equal to the lower bound and linear regression is used 

 to fit a lower line (X < X*), then an upper line {X > 

 X*) to the data. Third, X* is increased by some small 

 amount and the model is fit to the data iteratively un- 

 til X* equals the upper bound. The size of sexual 

 maturity is then equal to the antilog of the X* value, 

 which produced the minimum residual sum of squares 

 about the model. Chela and carapace measurements 

 and the best fitting pair of lines are shown in Fig- 

 ure 3. 



Although this technique will always find the best fit 

 of the model, the fit may not be statistically signifi- 

 cant, that is, the fit of the two line model may not be 

 significantly better than the fit of a single straight 

 line. Therefore a single straight line was fit to the data 

 and the residual sum of squares (RSS) of the two line 

 model was tested against the RSS from the single line 

 using a partial F test (Draper and Smith 1981). The 

 partialF test was significant (P<0.05) for all four sets 

 of blue king crab data. In cases where the fit of the two 



80 r 



80 

 60 



40 



20 



PRIBIL0F IS. 

 N=784 



A 1 1_ 



50 



100 



150 



50 100 



CARAPACE LENGTH (MM) 



150 



PRINCE 

 WILLIAM SD. 



N=150 



100 150 



CARAPACE LENGTH (MM) 



Figure 3.— Male chela heights and carapace lengths of the blue king crabs. The X axis intersection points of the two line model, or the 

 estimated sizes of maturity, are shown by dotted lines. Sample sizes (N) are indicated. 



624 



