Friday, May 28, 2010

Preferential attachment in ecosystem mutalism

Tree, vine, and bromeliad

In a previous post I made an analogy to illustrate the evolutionary pattern of "attenuated parasitism" -- a model for how antagonistic agents can evolve cooperation. I created that analogy while sitting on the edge of the Puerto Rican rain forest thinking about how it is that vines and trees can co-exist -- after all, being a vine is such a good strategy that it seems like they should have killed all the trees (and themselves) by now! That same day I had another idea that I didn't get around to writing down: such cooperative mechanisms should, given time, lead the forest to become one giant interconnected web of mutualist interactions.

The argument is simple. If a vine and a tree form an alliance while the same tree specie and some other specie, say, a bromeliad also form an alliance then it is logical that the vine and the bromeliad will have an increased probability of forming an alliance of their own owing to the simple fact that they co-occur in the same location (around the tree) more frequently than other random specie pairings. A small interaction network like this would likely grow by accumulating more and more interactions by the same mechanism.

There is a mathematical theory of such network growth called "preferential attachment" (also known by about half a dozen other names). The study of such networks dates back to at least Yule, 1925 who shows that such processes build what came to be called "scale free networks". Such networks end up with many more hyper-connected nodes than one might intuit. For example, the tree in the previous discussion is likely to become one such hyper-connected node with many, many mutualistic interactions both literally and metaphorically hanging off of it.

It is easy to imagine how the growth of such cooperative interdependence would tend to drive an ecosystem towards a single giant interconnected web of specialists. It is conversely hard to imagine how an outside generalist specie could successfully invade such a well-connected ecosystem. Therefore one would expect to see more internal differentiation from species whose interconnections into the web are already established as opposed to generalist invasive species whose ancestors came from the outside.

I haven't studied the field evidence well enough to know if this idea is supported or not. Following are a few random Google hits on the subject that I've only glanced at long enough to think that there's plenty of room for theory development in this field!