A taxonomic distinctness index and its statistical properties.
This paper explores the statistical sampling properties of Δ, the taxonomic diversity index, and Δ*, the taxonomic distinctness index. Taxonomic diversity is seen to be a natural extension of a form of Simpson's index, incorporating taxonomic (or phylogenetic) information. Importantly for practical comparisons, both Δ and Δ* are shown not to be dependent, on average, on the degree of sampling effort involved in the data collection; this is in sharp contrast with those diversity measures that are strongly influenced by the number of observed species. The special case where the data consist only of presence/absence information is dealt with in detail: Δ and Δ* converge to the same statistic (Δ+), which is now defined as the average taxonomic path length between any two randomly chosen species. Its lack of dependence, in mean value, on sampling effort implies that Δ+ can be compared across studies with differing and uncontrolled degrees of sampling effort (subject to assumptions concerning comparable taxonomic accuracy). This may be of particular significance for historic (diffusely collected) species lists from different localities or regions, which at first sight may seem unamenable to valid diversity comparison of any sort. Furthermore, a randomization test is possible, to detect a difference in the taxonomic distinctness, for any observed set of species, from the 'expected' Δ+ value derived from a master species list for the relevant group of organisms. The exact randomization procedure requires heavy computation, and an approximation is developed, by deriving an appropriate variance formula. This leads to a 'confidence funnel' against which distinctness values for any specific area, pollution condition, habitat type, etc., can be checked, and formally addresses the question of whether a putatively impacted locality has a 'lower than expected' taxonomic spread. The procedure is illustrated for the UK species list of free-living marine nematodes and sets of samples from intertidal sites in two localities, the Exe estuary and the Firth of Clyde.