Corso Gilberto, Ferreira Gabriel M F, Lewinsohn Thomas M
Departamento de Biofísica e Farmacologia, Centro de Biociências, Universidade Federal do Rio Grande do Norte (UFRN), Natal-RN 59072-970, Brazil.
Departamento de Biologia Animal, C.P. 6109, Instituto de Biologia, Universidade Estadual de Campinas (UNICAMP), Campinas-SP 13083-970, Brazil.
Entropy (Basel). 2020 May 7;22(5):528. doi: 10.3390/e22050528.
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.
基于熵的指数是衡量生物多样性的长期指标，如今用于评估不同空间尺度上的多样性分配。在这里，我们探讨两组生物之间相互作用多样性的测量，例如植物与其传粉者之间的相互作用。生态群落中的实际相互作用被描绘为二分网络或相互作用矩阵。最近的研究集中在不同相互作用模式中发现的独特结构模式，如嵌套性或模块性。相比之下，我们将互信息作为交互式网络结构的一般度量进行研究。互信息（MI）衡量相互作用生物之间的相互匹配或专业化程度。为了确定其作为一般度量的有用性，我们探索：（a）不同模型的解析解；（b）互信息对网络参数的响应，特别是大小和占有率；（c）嵌套、模块化和复合拓扑中的互信息。互信息随基本矩阵参数而变化：维度和占有率，可据此对其进行调整或归一化。拓扑之间的明显差异取决于维度和占有率，而不是拓扑模式本身。作为相互作用结构的一般度量，互信息适用于概念上和经验上富有成效的分析，例如沿着地理梯度比较相似的生态网络或互利或拮抗网络中的相互作用模式。
