Hierarchical complexity in ecology: a noneuclidean conception of the data space

Abstract

Vegetation is the consequence of the interaction of a series of widely differing processes, each uniquely scaled. Extensive slow processes pertain to high levels of organization, while fast local processes pertain to lower levels. Curvature in ordination gradients is often not artefact, but the result of interference between different levels. As straight gradients are lengthened by the inclusion of more heterogeneity in the data, the nature of relationships change between species and their environment and each other at distant places in environmental space. With change in these relationships, movement down the gradient does not always mean the same thing, and this causes curvature. In plotting a noneuclidean space onto a euclidean reference, the change in metrics causes apparent curvature. The technical causes of curvature (bimodality, double zeros, beta diversity) fit this model. Data transformations scale the analyses so that different levels are reflected in results. Between levels, when the processes of the lower level are not local enough to be trivial, the pattern from new upper level processes cannot assert a new straight gradient with coarser grained criteria. Thus transformation and the emergence of curvature followed eventually by new straight gradients allow the linking of different levels in an orderly fashion.

Nomenclature follows Gleason (1952), The New Britton and Brown Illustrated Flora of the Northeastern United States and Adjacent Canada.

I am grateful to Grant Cottam for permission to publish his ordination of the Wasatch Mountain data. Tom Givnish made many helpful suggestions for revision of this manuscript.