Chen and Montgomery: Modeling the dynamics of Jasus verreauxi 



31 



1.2 



time periods (per vessel versus 

 per trap-month). The CVs and 

 90% confidence intervals for 

 the parameters were small 

 (Table 3), indicating that esti- 

 mates of parameters for period 

 II had small uncertainties. 

 The estimated EMSY ranged 

 from 80 t to over 200 t with a 

 median value of 120 t (Fig. 5). 

 The median and 5'*^ and 95* 

 percentiles of the biomass of 

 the stock for each year in pe- 

 riod II are plotted in Figure 6. 

 The calculation of total catches 

 for 1994-95 and 1995-96 had 

 not been completed when this 

 study was conducted. How- 

 ever, the TAG of 106 t was 

 likely to have been fully real- 

 ized in each of these years. 

 Thus, the biomasses of the 

 stock for 1995-96 and 1996- 

 97 were projected based upon 



the assumption that catches in 1994-95 and 1995- 

 96 were 106 t. The 90% confidence intervals tended 

 to increase from 1969-70 to 1994-95 (Fig. 6), indi- 

 cating that estimates of the stock biomass in recent 

 years were less precise than those in earlier years. 

 The median value of the biomass of stock in the 1995- 

 96 fishing year was 1420 t, and the 5'^ and 95"^ per- 



Observed cpus 

 LMSE 



\ i i i h 



0.0 



1389-70 72-73 7S-7S 



i I i I I i i I I I I I I I I I 

 78-79 81-82 84-85 87-88 90-91 93-94 



Fishing year 



Figure 4 



Catch per unit of effort observed and predicted with the LMSE method for the NSW 

 eastern rock lobster fishery during the period of 1969-70 (i.e. 1 July 1969 to 30 June 

 1970) to 1993-94 (i.e. 1 July 1993 to 30 June 1994). 



Table 3 



Summary of the estimates of parameters using the LMSE 

 method from 100 runs of bootstrap simulation for CPUE 

 and catch data observed from 1969-70 to 1993-94. 



where CPUE and CPUE are observed and predicted catch per 

 unit of effort, respectively, and n is the number of years. 



centiles were 710 and 2719 t (Fig. 6). Median values 

 for the biomass of the stock fell until 1990-91 and 

 then started to increase from 1992-93. The plot of 

 the distribution of the ratio between biomass in year 

 1995-96 against the biomass of the virgin stock in- 

 dicated that there was more than 75% chance that 

 the biomass ranged between 15% and 30% of the vir- 

 gin biomass (Fig. 7). 



The distribution of the biomass of the stock in 

 1996-97 is summarized in Figure 8. There was more 

 than a 70% chance that the biomass of the stock 

 ranged between 1000 to 1750 t. The probabilities of 

 short-term overharvest (i.e. exceeding the selected 

 biological reference points) were calculated for dif- 

 ferent levels of catch in 1996-97 on the basis of the 

 distribution estimated for the biomass of the stock 

 in 1996-97 (Fig. 9). For example, the TAG of 100 t 

 would have a 30% chance of exceeding the reference 

 point f^^Y' ^^'^ ^ ^^0% chance of exceeding /q ^ (Fig. 9). 



Discussion 



The model used in this study is one of the simplest 

 models commonly used in fish stock assessment 

 (Hilborn and Walters, 1992). An essential assump- 

 tion of this model, as with similar models, is that the 

 relationship between GPUE and the biomass of the 

 stock remains constant over time. Because of the use 

 of the robust estimator, this assumption becomes the 

 following: the proportional relationship between the 



