8235

• UCREFRP Catalog Number: 8235
• Author: Douglas, M. E., R. R. Miller and W. L. Minckley
• Title: Multivariate Discrimination of Colorado Plateau Gila spp.
• USFW Year: 1998
• USFW - Doc Type: The "Art of Seeing Well" Revisited
• Copyright Material: YES

166

DOUGLAS ET AL.

nated groupS. This analysis was run for all species-
pairs and for the three species together with each
data type (meristic, morphometric, and field). A
jackknife procedure was used in each analysis to
estimate error probabilities for associating indi-
viduals to species.
The nonparametric analysis cannot produce a
discriminant function with which to classify un-
knowns. To correct this, and thus to classify ju-
veniles and unidentified specimens (as per Sofield
et al. 1984), a parametric discriminant analysis
(PROC DISCRIM; SAS 1989) was performed with
only five morphometric field characters (see be-
low) that maximally discriminated among the three
species and a variance-covariance matrix pooled
among species. Again, a jackknife procedure es-
timated error probabilities for the resulting dis-
criminant function. Kappa, a chance-corrected sta-
tistic to compare actual and predicted group mem-
bership (Titus et al. 1984; applied in Douglas
1993) was also calculated. A canonical variate
analysis (again, with the five field characters
above) was then performed to test significance of
the first three canonical variates and to plot them
in three-dimensional space.
To test efficacy of the five-character field subset
to correctly segregate individuals, the parametric
discriminant analysis was run a second time, but
with equal sample sizes among species (i.e., N =
28 for each) and within-group (rather than pooled)
variance-covariance matrices. To make the test
rigorous, those 28 G. robusta and G. cypha closest
to the center of the combined distribution were
selected (i.e., those individuals putatively most
difficult to discriminate). All G. elegans were used.

Results

Data Normality and Transformation

Only one meristic count (of 10) was normally
distributed in each species: gill rakers in G. elegans
and lateral-line scales in G. robusta and G. cypha.
Various transformations were unsuccessful in nor-
malizing the other nine meristic counts. The num-
ber of nonnormal morphometric characters was 5
for G. robusta, 4 for G. cypha, and 10 for G. ele-
gans. Width of left pharyngeal bone and depth of
skull's frontal depression were nonnormal in all
three species. Bony interorbital width, tip of snout
to occiput, and length of upper jaw were nonnor-
mally distributed in two of the three species.
Transformed morphometric data were also test-
ed by species for deviations from normality. For
G. robusta, three of the original five nonnormal

characters remained so after transformation, while
two (of four) and zero (of 10) remained so for G.
cypha and G. elegans, respectively. Only one nor-
mally distributed character (pectoral fin length) be-
came nonnormal in two of three species following
transformation. Homogeneity of within-species
morphometric covariance matrices was also tested
for and subsequently rejected. Thus, a pooled vari-
ance-covariance matrix was used to derive a dis-
criminant function for species separation.

Discrimination between Study Species
All 109 specimens of G. robusta and G. elegans
were discriminated 100% of the time by either two
meristic characters (dorsal rays and gill rakers) or
a single morphometric character (depth of caudal
peduncle; Table 1). With field data, depth of caudal
peduncle again proved maximally discriminatory.
In all, 98.8% (85 of 86) of Gila cypha and G.
elegans were discriminated by three meristic char-
acters (Table 1). This included 100% (28 of 28)
of G. elegans and 98.3% (57 of 58) G. cypha. With
the use of only morphometric characters, 96.5%
(83 of 86) of all individuals were correctly allo-
cated. Gila cypha was correctly designated in
98.3% of the cases (57 of 58), and G. elegans in
92.9% of cases (26 of 28). Field characters clearly
separated the two species in 95.3% of cases (82
of 86), with 98.3% of G. cypha allocated (57 of
58) and 89.3% of G. elegans (25 of 28). Only one
individual (of eight) allocated to the "wrong" spe-
cies was shared among the three data subsets.
Three meristic counts separated G. robusta and
G. cypha in 95.7% of cases (133 of 139; Table 1).
Gila cypha was correctly designated in 100% of
cases (58 of 58), and G. robusta in 92.3% (75 of
81). With only morphometric variables used,
99.3% (138 of 139) of individuals were correctly
designated; this amounted to 100% (81 of 81) of
G. robusta and 98.3% (57 of 58) of G. cypha. When
the field subset was used, 99.3% of all specimens
were again correctly designated to species (98.8%
[80 of 81] of G. robusta and 100% [58 of 58] of
G. cypha). None of eight specimens incorrectly
allocated among species was shared between the
three data subsets.
When the three species were evaluated together,
five meristic characters correctly designated 92.2%
(154 of 167) of all individuals. Gila robusta was
assigned in 91.4% of cases (74 of 81), G. cypha
in 89.7% (52 of 58), and G. elegans in 100% (28
of 28). When only morphometric characters were
used, specimens were designated in 95.6% of cases
(131 of 137). Gila robusta was allocated in 100%

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