FISHERY BULLETIN: VOL. 80, NO. 2 



Figure 3.— Size-at-age data for Pa- 

 rophrys vetulus captured in the Moo- 

 lach Beach nursery area. 



20 40 60 80 100 120 140 160 160 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 



Age (days) 



inflection point. There is no evidence of an upper 

 asymptote in the data, so the use of growth 

 models such as the Gompertz or von Bertalanffy 

 equations is inappropriate. A least squares mul- 

 tiple regression on these data was performed 

 using the following model: 



Y = Bo + BiX + B 2 Ai + B 3 A 2 + E (1) 



where Y is the standard length in millimeters, X 

 is the age in days, A\ is a dummy variable whose 

 value is zero to the left of the inflection point and 

 one to the right of the inflection point, and A 2 is 

 equal to X times A\, i.e., the interaction term. 

 The B terms are the regression coefficients and 

 E indicates the error terms. The point of inflec- 

 tion which produced the smallest residual sum of 

 squares was found to be 140 d for the Moolach 

 Beach data. The fitted equation is: 



Y = 16.87 + 0.051X - 32.92A + 0.2SA 2 . 



An analysis of variance for the regression (Table 

 1A) shows that a good fit was obtained with this 

 model, and the data set has a relatively low esti- 

 mated variance. The slopes of the regression be- 

 low and above 140 d were computed as 0.051 and 

 0.279, respectively. These slopes are estimates of 

 the mean growth rate per day for juvenile P. 

 vetulus utilizing the Moolach Beach nursery 

 area. The lower portion of the data, below 140 d 

 of age, shows a plateau in growth attributed to 

 the metamorphic period (Rosenberg and Laroche 

 1982). 



Regression of the size-at-age data for Yaquina 

 Bay juveniles (Fig. 4: 186 data points) yields the 

 fitted equation: 



Y = 13.01 + 0.083X - 33.45,4, + 0.201^ 2 . 

 248 



The analysis of variance for this model (Table 

 IB) once again shows that a good fit was obtained, 

 but the estimated variance is much higher than 

 for the Moolach Beach data. The inflection point 

 with the smallest residual sum of squares was 

 also 140 d of age for the Yaquina Bay data. The 

 slopes below and above the inflection are 0.083 

 and 0.284, respectively. 



The first step in comparing the regression 

 lines of growth for English sole from the two 

 nursery grounds was to test for statistical equal- 

 ity of variances. This was done by examination of 

 the ratio of the mean square errors of the fitted 

 regressions, 19.88 for the Moolach Beach data 

 and 95.01 for the Yaquina Bay data. The ratio is 

 distributed as F(184:216) and the variances are 

 significantly different at the P = 0.001 level. 

 Since the variances are unequal, statistical tests 

 for equality of slopes or intercepts are not strictly 

 valid (Scheffe 1959). However, the slopes are 

 similar, 0.279 and 0.284. 



Back-calculated growth for individuals from 

 both areas are in good agreement with growth 



Table 1.— Analysis of variance for the least squares multiple 

 regression analysis of size-at-age data. 



