(Proposal submitted on June 13, 2000)
In 1972, Robert May showed that randomly generated food webs decreased in stability as they increased in complexity. This result was paradoxical to many ecologists who experienced the opposite pattern in nature. Recently, ecologists have revisited this question by exploring the dynamics of interactions, examining the stability properties of more realistic food web configurations and adding hierarchical structure to food webs. In a recent paper published in Nature, McCann and Hastings analyzed realistic dynamic food web configurations and showed that weak to intermediate links between species tended to dampen oscillations between consumers and resources, thus promoting stability. Although this latest attempt claims to have answered May's paradox, it is only a beginning for the largest food web they considered contained only four species. McCann's work is a step in the right direction but it follows in May?s flawed approach by not taking into account evolution.
While real food webs are not subject to the rules of natural selection and genetic drift that govern evolution at the level of the individual (it would be hard to imagine two food webs competing against each other), their composition at one instant in time is dependent on the previous compostion and so they can be thought to evolve through time. By building food webs from the ground up, as might occur in nature following a disturbance, we hope to build more realistic complex webs that may shed new light on the complexity-stability debate.
We begin with two species with randomly chosen interaction strengths. We then analyze the stability properties of this system. If it is unstable, we kill a species at random. Conversely, if it is stable, we add another species to the mix with a random number of links and randomly chosen interaction strengths. We then analyze the stability properties of the system and repeat the above process.
In the next part of this project, we will add Lotka-Volterra dynamics to the system. This is a much harder problem because the analytical toolkit for studying a system away from fixed points is not well developed especially at the level of complexity we will be exploring. In order to make this more tractable therefore, we will simulate the interactions on a computer. After adding species to food webs in a manner similar to that described above we will run the simulation for a certain number of time steps. If a species population density falls below a preset minimum population level, we will delete that species from the mix.
Finally we hope to incorporate competition for resources into our model food webs. Webs will be limited by the amount of abiotic resources available and thus evolve accordingly. This final step concludes what we feel is necessary to accurately describe food webs in the real world, namely evolution (historical dependence), dynamics of interaction and resources.
The following is a list of questions we have concerning our food web models: