length of a limb after each of the five molts required 

 for complete regeneration is 27, 45, 65, 85, and 1009? 

 of the length of a normal limb (Edwards 1972). Limbs 

 in the last stages of regeneration are the hardest to 

 detect. 



Since measurements from regenerating chelae can 

 be quite deviant from normal measurements, they 

 can have a pronounced effect on the estimate of X* 

 and therefore must be detected and eliminated from 

 the sample. The method we used for eliminating such 

 outliers consisted of fitting a single straight line to the 

 logarithms of chela height and carapace length (fit- 

 ting the two line model is preferable if computer cost 

 is not a consideration) then excluding the datum with 

 the largest negative deviation. This is repeated itera- 

 tively until the mean square residual (MSR) is re- 

 duced to some level. 



Two criteria were examined as a means of determin- 

 ing when MSR had been reduced sufficiently. The 

 first criterion considered the change in MSR result- 

 ing from the deletion of each successive datum. Typi- 

 cally the change in MSR was initially large, then 

 decreased almost asymptotically as additional data 

 were deleted (Fig. 5). Elimination of regenerating 

 chela measurements was assumed to be complete 

 when the change in MSR became nearly constant. 

 For the Pribilof Islands population, data deletion was 

 halted after 50 values (6 f A of the sample) were re- 

 moved (Fig. 6). 



The second criterion was based on a comparison of 

 the MSR of the contaminated sample with the MSR 

 of a sample assumed to be free of regenerating chela 

 measurements. Deletion was halted when the MSR 

 of the contaminated sample was not significantly dif- 

 ferent from the uncontaminated sample, based on an 

 F ratio, at some probability level. Although this 

 criterion is more objective than the first, it requires 

 an uncontaminated sample and it assumes that the 

 true variance is identical between populations. For 

 the Pribilof Islands data, to achieve an MSR that was 

 not significantly different from the average MSR for 

 the Olga Bay and Prince William Sound data (both 

 of these data sets did not contain regenerating chelae 

 measurements) at the 0.001 probability level, 114 

 values (14% of the sample) had to be excluded (Fig. 

 7). Even with this low probability level, the deletion 

 of data was too severe, because the distribution of 

 chela measurements about the fitted line appeared 

 to have a positive skew. Since we believe that the true 

 variance is probably less in the Olga Bay and Prince 

 William Sound populations than in the Pribilof Islands 

 population, the first criterion was used to determine 

 when the deletion of data should be halted. 



The number of data deleted by these methods may 

 be too large, that is, some crabs with small, but other- 

 wise normal, chela may have been excluded. In one 

 study of limb regeneration in male red king crab, 

 14.7% of the adults and 25.6% of the juveniles had 



Figure 5.— Change in mean square error (MSR) about 

 a single straight line fit to the data of the blue king crab 

 from the Pribilof Islands as a function of the numberof 

 values deleted. Note that the change in MSR becomes 

 nearly constant after deleting 50 values. 



20 40 60 80 



NUMBER OF MEASUREMENTS DELETED 



626 



