Abstract. Three commonly used measures of diversity, Simpson's index, Shannon's entropy, and the total number of species, are related to Renyi's definition of a generalized entropy. A unified concept of diversity is presented, according to which there is a continuum of possible diversity measures. In a sense which becomes apparent, these measures provide estimates of the effective number of species present, and differ only in their tendency to include or to ignore the relatively rarer species. The notion of the diversity of a community as opposed to that of a sample is examined, and is related to the asymptotic form of the species-abundance curve. A new and plausible definition of evenness is derived.When ~e say that the humid tropics are more diverse than the tundra, we mean that there are more species there. More precisely, we mean that the species in the humid tropics have on average lower proportional abundances than those in the tundra-a fact which is amply visible to the naked eye and which can be demonstrated by the use of any measure of diversity we care to devise. But there is little point in merely confirming the obvious; the purpose of determining diversity by a numerical index is rather to provide a means of comparison between Jess clear-cut cases. Unfortunately, when we look for a suitable numerical definition, we find that no particular formula has a pre-eminent advantage, and that different authors have plausibly proposed different indices. In the ensuing confusion, Hurlbert (1971) has despaired, declaring diversity to be a nonconcept. Fortunately his despair is premature, and when carefuiJy defined according to an appropriate notation, diversity can be as unequivocal as any other ecological parameter.Many of the indices which have been proposed apply only to counts of individuals and not to continuous measures of quantity. There is no obvious intuitive reason why this should be so, and Goodall (1970) observes that in plant communities counts of individuals are often impossible. Ideally, indeed, we should like to compute the diversity of a sample of dry weights or of productivities, as well as that of a sample of counts of individuals. Another point, often noticed and repeatedly ignored, is that whereas it is easy enough to define measures of diversity which apply to a particular sample, very often they will have no meaning when applied to the whole community. Consider, for example, the diversity as measured by the number of species in a sample. As the size of the sample is increased, so also will the "di-1 Manuscript received April 21, 1972; accepted July 11, 1972. 9 Present address: Nature Conservancy, Penrhos Road, Bangor, Caernarvonshire, U.K. versity," almost without limit. On this basis MacArthur and Wilson ( 1967) propose a law of speciesarea relations: that the number of species encountered is proportional to a power of the area sampled. In symbols,where S is the number of species encountered, A is the area sampled, and z is an empirical constant which usually lies between 0.1 and 0.4. ...
