1

10 100 1000 10 000 100 000

10 100 1000 10 000 100 000

Number of individuals (N)

0 20 40 60 80 100 120 140

0 20 40 60 80 100 120 140

0 20 40 60 80 100 120 140 Number of species, S

Figure 2 Values of a range of diversity indices (y-axis), for simulated samples of increasing numbers of individuals (a-f ) or species (g and h) on thex-axis (log scaled), drawn randomly without replacement from a large data set of 140 344 macrobenthic organisms from the Bay of Morlaix, France. Note that values for species richness and evenness measures (a-d) are sample-size dependent, whereas those based on taxonomic relatedness (e-h) are not.

The standard assumption that all step lengths between taxonomic levels are given equal weight may appear arbitrary, and the natural alternative here is to make the step lengths proportional to the extent of group melding that takes place, larger steps corresponding to larger decreases in taxon richness. However, the relationship between these two approaches is very close, and the relative values of A+ have been shown to be robust to the precise definition of the step-length weights. Taxonomic distinctness measures have sometimes been criticized because Linnean classifications do no necessarily portray correct phylogenetic relationships.

Family

Species Individuals x1

Family

Figure 3 A simple classification tree with a three level taxonomic hierarchy and equal step-lengths between taxonomic levels.

Figure 3 A simple classification tree with a three level taxonomic hierarchy and equal step-lengths between taxonomic levels.

However, until we have fully resolved cladograms for all taxa, the use of Linnean classifications remains the only pragmatic approach, and such classifications clearly bear a reasonable relationship with phylogeny.

In certain cases biodiversity changes may involve situations in which some genera become highly species rich while a range of other higher taxa are represented by only one (or a very few) species. Such is the case, for example, of the effects of demersal fishing on the macro-benthos of the North Sea, where polychaetes are increasing at the expense of taxa such as mollusks and echinoderms. Such changes can be summarized in a further statistic, the variance of the taxonomic distances (!y) between each pair of species i and j, about their mean value a+:

termed the variation in taxonomic distinctness (VarTD).

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