Expected Distinctness Tests

The construction of taxonomic distinctness indices from simple species lists makes it possible to address another of the desirable features of a biodiversity measure: there is a potential framework within which these measures can be tested for departure from expectation. This envisages a master list or inventory of species encompassing the appropriate region/biogeographic area, from which the species found at one locality can be thought of as drawn. For example, Figure 4 uses the entire British faunal list of free-living marine nematodes, a total of 395 species identified to date. The species complement at any particular

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Figure 4 Histograms of simulated AvTD, from 999 sublists drawn randomly from a UK master list of 395 species of freeliving nematodes. Sublist sizes of (a) m = 122, (b) m = 112, correspond to the observed numbers of species in the Exe (a) and Clyde (b) surveys of sandflats. Measured A+ at each location is indicated by an arrow: the Exe value is central but the null hypothesis that AvTD for the Clyde equates to that for the UK list as a whole is clearly rejected.

m = 112 species

82 74 75 76 77 78 79 80 81 82 Average taxonomic distinctness, A+

Figure 4 Histograms of simulated AvTD, from 999 sublists drawn randomly from a UK master list of 395 species of freeliving nematodes. Sublist sizes of (a) m = 122, (b) m = 112, correspond to the observed numbers of species in the Exe (a) and Clyde (b) surveys of sandflats. Measured A+ at each location is indicated by an arrow: the Exe value is central but the null hypothesis that AvTD for the Clyde equates to that for the UK list as a whole is clearly rejected.

locality and/or historic period (e.g., in Figure 4 the unpolluted Exe estuary and the putatively impacted Firth of Clyde) can be compared with the master list, to ask whether the observed subset of species is representative of the biodiversity expressed in the full species inventory. Clearly, such a comparison is impossible for species richness S since the list at one location is automatically shorter than the master list. Also, comparison of S between different localities (or historic periods) is invalidated by the inevitable differences in sampling effort in constructing the lists for different places (or times). However, the key point here is that AvTD (a+) of a randomly selected sublist does not differ, in mean value, from AvTD for the master list. So, localities that have attracted differing degrees of sampling effort are potentially directly comparable, with each other and with a+ for the full inventory. The latter is the expected value for average distinctness from a defined faunal group, and reductions from this level, at one place or time, can potentially be interpreted as loss of biodiversity. Furthermore, there is a natural testing framework for how large a decrease (or increase) from expectation needs to be, in order to be deemed statistically significant. For an observed set of m species at one location, sublists of size m are drawn at random from the master inventory, and their AvTD values computed. From, say, 999 such simulated sublists, a histogram can be constructed of the expected range of a+ values, for sublists of that size, against which the true a+ for that locality can be compared (Figure 4). If the observed a+ falls outside the central 95% of the simulated a+ values, it is considered to have departed significantly from expectation. The construction of these 95% probability intervals can be repeated for a range of sublist sizes (m = 10, 15, 20,. ..) and the resulting upper and lower limits plotted on a graph of a+ against m. When these limit points are connected across the range of m values, the effect is to produce a funnel plot (such as seen in Figure 5). The

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Bristol Channel

Western Irish Sea

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Western Irish Sea

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Figure 5 Average taxonomic distinctness (circles) of groundfish communities from 277 ICES quarter-rectangles, divided into nine large sea areas of the NW European shelf, plotted against the species richness in each rectangle. Also shown are the expected taxonomic distinctness, in random subsamples of the 92 groundfish species included in the study (dashed line) and the 95% probability limits for a single A+ value (continuous lines). Clear differences in taxonomic distinctness within the large sea areas can be related to beam-trawling effort. In areas to the west of the British Isles (Bristol Channel, Irish Sea, Western Channel), data for individual ICES quarter rectangles generally fall within the limits of the 95% probability funnel produced from the global list of species found in the entire region. In theSE Channel and the SW North Sea individual points fall mostly belowthe mean, with somebelowthe 95% probability limit. For the SE North Sea and the EC North Sea all points fall belowthe mean and the majority belowthe 95% limit. This pattern is consistent with the very heavy beam-trawling effort in these last two areas, signaling a strong impact of this activity on groundfish biodiversity.

real a+ values for a range of observational studies are now added to this plot, allowing simultaneous comparison to be made of distinctness values with each other and with the expected limits. Similar comparisons can be made for VarTD.

The histogram and funnel plots of Figures 4 and 5 are univariate analyses, concentrating on only one index (a+or a+) at a time. Also possible is a bivariate approach in which (a+, a+) values are considered jointly by plotting one against the other, both in respect of the observed outcomes from real data sets and their expected values under subsampling from a master species inventory. The bivariate equivalent of the univariate 95% probability limits in the histogram or funnel plots is a 95% probability region, within which approximately 95% of the simulated values fall, represented by the ellipse from a fitted bivariate normal distribution to separately transformed scales for a+ and a+. In general, impacted assemblages are characterized by decreased AvTD (i.e., this index behaves monotonically) and increased VarTD, but the latter may not always be the case.

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