Game Theory in Food Webs

While some applications of network theory may seem less than obvious (offensive strategy in basketball, for example), most of us are quite familiar with the idea that ecosystems can be represented as networks.  Cartoon illustrations of “food webs”, as Carl Zimmer notes in a recent Yale E360 article, are standard fare for kids’ science textbooks.  (What Zimmer doesn’t note is that they make great poster board-centric elementary school projects: my food web poster was killed at the science fair.)

In spite of the status of food webs as a matter of common knowledge, they have not been subjects of rigorous analysis until recently.  Zimmer points to the fact that, for decades, many biologists found detailed graphs of ecological networks to be too dense to be meaningfully analyzed.  This changed with the development of the kind of network theory that we’re now studying in this class.

For example, game theory helps explain the structure of networks of plants and pollinating insects and how this network encourages biodiversity.  These networks take the form of small-world networks; most species are connected to only a few other species in highly specialized ways, while a handful of species are connected to a large number of other species.  These “generalizers”, as Zimmer calls them, act as hubs that connect otherwise distant sections of the graph.

Most interesting, I think, is the game-theoretical side of these networks.  Zimmer gives an example of a generalizer moth that pollinates specialized plants. He notes that ecosystems are competitive, so it might seem natural to believe that a plant species would do better to have a dedicated, specialized pollinating insect, one that would not spend it’s efforts pollinating other plants.  This would appear to be a zero-sum game, with any pollination of other plant species happening at the expense of competing species.

The empirical data shows, however, that this tends not to be the case.  Specialized plants tend to pair with generalized insects and vice versa.  It might be more accurate to describe the game thusly: The Plant and the Moth both have two strategies, specialize and generalize.  If both specialize, they both receive the lowest payoff.  This is because the moth, being specialized, will have a limited food supply and therefore there will be a limited number of moths to pollinate the plant.  The plant will also have a limited number of moths to help it reproduce, limiting the number of plants and the moths’ food supply.  This limits the ability of either to flourish.  On the other hand, if either or both species generalize, they will both benefit greatly.  The species that generalizes will flourish (by merit of its ability to interact with more than one species), and the other species will receive the benefit of either greater food supply or greater reproductive capacity.  What is interesting here is that specialize-specialize is the only low payoff strategy, while all other combinations benefit both players significantly.

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