fulltext - Mathematical Geology, Vol. 14, No. 6, 1982 U se...

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Mathematical Geology, Vol. 14, No. 6, 1982 Use of the Bray-Curtis Similarity Measure in Cluster Analysis of Foraminiferal Data j Michael G. Michie 2 Transformation of data effectively limits the distortion by outlying values on the Bray- Curtis similarity measure. It represents an effective method of using cluster analysis in distinguishing biotopes of benthic foraminifera. KEY WORDS: biotopes, Bray-Curtis, cluster analysis, foraminifera. Several recent papers involving analysis of patterns in benthic populations, not- ably of Australian origin (e.g., Stephenson and Williams, 1971, Stephenson, Raphael, and Cook, 1976, Stephenson and Campbell, 1977) have made use of the Bray-Curtis similarity measure. This measure is a city-block metric derived from Bray and Curtis (1957). In its currently used form it is expressed as where dij is the similarity between two operational taxonomic units (OTUs) i and j, each defined by a set of n attributes xik and xjk. In this study the OTUs are the sampling stations from a small estuary, and the attributes are the benthic foraminiferal species found at those stations. Some authors (Stephenson, Rafael, and Cook, 1976, Stephenson and Campbell, 1977) transform each datum xik to loglo(Xik + 1). This, and other possible transformations, are commonly used when the frequency range of the species encountered is excessive, since the Bray-Curtis measure is sensitive to outlying values (Williams, 1976). Although Bray and Curtis (1957) used standardized normal data in their original paper the present measure should be used with nonnegative data. In a previous paper (Michie, 1978) the author discussed the use of the lManuscript received 21 September 1981; revised 15 March 1982. ~Division of Natural Sciences, Northern Territory Museum of Arts and Sciences, PO Box 4646, Darwin NT 5794, Australia. 661 0020-5958 / 82 / 1200-0661 $03.00/0 © 1982 Plenum Publishing Corporation
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662 Michie z ~ ~ ~, r-5 i I I o" o l.J.J ©
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Bray-Curtis Similarity with Foraminiferal Data 663 Euclidean distance similarity measure with foraminiferal data. Three methods were examined, with preference given to the method where the data were cen- tered and normalized by site (using the standard deviation). The results obtained by this method are shown in Fig. 1. In this paper the Bray-Curtis measure is being used with the same data as in Michie (1978). Two techniques are used, the first with untransformed data and the second with data which had been transformed using the transformation
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fulltext - Mathematical Geology, Vol. 14, No. 6, 1982 U se...

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