Mutual information as a general measure of structure in interaction networks

Abstract

Entropy-based indices are long-established measures of biological diversity, nowadays used to gauge partitioning of diversity at different spatial scales. Here, we tackle the measurement of diversity of interactions among two sets of organisms, such as plants and their pollinators. Actual interactions in ecological communities are depicted as bipartite networks or interaction matrices. Recent studies concentrate on distinctive structural patterns, such as nestedness or modularity, found in different modes of interaction. By contrast, we investigate mutual information as a general measure of structure in interactive networks. Mutual information (MI) measures the degree of reciprocal matching or specialization between interacting organisms. To ascertain its usefulness as a general measure, we explore (a) analytical solutions for different models; (b) the response of MI to network parameters, especially size and occupancy; (c) MI in nested, modular, and compound topologies. MI varies with fundamental matrix parameters: dimension and occupancy, for which it can be adjusted or normalized. Apparent differences among topologies are contingent on dimensions and occupancy, rather than on topological patterns themselves. As a general measure of interaction structure, MI is applicable to conceptually and empirically fruitful analyses, such as comparing similar ecological networks along geographical gradients or among interaction modalities in mutualistic or antagonistic networks.