Energy budget models

In a previous post I mentioned a talk I gave on dinosaurs and promised more information at a later date. Now a paper related to this has appeared and I will keep the promise. A basic issue is the way in which dinosaurs regulated their body temperature. The traditional idea was that they were cold-blooded (exotherm) like crocodiles. Later it was suggested that they might have been warm-blooded (endotherm) like birds or mammals. Then it was claimed that this was unrealistic and that they were mesotherm. This means something in between exotherm and endotherm, with a limited control of body temperature. There do exist organisms like this, a notable example being the tuna. I was involved in a project with Jan Werner, Eva Maria Griebeler and Nikos Sfakianakis on this subject. The first published result coming from this effort has now appeared (J. Theor. Biol. 444, 83).

The long-term goal of this project is to understand the evolution of warm-blooded animals in connection with the evolution of birds from dinosaurs. This involves understanding the way in which animals allocate energy to different tasks. How much do they use for generating body heat and how much do they use for other tasks such as maintenance or reproduction? A first step is to find a parametrization of the possible energy allocation strategies. In other words we want to identify suitable variables which could be used to describe the evolutionary process we want to understand. This is the content of the paper which has just appeared. At this point it might be asked how we can find out about the energy consumption of dinosaurs at all. It turns out that there are general relations known between the energy consumption of an animal and its growth rate over its lifetime. Thus the growth curve of a dinosaur gives indirect information about its energy consumption. But how can we get information about the growth curve? This is something I learned in the course of this project. The large bones of dinosaurs exhibit annual growth rings like those known for trees. The rings are of different thicknesses and thus give information on the growth rate in different years.

The paper does not contain a detailed dynamic model of the energy use of an animal over its lifetime. Instead it introduces a set of possible time evolutions depending on a finite number of parameters and then tests (by numerical methods) whether these suffice to reproduce the experimental growth curves of a number of animals with sufficient accuracy. It is also checked that the results obtained are consistent with known facts about the age of sexual maturation of the different species. It turns out that the mathematical model is successful in fitting the experimental constraints. It is found that, as expected, the model predicts that exotherms continue to grow as long as they live while endotherms stop growing at a time comparable to the age of sexual maturity.

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