544 



Fishery Bulletin 89(4), 1991 



B = - I [Cj/aj] q, 



F k = £Z k /(l - e- z k) 



(6) 



(3) 



j = i 



where B = estimated biomass of P. borealis, 



A = total survey area (Pavlof Bay > 55 m; 302 



km 2 ), 

 aj = area covered in tow j, and 

 q = catchability coefficient of the sampling 



gear. 



In the absence of better information, the catchability 

 coefficient (q) in this analysis was set at 1.0. Strictly 

 speaking, this only applies to shrimp sizes that are fully 

 recruited to the sampling area and gear. Equation (3) 

 is modified from Alverson and Pereyra (1969). Biomass 

 estimates are conservative because small (< 18 mm CL) 

 shrimp are not fully vulnerable to capture. 



Finally, the number of P. borealis of a given year 

 class (R k ) caught by the fishery between research 

 sampling surveys was estimated as 



where £ = annual exploitation, the ratio of estimated 

 catch in numbers (R k from eq. 4) and 

 estimated abundance (N k from eq. 2) of 

 the 1971 and 1975 year-classes. 



Natural mortality (M) was calculated by subtraction: 



M k = Z k - F k . (7) 



Results and discussion 



Estimates of age, growth, and mortality rates in this 

 study were made for two dominant year-classes that 

 could be followed through most of their life span. 

 Assumptions underlying the estimates were that size 

 modes represented year-classes, and immigration and 

 emigration of Pavlof Bay shrimp were minimal. 



R k = P k N.. [L/W], 



(4) 



where P k is calculated similarly to survey catches 

 above, 

 N. . = total number of shrimp sampled from 

 the commercial catch in a given year, 

 L = total landed weight of P. borealis be- 

 tween surveys, and 

 W = total sample weight from which N . . was 

 calculated. 



Determination of growth and mortality 



Growth rates were estimated by following the 1971 and 

 1975 year-classes through a time series of length- 

 frequency distributions (Fig. 2). The dominance of these 

 year-classes minimizes the effect of overlap with adja- 

 cent modes. Nonlinear least-squares regression (Pro- 

 gram BCG2, Abramson 1971) was used to fit von Ber- 

 talanffy growth curves to average size-at-age data. 



Annual instantaneous total mortality rates (Z) for the 

 dominant year-classes were calculated as 



Z k = -In (N M+1 / N k>t ) 



(5) 



where t 



one year and N k t and N k t + 1 represent 

 the relative abundance of the kth year- 

 class in two consecutive years. 



Estimated fishing (F) mortality was derived from 

 estimated total mortality using Ricker's (1975) formula 



Identification of year-classes 



The 1971 and 1975 year-class modes were identified 

 and followed through 1981 in length-frequency plots 

 (Fig. 2, Table 2). The size at which dominant modes are 

 first identified is between 10 and 11mm CL. Pandalus 

 borealis of this size are approximately 1.4 years old if 

 it is assumed that larvae hatch in April, and early 

 growth is similar to that reported by other investi- 

 gators (Butler 1964, Ivanov 1970, Fox 1972, Skuladot- 

 tir 1981). The plots indicate similar patterns between 

 the two year-classes, as well as close agreement in loca- 

 tion of dominant modes in both the survey and com- 

 mercial data (Fig. 2 and Table 2). Close agreement in 

 the modal structure of the two independent data sets 

 supported the assumption that the survey and commer- 

 cial catch data were drawn from the same population 

 and made estimation of fishing mortality possible. Com- 

 mercial gear used comparable mesh and had a similar 

 fishing configuration to our survey gear, except for the 

 codend liner. The presence of a codend liner in survey 

 sampling gear may explain the better definition of 1.4 

 year-old modes in survey samples due to the smaller 

 effective mesh size. 



Problems in identifying the age of the smallest modal 

 group have been noted by other researchers (Frechette 

 and Parsons 1983). Entering year-class modes from 

 survey data were assigned the age of 1.4. A smaller 

 mode (mean of 6.5-7.5 mm CL; numbers not large 

 enough to be depicted in Fig. 2) was designated age 

 0.4 (~146 days assuming an April hatch). Nunes (1984) 

 reported that laboratory-reared P. borealis postlarvae 

 reached 3. 6-3. 9mm CL by about 110 days after hatch- 



