Back in 1972 Robert May wrote a paper that sparked a litany of research on the relationship between the complexity of a community and its associated stability. Previously the reigning paradigm had been developed by ecologists such as Elton and MacArthur who noted that the communities commonly observed in nature tended to be complex, with many pathways for energy to flow up trophic levels. Because of redundancy in energy pathways they believed that these systems should be stable, especially since obviously complex communities were still around, and not collapsing into instability.
May, however, generated randomly assembled communities (using SxS matrices) with random interaction strengths. He then systematically varied number of species, mean interaction strength, and the connectance (number of realized links) of these randomly generated webs. For each web that was generated May analyzed the stability based on the eigenvalues of the matrix (where in order to be stable the real part of the maximum eigenvalue must be negative). He found that as number of species, mean interaction strength, and/or connectance was increased, the stability of the system declined, results diametrically opposed to the reigning paradigm, and observation.
Obviously there are a number of issues involved with this type of analysis. Most significant is that real communities are not random, they have very specific topological structure that develops through community assembly and evolutionary processes. May noted that this was the case, however, and wrote that randomly assembled communities should serve as a null model and that future research should be devoted to finding those deviant strategies used by communities that allow them to be stable. To be fair, in the seventies in terms of network research, random networks were gaining a lot of steam in the world of physics and math as a result of the pioneering work of Erdos and Renyi.
So, this paper did what May had apparently intended, and it sparked a great deal of research over the past thirty years investigating why real communities are stable. Of particular interest is the research on topology of the network, showing how such architectures as nestedness and modularity can influence stability (mostly by altering the interaction strength combinations). Other work has focused on interaction strengths, demonstrating that most interactions are weak, as well as external influences (e.g. subsidies sensu Polis and Strong 1996) and other properties of networks.
What has surprised me most, however, as I read through the community ecology/food web literature is a surprising lack of knowledge about another paper that came out about a year after May’s by Alan Roberts. Roberts noted that May’s analysis allowed for what he called “ghost species,” those species whose equilibrium population size was negative (e.g. they would just go extinct). Clearly communities with such species are not likely to be stable, and communities with more species are more likely to have these ghosts. Critically, Roberts re-did May’s simulation with the added filter of feasibility. A feasible community was one whose equilibrium population densities are positive. When only feasible random communities were analyzed for their stability properties, May’s results were found to be exactly opposite. Roberts had clearly demonstrated that May was wrong (in 1974), yet his work is rarely cited despite being published in Nature. According to Google Scholar May 1972 is cited just over 1000 times (662 in Web of Science), while Robert’s paper has 116 (80 from Web of Science).