Ye and Mohammed: Analysis of variation in catchability of Penaeus semisu/catus in waters off Kuwait 



703 



which, depending on the year, may be supplemented 

 by a second, late-summer recruitment in August or 

 early September (Mohammed et al., 1996). The suc- 

 cess of the second recruitment was responsible for 

 record landings, for example, in the 1988-89 and 

 1989-90 seasons (Siddeek et al., 1994). Total land- 

 ings of P. semisu/catus in 1994-95 and 1995-96 were 

 699.7 and 925.0 tonnes, respectively, about 149f and 

 19% of the 1988-89 season's P. semisulcafus catch of 

 5022.4 tonnes (Siddeek et al., 1994). 



Kuwait's opening date for shrimping has been set 

 at 1 September since 1987 (Gulland, 1989; Siddeek 

 and Abdul-Ghaffar, 1989). The season is closed when 

 the CPUE for combined species of the industrial fleet 

 falls below 80-120 kg/boat-day (Xu et al., 1995). In 

 this case, shrimp trawling is a process that depletes 

 a single cohort. 



We start with three basic equations. The first equa- 

 tion is the relation between fishing mortality and 

 fishing effort: 



F,=q,f„ 



(1) 



where g = catchability in month j; 



Fg = fishing mortality in time interval t 



(5 days per interval); and 

 /", = fishing effort in time interval /. 



The second relates the population number at time t 

 to the initial cohort number and cumulative fishing 

 and natural mortalities: 



dependent of time throughout the season and 

 catchability is assumed to remain constant within a 

 month. 



Given catch and effort data, the initial population 

 number (/?), natural mortality rate (M), and six 

 monthly catchability rates iq-}, a total of eight pa- 

 rameters can be estimated in theory by a time-se- 

 ries fitting method of least squares between observed 

 and predicted catches. There exists, however, a prob- 

 lem of confounding the initial stock number, natural 

 mortality, and catchabilities. A high initial popula- 

 tion number with high natural mortality and low 

 catchability rates gives as good a fit as does a low 

 initial population number with a low natural mor- 

 tality and high catchability rates. The following three 

 measures were taken to solve this problem. 



1) We assumed that 



where C'^ = observed catch at time t. 



This assumption says, in effect, that for a given esti- 

 mate ofqj. we have an estimate of the initial popula- 

 tion number iR) from the average catch and effort 

 over the first three time intervals (Hilborn and 

 Walters, 1992). 2) It was presumed that natural 

 mortality was available from other sources. 3) Aux- 

 iliary abundance index was used in the time series 

 fitting as follows: 



A^, =Re 



(2) 



SS: 



fln(C, )-ln(C; 



) + 



H^X 



ln(A',)-ln(X')r,(5) 



where R = initial stock number; 



Ni = population number at time t\ 

 i = time interval; and 

 M = natural mortality. 



The final equation relates catch to current abundance 

 and fishing as well as to natural mortalities, and we 

 assume that fishing mortality acts independently of 

 natural mortality, taking a fraction of F/(F+M) of 

 the total mortality, so 



'F+M^ ' 



(3) 



where C^ = catch in time interval t. 



The three equations describe an exponential decay 

 process of a single cohort with fishing and natural 

 mortalitites. Natural morality is assumed to be in- 



where C^ = predicted catch at time t by Equation 



3; 



C^' = observed catch at time t; 



X' = observed index of stock number in 

 month j in relation to the beginning 

 point of a fishing season; 



X = predicted relative stock abundance in 

 the middle of month j, i.e. predicted 

 stock number in month ; divided by the 

 predicted stock number of the middle 

 point of the beginning month; and 



W = the weight given to the deviation be- 

 tween the predicted and the obsei-ved 

 stock indices. 



This procedure reduced the number of parameters 

 to be estimated to six. Monthly CPUE of the United 

 Fisheries of Kuwait (UFK) fieet was used as auxil- 

 iary information about stock abundance. 



