In an article entitled “A competitive network theory of species diversity” published in the April, 2011 issue of the Proceedings of the National Academy of Sciences (U.S.), Stefano Allesina and Jonathan Levine investigated how game and network theory can be used to understand interspecies competition and coexistence. Traditionally, species competing for the same resources are believed to be unable to coexist, as one would expect the best competitor to drive all the other species to extinction. However, Allesina and Levine hypothesized that if the competition for resources is intransitive; meaning, if different species are better at competing for different resources, then one might expect a stable coexistence of multiple species. This concept is very similar to how the game of rock, paper, scissors works: rock beats scissors, and scissors beats paper, but paper beats rock, allowing for all three strategies to be equally successful.
In order to prove this hypothesis, Allesina and Levine constructed networks composed of nodes representing hypothetical populations of different species, and directional edges representing competition events. The probability that an individual from one species outcompeted another was equal to the number of resources for which that species was a better competitor divided by the total number of limiting resources. If an individual “won” a competition event an arrow was drawn from the node representing the “loser” species to the “winner” species, and one individual was taken from the starting population of the “loser” species and placed in the population of the “winner” species. By running this simulation until a steady state equilibrium was reached, Allesina and Levine were able to figure out how the number of resources, the number of original species, and the competitive relationship between the species affected the final number and relative abundance of the competing species. What they found was that with very few limiting resources one species tended to dominate, and there was no stable coexistence equilibrium; however, with a large enough number of limiting resources, about half of the original number of species coexisted at equilibrium. They also found that the number of species existing at equilibrium was always an odd number.
The networks Allesina and Levine constructed combined a bit of graph theory and a bit of game theory to model species interactions. We did not see anything in class exactly similar to the intransitive model they created; however, the positive and negative edge networks we saw in class, and zero-sum game theory were vital in the creation of their models of species interaction.
Network theory is just beginning to enter the world of ecology, and Allesina and Levine’s paper is a prime example of how network and game theory could be used to model real world species interactions in a more powerful way than could be done previously.