Topological approaches to food web analyses: a few modifications may improve our insights

The topological analysis of food webs is a recently reinvigorated and rapidly growing area of inquiry in community ecology (Williams and Martinez 2000, Sole and Montoya 2001, Camacho et al. 2002, Montoya and Sole 2002). Topological studies assess system properties using the number and distribution of connections among nodes in an interconnected network. Analysis of a food web as a network of links (feeding relationships) and nodes (species) is not a new approach (MacArthur 1955, Gardner and Ashby 1970, Pimm 1979); however recent advances by physicists in the study of complex networks have revived this area of theoretical community ecology. Here we discuss a few characteristics of food webs that may cause them to respond differently to node loss than other types of networks. We also suggest ways in which empiricists can provide data to test predictions derived from complex network theory. Complex network analysis has shown that the sensitivity of a network to node loss depends on the frequency distribution of connections among nodes (Albert et al. 2000). Current theoretical developments suggest that networks can be classified into two broad categories based on the frequency distribution of links: exponential or scale-free. Each node in an exponential network has a similar number of links to other nodes. The frequency distribution of the number of links per node in this type of network has an exponential decay (Albert et al. 2000). Because nodes in an exponential network have similar numbers of links, the loss of any given node from this type of network causes a monotonic increase in the number of links required to connect any two nodes in the network. In contrast, a scale-free network has a few nodes with a large number of links and many nodes with only a few links. Although connectivity in scale-free networks does not decrease with the random loss of nodes as in an exponential network, scale-free networks are extremely sensitive to the loss of highly connected "hub" nodes (Albert et al. 2000). In recent work, researchers have used frequency distribution models to describe the properties of a broad array of complex networks such as social networks (Watts and Strogatz 1998), the World Wide Web (Albert et al. 1999), transportation networks (Banavar et al. 1999), and enzymatic pathways (Jeong et al. 2000). The obvious extension of this theory to food web dynamics has renewed interest in the topology of trophic webs. Williams and Martinez (2000) show that a simple topological model can reproduce properties of complex food webs. But when we examine empirical webs, does the frequency distribution of trophic connections show a general pattern? If so, is the structure of food webs generally exponential or scale-free? A recent assessment of several food webs suggests that they share the scalefree properties of many other complex networks, implying that their structure should be resistant to random attacks but quite sensitive to loss of "hub" species (Sole and Montoya 2001). The general applicability of recent findings in complex network theory to food web studies depends on whether topological descriptions capture key aspects of communities and ecosystems such as the flow of energy or factors regulating populations. An increase in biological realism may be merged with suitable data in future food web analyses to better understand processes structuring communities. Further work in this area will allow us to determine the appropriate role of complex network theory in the modeling and conservation of ecological communities.