Network ecology: topological constraints on ecosystem dynamics

Ecological systems are complex assemblages of various species with interactions between them. The interactions can be even more important than the species them-selves for understanding how the whole system is functioning and organized. For the representation of the topological space of interspecic relationships, graph theory is a suitable mathematical tool: the network perspective and the various techniques of network analysis are more and more elaborated and invading ecology. Beyond a static view on networks, fundamental questions can only be answered if dynamical analyses are also made, and now it is clear that structural and dynamical studies must not "compete " but strongly complement each other. Our aim is to give a menu of classical and more recently suggested network indices and to discuss what do we know about their relations to ecosystem dynamics. Since ecologists have very diverse problems, they need diverse techniques and a good insight in matching the adequate method to a particular problem. The main question is how to link certain graph properties to understanding and predicting the behaviour of an ecosystem. We wish to contribute to bridging the gap between extreme structural and extreme dynamical views. Key words: community organization, food web, graph theory, ecosystem stability "Most of what is interesting about biological communities cannot be pinned, stued, pressed onto herbarium sheets