Exploring Network Space with Genetic Algorithms: Modularity, Resilience, and Reactivity

Abstract

The relationship between stability and complexity in food webs was originally addressed with random networks of links. Non-random structures are evident in data, and in webs resulting from a variety of modeling approaches, including assembly and coevolution. As a basis for interpreting the population dynamics of such networks, a better understanding is needed of the large space of possible structures and their associated dynamical properties. We illustrate here the use of genetic algorithms to explore this large space, by focusing on two dynamical properties related to the stability of equilibria: resilience and reactivity, for long- and short-term responses of the system, respectively. These properties define the "fitness" criteria used for the search of the structural space. We analyze the resulting patterns of clustering and interaction strength distributions in the most resilient and less reactive networks, relative to random ones. Historically, the effect of network modularity on long-term stability has been of interest but it still remains theoretically unclear and empirically controversial. Our main finding is that modularity in community matrices relates to short-term responses in the transients. We discuss related recent work on clustering and complexity measures (from information theory) obtained for large networks in the brain. Similar approaches to the one presented here, albeit more computationally intensive, should be applicable to the nonlinear dynamics of ecological networks.