Biocomplexity theory has become increasingly important in understanding ecosystem dynamics as we realize that the interactions among subunits in a multi-component system often produce elaborate states that are not easily explained in terms of the individual parts of the system. A Euclidean geometric model of biocomplexity is presented and illustrated using protistan communities. The model is based on three quantitative biotic dimensions (indices) for small subsamples (0.01 g) taken from each sample core of substratum: (1) richness of morphospecies expressed as mean count per 0.01 g, (2) spatial diversity of protists expressed as the number of unique morphospecies (i.e. those occurring in only one of the 0.01-g subsamples and not in any of the other subsamples), and (3) patchiness (non-uniform aggregation) of the distribution of protists across the 0.01-g subsamples. These three indices are mapped into a three-dimensional Euclidean space model, and the position of each point and its geometric distance from the origin are used as a general index of biocomplexity. The usefulness of the model is illustrated by applying it to a range of terrestrial and marsh communities. Within the set of 15 samples examined in this study, the marsh rhizosphere samples are among the most complex.
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