Fuzzy Clustering of Ecological Data

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Abstract
Many concepts in ecology are imprecise because ecosystems are large, loosely organized objects. Fuzzy-set theory provides a mathematical approach that is able to cope with imprecision. The aim of this paper is to demonstrate that fuzzy sets are a suitable description of ecological communities, using Calluna vulgaris moorland data from the North York Moors National Park as an example. The clustering apprach used, the fuzzy c-means algorithm (or fuzzy ISODATA), requires a starting classification that is refined by a least-squares criterion. In starting strategy used in the example was based on the division of one ordination axis. Ordination axwsa were also used to reduce the high level of noise present in the ecological data. Fuzzy clustering was compared with the classification produced by TWINSPAN. The first division of TWINSPAN contrasted species of wet environments (Agrostis canina, Sphagnum recurvum, Polytrichum commune an Eriophorum angustifolium) with Pohlia nutans, a moss which grows on peaty or sandy banks and ofter under mature Calluna vulgaris. Fuzzy c-means show a strong clustering into two groups, although there were indications of a substructure at three or perhaps five groups. The two groups contrasted sites from wet habitats and those from drier habitats, in close agreement with TWINSPAN results. When clustering into three or more groups, it is hypothesized that the clusters of drier habitats are associated with the C. vulgaris development cycle. As an exploratory approach to vegetation classification, fuzzy clustering may be more appropriate than classification into ''hard'' bounded groups. In comparison with TWINSPAN, fuzzy clustering produces clusters which are more strongly correlated with relevant external environmental variables. This may reflect the fact that ecological communities are more similar to fuzzy sets than to ordinary sets with sharp boundaries.

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