A further biodiversity index is proposed, based on taxonomic (or phylogenetic) related- ness of species, namely the ‘variation in taxonomic distinctness’ (VarTD, Λ+) between every pair of species recorded in a study. It complements the previously defined ‘average taxonomic distinctness’ (AvTD, ∆+), which is the mean path length through the taxonomic tree connecting every pair of spe- cies in the list. VarTD is simply the variance of these pairwise path lengths and reflects the uneven- ness of the taxonomic tree. For example, a species list in which there are several different orders rep- resented only by a single species, but also some genera which are very species-rich, would give a high Λ+ by comparison with a list (of equivalent ∆+) in which all species tended to be from different families but the same order. VarTD is shown to have the same desirable sampling properties as AvTD, primarily a lack of dependence of its mean value on the sample size (except for unrealistically small samples). Such unbiasedness is of crucial importance in making valid biodiversity comparisons between studies at different locations or times, with differing or uncontrolled degrees of sampling effort. This feature is emphatically not shared by indices related to species richness and also not by properties of the phylogeny adapted from proposals in other, conservation contexts, such as ‘average phylogenetic diversity’ (AvPD, Φ+). As with AvTD, the VarTD statistic for any local study can be tested for ‘departure from expectation’, based on a master taxonomy for that region, by constructing a simulation distribution from random subsets of the master list. The idea can be extended to sum- marising the joint distribution of AvTD and VarTD, so that values from real data sets are compared with a fitted simulation ‘envelope’ in a 2 d (∆+, Λ+) plot. The methodology is applied to 14 species lists of free-living marine nematodes, and related to a master list for UK waters. The combination of AvTD and VarTD picks out, in different ways, some degraded locations (low ∆+, low to normal Λ+) and the pristine island fauna of the Scillies (normal ∆+, high Λ+). The 2 indices are also demonstrated to be measuring effectively independent features of the taxonomic tree, at least for this faunal group (al- though it is shown theoretically that this will not always be the case). The combination of ∆+ and Λ+ is therefore seen to provide a statistically robust summary of taxonomic (or phylogenetic) relatedness patterns within an assemblage, which has the potential to be applied to a wide range of historical data in the form of simple species lists.
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