Chen and Montgomery: Modeling the dynamics of Jasus veireauxi 



29 



Table 1 



Coefficients used to adjust reported catch data in the pe- 

 riod of 1969-70 to 1993-94. 



Year 



Adjustment coefficient 



1969-70 to 1979-80 

 1980-81 to 1989-90 

 1990-91 to 1991-92 

 1992-93 to 1993-94 



0.5 

 0.7 

 0.45 

 0.15 



Evaluation of probability of overexploitation for 

 next fishing season 



The probability of short-term overexploitation (i.e. 

 the probability of the fishing mortality rate being 

 higher than defined biological reference points) was 

 defined with respect to different levels of catch for 

 the 1996-97 fishing season. The two biological refer- 

 ence points used in our study were /], j and Ay<,y- '^^^ 

 /Ji J is equivalent to the more commonly used F,, j 

 (Hilborn and Walters, 1992) and is defined by the 

 equation 



dC{E) 



dE 



= 0.1 



dC(E] 



E=t„,.q 



dE 



E=0 



where C(E) - the equilibrium yield corresponding to 

 efforts (Punt, 1993). 



From the above equation and Equation 1, /"o j can be 

 calculated as/"„ , = 0.45/-. The TAG in year,/ based on 

 the/j^i , can be calculated as TAC^ ^(j) - 0A5rB where 

 B is the estimate of stock biomass in yearj. The rate 

 of fishing mortality 'fv/sy' producing maximum sus- 

 tainable yield (MSy) can be calculated as/'^^^^.y. = 0.5/-. 

 The TAC in year j, based on /"^^^y, can be calculated 

 as TACi^fgy ij) = 0.5rB^. It should be noted that the 

 TAC^jgY 0' calculated above changes with the cur- 

 rent stock biomass and is thus dynamic over time. It 

 differs from the commonly used equilibrium maxi- 

 mum sustainable yield (EMSY) calculated as rK/4 

 (Hilborn and Walters, 1992). The use of TAC 



MSY 



C7» 



is more robust with respect to interannual variabil- 

 ity in the biomass of the stock than is a TAC based 

 on the more commonly used EMSY. 



Results 



,, (7,, and K^ estimated with the LMSE 

 method were 0.203, 1.76 x lO*^ ' 



Parameters '"i , , 



(per vessel, and 3208 1, 

 respectively This results in an EMSY of 163 t. The 

 predicted CPUEs tended to follow the CPUEs ob- 



Table 2 



Summary of the estimates of parameters with the 

 bootstrapped LMSE method from 100 runs of bootstrap 

 simulation for CPUE and catch data observed during 1903 

 to 1936. 



where CPUE and CPUE are observed and predicted catch per 

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



served in the majority of years in period I (Fig. 2). 

 However, CPUEs observed in the years 1904 and 

 1917-24 differed considerably from the LMSE-pre- 

 dicted values, indicating that they virtually were ig- 

 nored in the parameter estimation. The estimated 

 stock size in year 1936 was 37. 6^^ of the virgin biom- 

 ass. The median value for K^ from the 100 boot- 

 strapped LMSE estimates was 4084 1 (Table 2), about 

 27*7^ higher than the LMSE-estimated K^. The coef 

 ficient of variation (CV) for the LMSE-estimated K^ 

 was only 269f , indicating that the uncertainty asso- 

 ciated with the LMSE-estimated K^ was small. The 

 median values of bootstrapped r and q were 0.155 

 and 1.2 x lO"*^ (per vessel) (Table 2), about 24% and 

 32% lower than the LMSE-estimated r and g, respec- 

 tively. The higher CV for /-, compared with the CVs 

 for q and K^, indicates that the estimate of r is more 

 uncertain than the estimates of g and K^. The distri- 

 butions of all three parameters tended to be posi- 

 tively skewed (Fig. 3). The estimated EMSY ranged 

 from 50 t to 200 t with the median value of 151 t 

 (Fig. 3). 



By assuming K^^ to be the same as the median value 

 of if J estimated in the bootstrapped LMSE estimation, 

 we estimated parameters rjj, Qjj, and 5i9g9_7y The 

 LMSE-estimated Sjggg_.yg was close to the value of Xj 

 (4,365 t). The r„ was 0.218, about 7% higher than the 

 LMSE-estimated r,. The LMSE-estimated gjj was 0. 15 

 X 10"*' ( per trap-month ). The model was fitted by means 

 of the LMSE method by ignoring the data observed in 

 the two fishing seasons 1971-72 and 1974-75 because 



