486 



Fishery Bulletin 90(3), 1992 



CT> 



C 



■o 



c 



Year 



Figure 2 



Total slipper (Scyllarides squammosics) and spiny (Panulirus marginatus) lobster land 

 ings and CPUE from the Northwestern Hawaiian Is., 1977-90. 



haul (Fig. 2), based on catch and effort data reported 

 in the logbooks. Catch data in the logbooks are checked 

 against landings by enforcement agents, so misreport- 

 ing is not a problem. Common assessment approaches, 

 such as length-based cohort analysis, are not applicable 

 to this fishery, given the relatively short time-series 

 of catch and effort data, the difficulty in routinely 

 ageing lobsters, and the lack of information on the size- 

 frequency from the landings and the nature of a stock- 

 recruitment relationship. While a dynamic surplus pro- 

 duction model has been applied to the data, an implicit 

 assumption about the form of the stock recruitment 

 relationship is required (Polovina 1991). 



A more general approach is to begin with a model 

 which expresses Nj as the number of exploitable lob- 

 sters at time t as a function of Nt_ i , Z as the total in- 

 stantaneous mortality from time t - 1 to t, and r as the 

 number which recruit and survive from t - 1 to t as 



Nt = r -I- Nt^i e-^ 



Using the relationship that the product of catchability 

 (q) and N(t) is CPUE(t), this model becomes 



CPUEt = q*r -H CPUEt.i e-M-qf, 



where M and f are annual instantaneous natural mor- 

 tality and fishing effort, respectively, during the period 

 t- 1 to t. This CPUE model, a simple version of a size- 

 structured model developed by Schnute et al. (1989), 

 was used to estimate population parameters and to 



evaluate the extent that fishing 

 effort explains the observed vari- 

 ation in CPUE. This model as- 

 sumes constant catchability and 

 recruitment; hence, the differ- 

 ences between predicted and 

 observed CPUE are interpreted 

 as variation in recnoitment, catch- 

 ability, or both. 



The commercial data do not 

 indicate whether effort was di- 

 rected at slipper or spiny lobster. 

 However, the catches can be 

 grouped into two periods based 

 on the proportion of spiny to slip- 

 per lobsters. In period 1 (1983- 

 84 and 1988-90), ~80% of the 

 landings were spiny lobster; in 

 period 2 (1985-87), ^56% of the 

 landings were spiny lobster 

 (Table 1). The change in propor- 

 tion of spiny lobster catches is 

 likely due to changes in targeting 

 and abundance. The CPUE 

 model is modified so that a catchability coefficient can 

 be estimated for each period. Our modified CPUE 

 model regresses the CPUE of spiny lobster above the 

 minimum size in month t (CPUEt) on the CPUE of the 

 same month in the previous year: 



(M + Q,f.) 



CPUEt = K*Qt e 



+ (CPUEt_i2)(e-M-Q,f,) 



with 



' Qt 



Qt-12 



Qt = qiii.t + q2i 



2,t 



where qj is the catchability of spiny lobster during 

 period 1, q2 is the catchability during period 2, M is 

 the annual instantaneous natural mortality, R is the 

 annual recruitment, f is the cumulative fishing effort 

 during the period (t- 12, t- 1), and Ij , (i= 1,2) is the 

 indicator or set function which takes the value 1 if t 

 is within period i or otherwise takes the value 0. Esti- 

 mates of R, q] , qo , and M were obtained by minimiz- 

 ing the sum of squares of the difference between the 

 square root of the observed and predicted CPUE with 

 a simplex algorithm. 



Sea level data 



To examine the relationship between lobster recruit- 

 ment variation at Maro Reef and physical factors such 



