This is a lovely simple article: How Large Should Whales Be? It’s a simple article because it builds on an earlier article about the sizes of land mammals.
The model in the article rests on some stylized facts about animal size. Fossils show that over time species tends to get larger; we can presume there is a benefit to being larger. Warm blooded animals have a minimun size; if your tiny it’s hard to keep warm. Most warm blooded animals are about the size of a large rat (or squirrel). Which doesn’t really make sense since we already said that larger is better.
The tension between the advantages of size and the fact that most warm blooded animals aren’t huge is – they say – about extinction. On the one hand it takes time to evolve into something huge and on the other hand the speicies is always at some risk of going extinct. This is almost enough to build a model that explains the distirbution of sizes for warm blooded animals. We need only one more detail – i.e. that larger animals are more likely to go extinct. I gather the model works extremely well.
The paper just extends the model from land to sea. Showing that the model works very nicely for whales and such. It’s harder to keep warm in the water, so the minimum size for a aquatic mammal is larger than that of a land mammal. My favorite factoid from the paper is that land mammals moved into the water as soon as grew larger than the warmblooded aquatic minimum.
Why are larger species are more likely to go extinct? It’s bit counter intuitive. Size has a short term advantage, otherwise they wouldn’t evolve toward larger sizes. A large animal has, in effect, a larger bank account and that let’s him buffer life’s vicissitudes. But why would it be good in the short term and bad in the long term. A possible logic is that any species resides in some niche, and it’s a bigger then you get a smaller population filling the niche. Small populations are easier to wipe out.
I don’t really see any hope that this model is useful in other contexts closer to my interests: firm size, wealth distributions, city size, etc. Their size distributions don’t look like that illustration, not at all. They have much longer tails to the right. Suggesting the extinction events are rare for them. But it’s an amusing exercise to try. Look for the analogies to theromodynamics, evolution, and extinction events.