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.
Highlights
Entropy models and measures have been applied in a variety of areas in ecology, such as ecological genetics [1], macroecology [2], landscape ecology [3] and ecological economics [4]
By combining Equations (4) and (6), it is possible to show that H20, a widely used metric of specialization in ecological networks [34], is the mutual information normalized by its maximal value, given the marginal totals of the matrix: H20 =
The chief goal of this study was to assess the suitability of mutual information as the basis for a general measure of reciprocal correspondence in a bipartite set of interacting entities, notably biological species
Summary
Entropy models and measures have been applied in a variety of areas in ecology, such as ecological genetics [1], macroecology [2], landscape ecology [3] and ecological economics [4]. The second is the measurement of interactions between species in ecological networks, and is the subject for the current paper. To examine entropy and its components in interactive systems we represent them here as bidimensional matrices, with cross-references to their equivalents in network terminology that are widely used in the current ecological literature. We scrutinize the effect of an array of matrix (or network) attributes on mutual information, starting from primary or first-order parameters of simple patterns [27] and progressing to more complex structures, notably topologies which have been intensively investigated by ecologists in recent years [26,28]. We do not deal with a global entropy or information measure for a network, but rather to the mutual information between the two marginal sets that constitute a bipartite network
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