What do beta diversity components reveal from presence-absence community data? Let us connect every indicator to an indicandum!

Abstract Extracting meaningful information from community data is among the most challenging tasks of community ecology. Whereas presence-absence data matrices are commonly used in different analytical frameworks, we argue that the conceptual distinction among community patterns (on which inference is made), pairwise pattern components (PPCs, which reflect the unique response of communities for pairs of sites), and measures (which quantify a relevant property of PPCs), liberates our field from the possible misinterpretation of results derived from existing approaches. The novel concept suggested here is the PPC, which can be efficiently used to identify response types of communities, thereby shortening the list of potential explanatory processes. Consequently, the introduction of PPCs supports the analysis of real data sets and links patterns to ecological hypotheses. Based on PPCs, we proposed a new partitioning of beta diversity (SET framework) into intersection (I) of nestedness and beta diversity and the relative complement (RC) of nestedness in beta diversity. We performed an algebraic assessment of three existing partitioning frameworks of beta diversity: the BAS (Baselga, 2010, Global Ecology and Biogeography), POD (Podani and Schmera, 2011 Oikos) and SET (present paper). We found that when a community pattern is anti-nested, which is characterized by the presence of both Replacement and Richness difference PPCs, the BAS framework falsely indicates a 100% share of replacement from beta diversity. In contrast, the POD and SET partitioning procedures detect the presence and the proper size of PPCs for all types of community patterns. In conclusion, we argue that breaking down community patterns into PPCs and then quantifying the importance of these PPCs form a straightforward strategy to extract information from community data under a broad range of circumstances.