FISHERY BULLETIN: \'0L. 69, NO. 2 



Table 3. — Regression of measurements (Y) on SL (X) in the point-slope form of the log-transformed allometric 

 equation Y =: aX'' over the interval 109<SLmm<286, Sehastes variegatus. 



Character (No. specimens) 



4(±95%)i 



Head length (38) 



Upper jaw (38) 



Prenarial pore (38) 



Subnoriol pore (38) 



Orbit (38) 



Interorbital (38) 



Raker (37) 



lower jaw projection (35) 



Snout (35) 



Suborbital (35) 



Head width (34) 



Pectoral fin (35) 



Pectoral base (38) 



Cauda! peduncle depth (35) 



Dorsal caudal peduncle (35) 



Ventral coudol peduncle (35) 



Body depth (pelvic) (38) 



Body depth (anal) (35) 



Anal spine I (38) 



Anal spine II (37) 



Anol spine III (35) 



Soft dorsal base (35) 



Anal base (35) 



Pelvic fin spine (34) 



Pelvic fin (38) 



Pelvic insertion to midvent (38) 



Midvent to anal fin (35) 



Longest dorsal fin spine (36) 



Longest dorsol soft ray (34) 



Longest anal soft ray (35) 



1 Asterisk indicates a difference in the slope exponent (i) significantly different from unity at the 95% 

 ence at this confidence level. 



n,s. indicates no significant differ- 



were explored, the power or allometric equation, 

 Y — aX'", in logio transformed form, and the 

 first degree or rectilinear equation, Y — a + bX, 

 untransformed. Both functions were fit by a 

 computer regression program (Sokal and Rohlf, 

 1969:696). Degree of fit was judged by the 

 "coefficient of percentage variation explained by 

 regression," the square of the correlation co- 

 efficient for regression, /- (Table 3). In 18 of 

 the 30 characters, nearly identical r^'s were ob- 

 tained by the alternative equations, including 

 9 characters for which the allometric exponent 

 differed in a minor (<0.20) but significant de- 

 gree from unity at the 95% confidence level, 

 i.e. the growth relationships seemed to depart 

 significantly from isometry. Plots of selected 

 examples from the nine characters showed only 

 minor differences between the two functions in 

 these instances. In four comparisons, three of 

 which showed significant departure from unity 

 in the allometric exi)onent (subnarial pore, low- 

 er jaw projection, and suborbital), the first- 



degree equation appeared to give a superior fit. 

 For the remaining eight comparisons, the allo- 

 metric equation was superior. 



In the light of these considerations, the logio 

 transformations of the allometric equation (log 

 Y = log a + b log X) was chosen for general 

 application because it is more versatile and gave 

 a satisfactory fit in all comparisons. Those 

 few characters which were fit somewhat better 

 by the first-degree equation appear to be of rel- 

 atively minor utility in rockfish systematics. 

 Parameters are presented in the point-slope 

 form of^ the transforrned allometric equation 

 {Y = Y + b (X — X), where Y = logic Y 

 and X = logio X) to emphasize the working in- 

 terval about the means of the variates and to 

 de-emphasize the I'-intercept which has no 

 theoretical value in these representations. 



The measurements are also presented in the 

 form of Q^-i'r confidence limits for proportions 

 of future individual specimens, based on the 

 material examined (Table 4). The limits were 



394 



