The robustness of keystone indices in food webs.

Species that have outstanding importance in the functioning of a community are called keystone species. Network indices are increasingly used to identify them, e.g. for conservation biological purposes. The problem is that the calculation of these indices is based on the particular network model of the studied food web, which can include network construction errors. For example, additional, unnecessary trophic links can be built in, or, to the contrary, functional links can be left out. What is the effect of such errors on the result of network analysis, e.g. the centrality values of species? Can you rely on the importance rank of species that you calculated? We developed a robustness measure (R) for network indices to answer these questions. R is proportional to the likeliness that the importance rank of nodes in the given network according to a given index would not change due to possible errors in network construction. For calculating R, first the maximum expected error (P) has to be computed which represents the potential range of error in estimating the keystone index in question. Basically, R is calculated by comparing P to the keystone indices of species to assess the reliability of the importance rank of species based on the network model. We calculated the robustness of 13 different structural indices in 26 food webs of different size to test the P and R values. We found that fragmentation indices and the number of dominated nodes can be characterized by quite low R values, while betweenness, topological importance, keystoneness and mixed trophic impact have high R values, which means that they are relatively more reliable for assessing the importance rank of species in an uncertain network model. However, as R was found to be very variable, depending on the topology of a given network, a detailed description is provided for performing the actual calculations case-by-case.