known differences in absolute energy intake between ectothermic fish and reptiles and endothermic birds and mammals. From a mathematical point of view, the model comes in two equivalent formulations, a differential and an integral one. It is derived from a discrete level approach, and it is shown to be well-posed and to attain a unique solution for (almost) every parameter set. Numerically, the integral formulation of the model is considered as an inverse problem with unknown parameters that are estimated using a series of experiments/realistic data.