Quantifying and estimating ecological network diversity based on incomplete sampling data.

An ecological network refers to the ecological interactions among sets of species. Quantification of ecological network diversity and related sampling/estimation challenges have explicit analogues in species diversity research. A unified framework based on Hill numbers and their generalizations was developed to quantify taxonomic, phylogenetic and functional diversity. Drawing on this unified framework, we propose three dimensions of network diversity that incorporate the frequency (or strength) of interactions, species phylogenies and traits. As with surveys in species inventories, nearly all network studies are based on sampling data and thus also suffer from under-sampling effects. Adapting the sampling/estimation theory and the iNEXT (interpolation/extrapolation) standardization developed for species diversity research, we propose the iNEXT.link method to analyse network sampling data. The proposed method integrates the following four inference procedures: (i) assessment of sample completeness of networks; (ii) asymptotic analysis via estimating the true network diversity; (iii) non-asymptotic analysis based on standardizing sample completeness via rarefaction and extrapolation with network diversity; and (iv) estimation of the degree of unevenness or specialization in networks based on standardized diversity. Interaction data between European trees and saproxylic beetles are used to illustrate the proposed procedures. The software iNEXT.link has been developed to facilitate all computations and graphics. This article is part of the theme issue 'Detecting and attributing the causes of biodiversity change: needs, gaps and solutions'.