Ecosystems, and the biological diversity they harbor, are complex things. Yet simple mathematical models can often capture important features and teach us about their dynamics.
You might once have learned about food chains in school. For example, plants producing energy from the sun are eaten by rodents which are preyed on by owls. That’s a food chain with three links. Because just about everything has some kind of predator or parasite or other natural enemy, and just about everything must compete for resources of some kind, let’s focus on the middle link in this chain.
To study how many species can be supported in a middle link of such a chain, think first of two species. If each one can invade the system with the other species present, they can coexist. A simple model proposed early in the 20th century by Alfred Lotka and Vito Volterra can be solved for when two species would coexist, increasing biodiversity.
But this model leaves out a major piece of how animals function in the world around them: behavior. What if both kinds of rodents learn to hide from the owls under plants? Does it make them more or less likely to coexist?
In research I did with my doctoral adviser, Peter Chesson, published online recently by The American Naturalist, we show that the answer depends on how much those animals overlap in their resource requirements, like the types of food they like to eat, and in their vulnerability to different predators. When both prey can avoid predators, if they need exactly the same types of plants to survive and ground to dig their burrows, one may drive the other extinct. But if they are more different ecologically in their resource use than in which owls prey on them, then avoiding owls could make them even better able to coexist. (In an appendix, we even show how this scales to more than two species.)
I started this research in 2009 as a brand new graduate student, and worked on it off-and-on for the last decade. Peter’s guidance on this project taught me how to do research, and how to present it and to write about it.
You can see a plain-language summary of article here, or download the paper itself with all the equations here. Feel free to email me for a copy if you don’t have a university hook-up to access it without paying an arm and a leg.