36 



Fishery Bulletin 97(1), 1999 



Walters, 1992; Polacheck et al., 1993; Chen and An- 

 drew, 1998). In our study, when the maximum hkeh- 



hood (ML) method was used, the Tj, q^. 



and /ij had 



values of 0.041, 0.40 x 10"'' (per vessel), and 8,667 t, 

 respectively. These are 20%, 23%, and 270% of the 

 LMSE-estimated parameters, and 26%, 33%, and 

 213% of the median values of the bootstrapped LMSE 

 estimates. According to the ML method, the eastern 

 rock lobster stock had a large biomass with a low 

 productivity rate. In contrast, the LMSE method 

 predicted a smaller stock with a relatively high pro- 

 ductivity rate. This difference arises from different 

 methods used to fit the model to CPUE data. The 

 ML was heavily influenced by the CPUEs obsei-ved 

 from 1916 through 1924, whereas the LMSE virtu- 



> 



HI 



z> 

 a. 

 o 



3 

 Q. 

 O 



ally ignored these observations and tended to follow 

 closely the CPUE in the majority of years (Fig. 11). 

 Because of the high likelihood of under-estimation 

 of CPUEs ft-om 1916 through 1924, the LMSE method 

 is probably more suitable. The estimates of rjj, g^, 

 and Sjggg_^o by the ML method were 0.17, 0.13 x 10"^ 

 (per trap-month) and 7174 t, differing from those 

 estimated with the LMSE and bootstrapped LMSE 

 methods (Table 3). This difference may result from 

 different weightings of data for years 1971-72 and 

 1974-75. Fitting the model with the LMSE method 

 virtually ignored the data observed in these years, 

 which had much higher CPUEs than other years. How- 

 ever, fitting with the ML method was heavily influenced 

 by these two years of high CPUEs (Fig. 11). Because 

 of the patchy distribution of lobsters 

 in their habitat and the expansion 

 of fishing grounds out to the conti- 

 nental slope off the NSW coast dur- 

 ing the early 1970s, it is very likely 

 that these two years of exception- 

 ally high CPUEs resulted from high 

 fishing efficiency (i.e. high (7 values), 

 which should not be taken as an in- 

 dicator of high biomass. 



We suggest using the bootstrapped 

 LMSE method as an alternative 

 approach to fitting production mod- 

 els to catch-effort data. The results 

 derived from such an analysis 

 should be evaluated carefully with 

 respect to the biology and ecology of 

 the targeted fish species and with 

 respect to how the catch-effort data 

 were collected. Such an evaluation 

 may shed some light on why some 

 obsei-vations differ from the major- 

 ity which the LMSE estimated line 

 tends to follow. A comparison of re- 

 sults between robust and traditional 

 least squares approaches may lead 

 to a better understanding of the dy- 

 namics of the studied fish stock and 

 identification of years in which 

 atypical data are observed. 



1940 



1969-70 72-73 



84-85 87-88 



Fishing year 



Figure 11 



The predicted catch per unit of effort with the maximum likehhood <ML) and 

 lea.st median of squared error.s (LMSE) methods for the period of 1903 to 1936 

 and the period of 1969-70 to 1993-94. 



Acknowledgments 



We would like to thank G. Gordon, 

 L. Diver, N. Andrew, D. Reid, and 

 A. Kathuria at NSW Fisheries Re- 

 search Institute, and D. A. Jackson 

 at Zoology Department of the Uni- 

 versity of Toronto for their helpful 



