Persistence Versus Representativeness
I argued above that Ferrier et al. perhaps inaccurately characterised their formula as estimating “the proportion of species represented”, and I questioned the conclusion of Zerger et al. (2013) that the method of Ferrier et al. (2004) and Allnutt et al. (2008) “allows estimation of the proportion of species expected to be retained in any defined region of interest,” These problems naturally extend from species-level to the features defined by PD-dissimilarities. Both Allnutt et al. (2008) and Ferrier et al. (2009) have suggested that the Ferrier et al. method contrasts with ED because it is intended to address expected persistence, and not just representation. While it seems doubtful that a measure that performs poorly in assessing representation will do well in assessing overall persistence, more work is needed to evaluate whether the Ferrier et al. method provides useful information about biodiversity persistence.
On a positive note, the persistence and the representation goals do not have to be addressed by different frameworks. One ED variant, departing from p-median, captures expected diversity or persistence in a “probabilistic ED” method:
…when we assign probabilities (of expected features persistence or 'presence') to sites … the p-median, which strictly depends on nearest neighbours, is relaxed, and the total estimated diversity now depends on summation over ordered nearest neighbours (Faith et al. 2004).
These probabilities form the analogue to the state or condition of habitat in each site j, given by sj, in the Ferrier et al. formula. Given the advantages of ED over p in the basic representation case, the “probabilistic ED” method deserves investigation as an alternative way to integrate state or condition of habitat in sites, for analysis of persistence.
These variants highlight the idea that the critical ingredient of the ED framework is unimodal response, refl the shared-habitat/shared-features model. Indeed, once we have an environmental space, under this model, we can simulate the sets of branches/features that would correspond, for example, to a nominated subset of sites. Faith et al. (2003) used this approach to map the distributions in geographic space of the hypothetical elements (species or features). This “biodiversity viability analysis” (BVA) uses this spatial information for each element for various biodiversity assessments. Thus, BVA translates information about any inferred element from ordination space to its implied distribution in geographic space (taking advantage of the link that environmental data for all areas provides from ordination space to geographic space). Mokany et al. (2011) provide a method that mimics the ED/BVA generation of hypothetical species (or other elements) based on unimodal response and related models. However, their method loses some useful information that BVA/ED derives from explicitly sampling from the environmental space under the unimodal response model. Further work is needed to evaluate these methods.