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<br />340
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<br />COPEIA, 1993, NO.2
<br />
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<br />DO D a:a:tca&xiBiaJ. o~co.di. I...CO". .
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<br />
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<br />-3.0
<br />
<br />CArfONICAL 'VARIATE I
<br />
<br />Fig. 4. Projections of 29 male (solid bars) and 34
<br />female (open bars) humpback chubs onto the first
<br />discriminant function axis designed to separate the
<br />sexes. Some individuals are superimposed in drawing.
<br />
<br />ponents explained 87.1 % of the observed
<br />morphological variation.
<br />The first component (PC1), which explained
<br />78.1% of the total variation, provided no sep-
<br />aration between males and females (Fig. 5). This
<br />component had high correlations with essen-
<br />tially all characters (Table 1), suggesting that it
<br />represents a general body size factor. The dis-
<br />tribution of males and females overlapped con-
<br />siderably along this component (Fig. 5).
<br />The second component (PC2) explained con-
<br />siderably less of the total variation (i.e., 4.2%;
<br />eigenvalue = 2.24), with only 11 relatively im-
<br />portant characters (i.e., with loadings> 0.25).
<br />These characters are the vertical distances from
<br />pupil to dorsal (3) and ventral (4) aspects of the
<br />head; distances from pectora] origin to various
<br />landmarks on the dorsal edge of the head (i.e.,
<br />9-13); and the distances between discrete land-
<br />marks along the nuchal hump and those im-
<br />mediately preceeding it (i.e., 24-27; see above).
<br />Thus, PC2 was interpreted as a head depres-
<br />sion-head length-nuchal hump component.
<br />However, no separation of males from females
<br />was apparent on this axis (Fig. 5).
<br />The third and fourth components explained
<br />2.9% and 2.5% of the variability, respectively.
<br />These components summarized a modest
<br />amount of the total morphological variation and
<br />appeared to be biologically unintcrpretable.
<br />Plots of PC3 and PC4 against one another, or
<br />against the other components (not shown), did
<br />not segregate males from females.
<br />
<br />Sheared principal componenl analysis.- Three size-
<br />free components (i.e., H2, H3, H4) were gen-
<br />erated using sheared PCA, but only loadings
<br />for the first (which accounted for 92% of the
<br />size-free variation) are presented in Table 1.
<br />Those variables which loaded heavilv onto H2
<br />were the same variables that loaded h~avilv onto
<br />PC2 [i.e., characters (3), (4), (10)-( 13), and (24)-
<br />(27); character (9) was not important in H2].
<br />Loadings for all characters were slightly lower
<br />than those recorded in the initial PCA (reduc-
<br />
<br />.
<br />3.0
<br />
<br /> PCI
<br /> 00 0.3
<br /> 000 P
<br /> . . 0 ..
<br /> 0 0.0 C
<br /> 0
<br /> 0 2
<br /> 0 0 .
<br /> 0 . 0
<br /> o .
<br /> 0 -0.3
<br /> 0
<br />-2.0 -1.0 0.0 1.0
<br />
<br />
<br />Fig. 5. Humpback chubs plotted with respect to
<br />the first two principal components, based upon 53
<br />measurements. Characters were standardized on the
<br />basis of within-sex standard deviations.
<br />
<br />tions ranged from 0.08-0.22, Table I). These
<br />reductions suggest that, although body size con-
<br />tributed to most ofthe morphological variation,
<br />size-free shape variation was also present. As
<br />before, males and females were completely in-
<br />termingled on the sheared PC axes (much as in
<br />Fig. 5). Plots of sheared components are, thus,
<br />not presented.
<br />
<br />DISCUSSION
<br />
<br />In this study of morphological variation in G.
<br />cYPha, the influences of geographic and tem-
<br />poral variation were minimized by collecting
<br />specimens within a short time span and from a
<br />relatively small geographic area (as in Schnell
<br />et a!., 1985). Variation associated with ontogeny
<br />(i.e., growth), however, is pervasive in these (and
<br />most) western North American fishes and can-
<br />not be adequately dealt with unless individuals
<br />are in some way aged. Because of the nonde-
<br />structive sampling approach used, specimens
<br />were not aged in this study. However, by se-
<br />lecting adult-sized fishes (greater than 230 mm
<br />TL), ontogenetic variation was at least reduced
<br />in significance.
<br />lntercorrelations between many of the char-
<br />acters were relatively low, suggesting that, al-
<br />though some individuals were larger (or small-
<br />er) than others (e.g., see PC 1; Fig. 5), there were
<br />proponional and shape differences among in-
<br />dividuals rather than between sexes. Two mor-
<br />phological characters differed statistically be-
<br />tween sexes (ANCOV A, Table 1): however the
<br />magnitudes of these differences were, from a
<br />statistical standpoint, only marginal. In fact, giv-
<br />en the large number of characters evaluated,
<br />one out of 20 (i.e., 5%) should be significant
<br />because of chance alone. Hence, finding two
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