28 



Fishery Bulletin 97(1), 1999 



timate the sampling distribution for 

 model parameters. This approach is 

 referred to as the bootstrapped 

 LMSE method and its precedure fol- 

 lows: 



1 estimate the model parameters 

 using the LMSE method; 



2 calculate the predicted CPUEs 

 using the LMSE-estimated pa- 

 rameters; 



3 calculate the residuals between 

 observed and predicted log 

 CPUEs; 



4 randomly sample the residuals 

 with replacement to add to the 

 predicted logarithm CPUEs to 

 yield pseudo observed CPUEs; 



5 apply the LMSE algorithm to the 

 pseudo observed CPUEs to esti- 

 mate bootstrapped estimates; 



6 repeat steps 4 to 5 100 times to 

 simulate 100 sets of pseudo CPUE 

 data and to estimate subsequently 

 the corresponding 100 sets of boot- 

 strapped parameters; and 



7 calculate the median value and 

 90% confidence intervals for each 

 parameter using the 100 boot- 

 strapped estimates. 



500 



400 - 



300 



200 - 



100 



J^ 1900 



1905 



1910 



1915 



1920 



1925 



1930 



1935 



1940 



(0 

 O 



600 



100 - 



-"S- Adjusted catch 

 ~^ Reported catch 



69-70 72-73 75-76 78-79 81-82 84-85 87-88 90-91 93-94 



The landed 

 lia, during 

 .June 19701 



Following Efron and Tibshirani ( 1985) 

 and Manly ( 1991 ), the median values 

 and 90% confidence intervals derived 

 from the 100 sets of bootstrapped pa- 

 rameters were used as the parameter 

 estimates and their associated uncer- 

 tainties. The 100 bootstrap runs were 

 considered sufficient for the LMSE method in this study 

 because a preliminary analysis indicated that differ- 

 ences in the distributions of estimated parameters de- 

 rived from 100 and 2000 bootstrap runs were small. 



Since K^^ was assumed to be the same as /C,, there 

 were three parameters, Tj,, (Jjj, and Sgg y^, to be esti- 

 mated in modelling CPUE and catch data observed 

 in period 11. Although CPUE for period 11 was de- 

 rived from accurate records of catch and effort asso- 

 ciated with part of the commercial fishery, under- 

 reporting of total catch occurred to a significant ex- 

 tent during period II (Montgomery and Chen, 1996). 

 The extent of under-reporting in different fishing 

 seasons was estimated on the basis of a survey of 

 fishermen (Table 1; Montgomery'; Montgomery, 

 unpubl. data). Thus, catch in fishing year J was ad- 

 justed from the reported catch (Fig. 1) as 



Fishing year 



Figure 1 



catch of eastern rock lobsters in New South Wales (NSW), Austra- 

 the period of 1903-36, and from 1969-70 (i.e. 1 July 1969 to 30 

 to 1993-94. 



{reported catch) j 



( Adjusted catch) . = 



1 - (adjustment coefficient } J 



where adjustment coefficient = the proportion of 

 der-reporting estimated. 



un- 



The seven-step procedure described above was 

 modified to include the uncertainties in K^ in esti- 

 mating the parameters and associated uncertainties 

 in period II. The modification was accomplished by 

 using values of K^ randomly sampled from the 

 bootstrapped samples generated in the bootstrapped 

 LMSE analysis for period I. Such a modification takes 

 into consideration the variation in K^ (thus K^^) when 

 estimating q,,, r„, and Bjgyg ^^and their variabilities. 



