A taxonomic distinctness index and its statistical properties

1. For biological community data (species-by-sample abundance matrices), Wa rwick & Clarke (1995) defined two biodiversity indices, capturing the struc ture not only of the distribution of abundances amongst species but also th e taxonomic relatedness of the species in each sample. The first index. tax onomic diversity (Delta), can be thought of as the average taxonomic 'dista nce' between any two organisms, chosen at random from the sample: this dist ance can be visualized simply as the length of the path connecting these tw o organisms, traced through (say) a Linnean or phylogenetic classification of the full set of species involved. The second index, taxonomic distinctne ss (Delta*), is the average path length between any two randomly chosen ind ividuals, conditional on them being from different species. This is equival ent to dividing taxonomic diversity, Delta, by the value it would take were there to be no taxonomic hierarchy tall species belonging to the same genu s). Delta* can therefore be seen as a measure of pure taxonomic relatedness . whereas Delta mixes taxonomic relatedness with the evenness properties of the abundance distribution. 2. This paper explores the statistical sampling properties of Delta and Del ta*. Taxonomic diversity is seen to be a natural extension of a form of Sim pson's index, incorporating taxonomic (or phylogenetic) information. Import antly for practical comparisons, both Delta and Delta* are shown not to be dependent, on average, on the degree of sampling effort involved in the dat a collection; this is in sharp contrast with those diversity measures that are strongly influenced by the number of observed species. 3. The special case where the data consist only of presence/absence informa tion is dealt with in detail: Delta and Delta* converge to the same statist ic (Delta(+)), which is now defined as the average taxonomic path length be tween any two randomly chosen species. Its lack of dependence, in mean valu e, on sampling effort implies that Delta(+) can be compared across studies with differing and uncontrolled degrees of sampling effort (subject to assu mptions concerning comparable taxonomic accuracy). This may be of particula r significance for historic (diffusely collected) species lists from differ ent localities or regions, which at first sight may seem unamenable to vali d diversity comparison of any sort. 4. Furthermore, a randomization test is possible, to detect a difference in the taxonomic distinctness, for any observed set of species. from the 'exp ected' Delta(+) value derived from a master species list for the relevant g roup of organisms. The exact randomization procedure requires heavy computa tion, and an approximation is developed, by deriving an appropriate varianc e formula. This leads to a 'confidence funnel' against which distinctness v alues for any specific area, pollution condition, habitat type, etc., can b e checked, and formally addresses the question of whether a putatively impa cted locality has a 'lower than expected' taxonomic spread. The procedure i s illustrated for the UK species list of free-living marine nematodes and s ets of samples from intertidal sites in two localities, the Exe estuary and the Firth of Clyde.