Thermodynamic equilibria of animals with envirrnment, Porter and Gates (1969)

In which two scientists endeavor to prove that animals do not, in fact, violate the laws of thermodynamics.

It is interesting to think of this paper as the authors sought to include it, demonstrating three concepts that were being explored in ecology at the time. Using mathematical models to better understand factors that might affect organisms in real life. Using physical models to try and recreate at least a simulacrum of the study organism and be able to analyze factors that affect them. Lastly, the idea of a "climate space" which we have been talking about through a lot of these paper. The idea behind this is the climate part that N-dimensional hypervolume that we consider when we are thinking about a niche.

The paper starts out talking about the idea of the climate space right away and gives us the first four dimensions of the hypervolume they will be considering: radiation, wind, air temperature, and humidity. These four factors are a pretty good approximation of climate. I am sure there are a number of other things that we could all come up with that might go in to climate but almost everything that goes into what a climate is comes from these four factors. These abiotic factors affect three factors they consider on the animal: body temperature, rate of moisture loss, and metabolic rate. They are analyzing the animals to be part of a steady state system and fully admit that this is not necessarily the case in the wild. But, the idea behind it is sound. Over a long period, the animal must be in a steady state. To not be in a steady state would mean that the animal was either cooling or warming over the long term. This is fairly contrary to what we know about animals, barring some age-based body temperature differentials.

These ideas about what goes into and out of an animal form this idea in the paper called the "energy budget" and this is just the idea that Energy IN = Energy OUT. But what they are really trying to do is to determine what the parts of these in and out equations. A quick rundown of the variable might be helpful.

Energy In

• Metabolic Rate
• Radiation Absorbed

Energy Out

• Epsilon-sigma-Tr^4 is the energy lost by radiation of the animal
• hc(Tr-Ta) is the energy lost by convection coefficient
• Eex is the energy lost from expiration
• Esw is the energy lost to sweating
• C is the energy lost by conduction to substrates
• W is the work done by the animal

The reset of this section is talking about how they obtained these values and decided on specific ones. It discusses some other factors (like color) that will have to go into calculating these values and discusses the effect of size on things like the convection coefficient.

In the next section, Heat Transfer Within The Animal, Porter and Gates go on to talk about a really important part of how animals interact with their environment, their adaptations to the environment around them. The are specifically concerned with the fat layer and the feather/fur layer that many animals have to help them adapt to different climates. Since they are treating all animals as cylinders, they look at the idea of concentric cylinders with the heat generating stuff in the middle most cylinder, a cylinder of fat around that, and a cylinder of feathers/fur on the outermost layer. These approximations give them a means to talk about how animals adapt to their environments to prevent or enhance heat loss.

This section leads into the next two sections which are more explanation of the equations. Specifically they talk about the energy that can be exchanged on the surface of the animal and the radiation that will be absorbed on the surface of the animal. These are both a function of the shape(cylinder)/size of the animal, and the energy exchange also has to do with the idea of the concentric cylinders that they are using as their animal model.

Finally they get in to their modeling of different animal's climate spaces. Using molds of animals as well as mathematical approaches, they took measurements of the energy absorbed by animals at different temperatures and amount of radiation absorbed. They admit that some things have to be known before their analysis can work and that animals can change some of these values about themselves, but they are still confident, and rightfully so, that their calculations and experimentation can show some valuable results. In their analysis they are able to find temperature ranges and sun radiation absorptions that would let an animal live in the temperatures that are within it physiological range. They do this with a number of animals (iguana, shrew, finch, pig, etc.) as well as some theoretical animals, showing that it works and can be extrapolated for other organisms.

In conclusion, they are defining their climate spaces as a three dimensional space of radiation absorbed, wind speed, and ambient temperature. While we know that there are definitely more factors, this is a really great step towards understanding the fundamental niche of an organism. This paper shows methodological advancements in a way that we haven't really seen before, using both mathematical models as well as physical models to test concepts. These two modeling methods are still used extensively today.