A Table for Calculating the `Equitability' Component of Species Diversity

Abstract

where s is the total number of species in a sample and Pr is the observed proportion of individuals that belong to the r-th species (r = 1, 2, . .. , s). Fig. 1 (a) exemplifies the sort of sample to which H(s) might be applied; the data are drawn from experimental work in progress near Oxford on the mesofauna of beech litter. In this sample, our technique of extraction (Kempson, Lloyd & Ghelardi 1963) got out 632 individuals of forty-four species, mostly micro-arthropods. By equation (1), we have H(44) = 4-16. In general, H(s) will increase with s, but the function is also influcnced by the evenness with which the individuals are distributed among the species. The maximum possible value, for a given s, could be realized only if all the species were equally abundant. In this case, Hmax(s) log2(s), so with forty-four equally abundant species, we would have Hmax(44) = log2(44) = 5x46. This mathematical maximum is never achieved in practice, because one never finds all species equally abundant-not even among species of comparable size that are presumably using the same kinds of resources, much less in the community as a whole. If one accepts H(s) as a valid empirical measure of species diversity, then one can imagine two quite separate pathways whereby the species diversity of an existing community might be enhanced. One way would be for more species to come and live there, and the other way would be for the existing species to adjust their numbers so that the rare ones become commoner and/or the common ones rarer. There are two components of species diversity, so to speak: number of species and 'equitability'. (We choose the word 'equitability' here rather than 'evenness', since numerical equality among the species is too much to expect. For some purposes, it is highly desirable to have a parameter like H(s) which takes two such different things into account and reduces them to a common scale. (The 'intrinsic rate of natural increase' is another example of such a parameter-see Birch 1948.) For other purposes, it may be more interesting to separate them. For example, one might wish to consider, as a working hypothesis, that whereas number of species depends primarily on the structural diversity of a habitat, 'equitability' is more sensitive to the stability of physical conditions. In this case, one needs a way to measure 'equitability' per se. The Shannon-Wiener function provides a basis for such a measure, when combined with some theoretical distribution of abundances among the species, to serve as a 'yardstick'.