WSP04463

• File Number: 8460.500
• Description: Platte River Recovery Plan
• Basin: South Platte
• Date: 6/1/1997
• Author: Colo Div of Wildlife
• Title: Inventory and Status of South Platte River Native Fishes in Colorado
• Water Supply Pro - Doc Type: Publication

Several statistical methods were employed to divide species into distinct groups and link
species occurrences with physical habitat and water qu~lity parameters. Because of a lack of
statistically unifonn sampling effort, rigorous statistical iassumptions could not be met. Presence-
absence data was used and abundance and reproductive health of populations were not considered
at this time. In addition, only species which occurred at six or more sites were used in the cluster
analysis procedures to avoid chance occurrences which might influence the species groupings.

Cluster analysis techniques have been widely u$ed in the fields of medicine, taxonomic
studies of various organisms, and archeology (Hartigad 1975). These techniques have also
provided useful infonnation on the occurrence and distnbution of insect species (Roback et al.
1969), protozoa (Cairns and Kaesler 1969), diatoms and other algae (Cairns et al. 1970), and
noninsect macroinvertebrates (Kaesler et al. 1971). Cairns and Kaesler (1971) used cluster
analysis to group fish species distnbutions on the Potomac River, which revealed useful species
aggregations.

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The SAS procedures CLUSTER and TREE (SAS Institute Inc. 1989) were used to
perfonn the cluster analyses. Six cluster analysis link~ge methods were explored using two types
of coefficients of association: complete and average linkage of Jaccard coefficients, and
correlation coefficients. In addition, Ward's method (I963) was used with both the Jaccard
coefficient and correlation coefficient. Ward's method is distinct from the other methods in that it
uses an analysis of vanance to evaluate the distances between clusters.

The Jaccard coefficient (Jaccard 1908) is based on the presence or absence of species at
stations, rather than on absolute numbers sampled or relative abundances. This methodology has
been used successfully in other studies to group alga~, protozoans, insects, and fish (Hansen and
Ram 1994, Cairns and Kaesler 1971, Roback et el. 1969). The equation for this coefficient is:

s- a
"j a+b+c

where a is the number of species included in the study that occur afboth of two sites being
compared, b is the number that occurs at one site and not the other, and c is the number that
occurs at the other station and not the first one. An important consideration of the Jaccard
coefficient is that it omits negative matches from consideration; thus, the mutual absence of a
species from two sites does not contnbute to their similarity. We felt this feature was beneficial
considenng the somewhat nonunifonn sampling effort across the basin.

,
The Jaccard coefficients and correlation coefficients were used to construct similarity
matrices which were used in the cluster analysis to ~onn two-dimensional dendrograms. These
showed a hierarchy of species associations which were commonly found together at the same
sample sites. The distance at cluster separation, based on the various amalgamation rules, was
plotted for each method and a species group cut-off was chosen arbitrarily on each dendrogram.

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