Ecosystems are characterized by numerous species that interact in complex ways. These can be described as ecological interaction networks. We have developed tools / metrics to analyse the specificity of such interactions between two parties, which can also be used for other kinds of networks. Some examples for such bipartite interactions:
The idea behind these metrics of "complementary specialization" (or "exclusiveness") d' and H2' is that links of each species are evaluated against each other, or against the availability of resources or partners. A species is most specialized (d'=1) if it has only exclusive links, and least specialised (d'=0) if it shares the links in the same proportions with all other "competitors". If all species behave highly exclusively, H2'=1 for the whole network, if they overlap as much as possible H2'=0.
Many other quantitative network metrics exist, and some of them are quite simple and more intuitive than the above, e.g. "partner diversity" or "interaction diversity" which are closely related to H2' (both based on Shannon entropy). However, all indices except d', H2' and Q have the disadvantage that they simply increase with the number of observations per species. This is undesirable when observations are limited, requiring appropriate corrections, e.g. null models or rarefaction. A very suitable null model has been proposed by Patefield in order to analyse contingency tables, a replacement for chi-square tests which are not allowed for large and poorly filled matrices. You can simply use this null model in conjunction with H2' instead of chi-square tests then (here or as "r2dtable" in R).
A formal definition of our network metrics is found here, more on comparisons and problems across network metrics here and (most readable) here. For relevance of metrics for conservation, see here. Analyses of many mutualistic networks are here and here. The tools were developed in close collaboration with my brother Nils.