Much ecological and paleoecological work is based on a quantitative study of the relative abundance of species. Such studies attempt to interpret geographic or stratigraphic trends in terms of ecologic gradients. If the trend for each species is considered separately, interpretations relatively are straightforward. It is advantageous commonly, however, to search for patterns of covariation among species; if present, they sharpen and simplify environmental interpretation, and provide some basis for synecological reconstruction.

Discovery and description of covariation patterns are not straightforward, and it is helpful therefore to have available several alternate models of community structure along an ecological gradient. One may consider a sampling traverse along which species abundances may reflect the direct in-situ operation of environmental factors, as well as the indirect influence of water-mass biogeography. Four simple models are postulated. In Model A (Random Fluctuation), species abundances are random with respect to traverse position. In Model B (Staggered Peaks), species have narrow, overlapping ranges and optima staggered along the traverse. In Model C (Simple Covariance), reaction groups consist of two or more species having the same optimum and exhibiting proportional variation; groups overla , but no species belongs to more than one group. Model D (Complex Covariation) is like C, except that species may belong to more than one group. Numerical examples are given for each model. By inspecting species plots and treating data by R- and Q-mode factor analysis, criteria are developed for recognizing model situations. Study of natural data suggests that real community variations are mixtures of the four model types.

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