Abstract
Shannon’s entropy measure is a popular means for quantifying ecological diversity. We explore how one can use information-theoretic measures (that are often called indices in ecology) on joint ensembles to study the diversity of species interaction networks. We leverage the little-known balance equation to decompose the network information into three components describing the species abundance, specificity, and redundancy. This balance reveals that there exists a fundamental trade-off between these components. The decomposition can be straightforwardly extended to analyse networks through time as well as space, leading to the corresponding notions for alpha, beta, and gamma diversity. Our work aims to provide an accessible introduction for ecologists. To this end, we illustrate the interpretation of the components on numerous real networks. The corresponding code is made available to the community in the specialised Julia package EcologicalNetworks.jl.
Highlights
The use of networks to address ecological questions has become increasingly popular [1,2,3]
We introduce a conversion to effective numbers to clarify the relation between entropy and diversity, and Entropy 2021, 23, 703 to prevent misinterpretation of entropy as a diversity index
Three fictive interaction networks with extreme distributions are added to the triangle shown in Figure 4 in order to illustrate the use of the balance equation and the entropy triangle
Summary
He used information theory to analyse the stability of ecosystems by computing the entropy of the energy transfers in food webs. The use of diversity indices, including entropy, has been criticised on many occasions, since applying different indices to the same ecological community has resulted in contradictory outcomes [23]. This has led to several incorrect conclusions, causing some ecologists to mistrust information theory [16]. Barplots are especially useful in visualising the relative importance of the different information-theoretic components of a given interaction network, while the entropy triangle is especially suited to comparing multiple networks. We illustrate the proposed methodology on several types of ecological networks
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