Given a resource gradient (e.g. light intensity, prey size) in a community, species evolve to use different parts of this gradient; competition between them is thereby reduced. Species relationships in the community may be conceived in terms of a multidimensional coordinate system, the axes of which are the various resource gradients (and other aspects of species relationships to space, time, and one another in the community). This coordinate system defines a hyperspace, and the range of the space that a given species occupies is its niche hypervolume, as an abstract characterization of its intra-community position, or niche. Species evolve toward difference in niche, and consequently toward difference in location of their hypervolumes in the niche hyperspace. Through evolutionary time addi- tional species can fit into the community in niche hypervolumes different from those of other species, and the niche hyperspace can become increasingly complex. Its complexity relates to the community's richness in species, its alpha diversity. Species differ in the proportions of the niche hyperspace they are able to occupy and the share of the community's resources they utilize. The share of resources utilized is expressed in species' productivities, and when species are ranked by relative productivity (or some other measurement) from most to least important, importance-value or domi- nance-diversity curves are formed. Three types of curves may represent manners in which resources are divided among species: (a) niche pre-emption with strong dominance, expressed in a geometric series, (b) random boundaries between niches, expressed in the MacArthur distribution, and (c) determination of relative importance by many factors, so that species form a frequency distribution on a logarithmic base of importance values, a lognormal distribution. The forms of importance-value curves do not permit strong infer- ence about resource division, but are of interest for their expression of species relation- ships and bearing on measurement of diversity. Two aspects of alpha diversity are to be measured. Diversity in the strict sense is richness in species, and is appropriately measured as the number of species in a sample of standard size. Slope measurements, in contrast, express the steepness of the importance- value sequence. Of the slope measurements the Simpson index expresses dominance or relative concentration of the importance values into the first or first few species, whereas the Shannon-Wiener index expresses the relative evenness or equitability of the importance values through the whole sequence. A new index, expressing equitability as number of species per logarithmic cycle of the importance-value sequence, is suggested. Given a habitat gradient (e.g. elevation or soil moisture conditions) species evolve to occupy different positions along this gradient. The various habitat gradients of a landscape may also be conceived as a multidimensional hyperspace, and species evolve toward occupa- tion of different positions in this hyperspace. Along a particular habitat gradient species populations have scattered centers and usually overlap broadly, forming a community continuum or coenocline. Through evolutionary time additional species can fit themselves in along the coenocline. As they do so the extent of change in community composition along the gradient increases. The extent of differentiation of communities along habitat gradients is beta diversity. The total or gamma diversity of a landscape, or geographic area, is a product of the alpha diversity of its communities and the degree of beta differentiation among them. The species' position in a landscape of communities, as described in terms of both habitat and niche relationships, may be termed its ecotope. Two approaches to measuring beta diversity have been most useful. For a transect along a given coenocline, the degree of species turnover or compositional change may be measured through sample similarities and expressed as half-changes. When a set of samples are taken to represent differences in communities of a landscape or range of habitat along more than one habitat axis, beta differentiation for these samples may be expressed by the ratio of the total number of species represented in the samples to the mean number per sample. Diversity of communities seems a resultant of non-extreme conditions, stable condi- tions, evolutionary and successional time, and the kind of community developed in that time. It is difficult to separate the effects of chronic environmental rigor, amplitude of regular fluctuation, and irregularity or unpredictableness of fluctuation. Diversities are low in many unstable environments, but certain desert communities subject to wide and irregular variation in precipitation have evolved high diversities in relation to this varia- tion. Evolutionary time is difficult to measure, but is important as the dimension through which increase in alpha and beta diversity occurs. Alpha diversities of birds, and gamma diverstities of islands, appear to reach saturation or steady-state levels. It is suggested, however, that for terrestrial plants and insects increase of species diversity, with elabora- tion of the niche hyperspace and division of the habitat hyperspace, is a self-augmenting evolutionary process without any evident limit.
Whittaker, R. H. (1972). EVOLUTION AND MEASUREMENT OF SPECIES DIVERSITY. TAXON, 21(2–3), 213–251. https://doi.org/10.2307/1218190