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Chapter 2 - Analyses
to be maintained, so that the resulting dendrogram
reflects the similarity between adjacent cases. This is
obviously very useful for stratigraphical studies in
which the original order is of importance.
Constrained clustering can be performed as a variation
of any of the above agglomerative procedures. Instead of
scanning the whole distance matrix for the most similar
objects, constrained clustering scans just the distances
of adjacent cases. Otherwise it can be calculated as
described above.
Diversity Indices
This procedure computes three diversity indices
commonly used in ecology, Simpson’s, Shannon’s, and
Brillouin’s. See Pielou (1969) and Krebs (1989) for a
discussion of the use and derivation of these indices.
Two variations of Simpson’s are available. The most
commonly presented form, which is labeled simply
“Simpson’s” in the drop-down list on the dialog box, is
based on the following formula:
s
D = 1 − ∑ pi
2
i =1
where: D = Simpson’s diversity index
pi = Proportion of species i in the community
s = Number of species
This version is appropriate for samples taken from an
infinite population and may be applied to measures of
biomass and cover as well as individual counts.
However, it is a biased estimator of the true diversity
index for the whole population. An unbiased version
(labeled “Simpson’s unbiased” in the MVSP diversity
dialog) is proposed by Pielou (1969):
s
 n ( n − 1) 
D =1− ∑ i i

i =1  N ( N − 1) 
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