The Method

From a traditional ecological viewpoint diversity may be thought of as the number of groups (usually species) present in an assemblage, or how evenly those groups occur in the assemblage. These aspects of diversity are generally termed richness (species richness for example) and evenness. High richness equates to high diversity, and a highly dominated assemblage (i.e., one with low evenness) is considered to be less diverse than a more even one.

Diversity measures tend to be measures of richness (e.g., Margalef's richness index, see Margalef's Index), evenness (e.g. Simpson's index, see Simpson Index), or are constructed in such a way as to combine the two components in one measure (e.g. Shannon-Wiener index, see Shannon-Wiener Index). The Berger-Parker index (see Berger-Parker Index) is the proportional abundance of the most abundant species in an assemblage and is a measure of dominance. Where no single species is overwhelmingly dominant, it is useful also to consider the dominance of the two most abundant species, the three most abundant, and so on. In an assemblage a family of indices may be defined: 1-dominance, 2-dominance, 3-dominance, and in general ¿-dominance, which is the combined dominance of the k most abundant species. Plotting values of k-dominance against species rank gives the k-dominance curve. Ranked species abundance (dominance) curves are based on the ranking of species (or higher taxa) in decreasing order of their importance in terms of abundance (or biomass). The ranked abundances, expressed as a percentage of the total abundance of all species, are plotted against the relevant species rank. The k-dominance curve, therefore, is simply a 'cumulative' ranked species abundance curve in which cumulative proportional abundances are plotted against species rank, or often log species rank. The log scale compresses the information about low-ranked species so that the curves reflect a greater contribution from evenness than richness components of diversity. Obviously, the length of a curve along the x-axis is determined by the number of species in the assemblage under consideration, while dominance may be assessed by the height and shape of the curve. The higher the curve, the less diverse (and more dominated) is the assemblage it represents. To compare dominance separately from the number of species, the x-axis (species rank) may be rescaled from 0 to 100 (relative species rank), to produce Lorenz curves.

Figure 1 shows k-dominance curves calculated from species abundances of infaunal invertebrates from a marine intertidal sand-flat. Animals were collected using different sieve meshes, and sample sizes were scaled with mesh size. Each curve is calculated from the

10 100 Species rank

1000

Figure 1 k-Dominance curves for samples of invertebrates from a marine intertidal sand-flat. Each curve is based on average abundances in four replicate samples collected using a particular combination of sieve mesh and sample area: 0.1 m2 sieved on a 1 mm mesh (circles); 0.006 25 m2 sieved on a 250 mm mesh (squares); 0.00039 m2 sieved on a 63 mm mesh (triangles).

averaged abundances from four replicates. Note that there is little or no overlap in species composition between samples collected on the largest mesh and on the two smaller meshes, but the method allows a simultaneous comparison of the dominance/diversity structure in each. The curve for invertebrates extracted using a 1 mm mesh is higher than the curves for invertebrates extracted using 250 or 63 mm meshes for all values of k. Thus, the assemblage in the 1 mm-mesh samples is unambiguously less diverse than the others.

The curves for invertebrates sieved on 250 and 63 mm meshes in Figure 1 cross. It has been argued that diversity can only be unambiguously assessed when the curves to be compared do not overlap or cross, as different diversity indices biased toward species richness or evenness will rank these assemblages in opposite ways. However, intersecting plots are informative in that they illustrate differences in dominance relative to species richness in a way that a single univariate index does not.

Whether k-dominance curves are plotted from the species abundance distribution or from species biomass values, the j-axis is always scaled in the same range (0-100). This facilitates the abundance/biomass comparison (ABC) method of determining levels of disturbance (see Abundance Biomass Comparison Method).

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