Anderson: Age. growth, and mortality of Pandalus borealis Krbyer 



543 



Carapace 



Length (mm) 



Figure 2 



Size-frequency distributions of Pandalus borealis from Pavlof Bay, Alaska, 

 in catch per kilometer from (A) annual research surveys, 1972-81, and (B) 

 total numbers in the commercial catch, 1972-78. Dominant 1971 and 1975 

 size modes are shaded. 



from each survey tow. Endopodite structure 

 of the first two pleopods (Allen 1959) was 

 used to separate the sexes. Length -frequen- 

 cy data by sex from commercial catch sam- 

 ples were provided courtesy of the ADF&G 

 (211 Mission Rd., Kodiak, AK 99615). 



Estimating mean size 



and abundance of year-classes 



The total number of P. borealis in a survey 

 or commercial catch was estimated for each 

 0.5 mm CL group as 



N, 



c, 



w, 



(1) 



where 

 Nh = 



n,; = 



G = 



w, = 



number of P. borealis in the ith size 

 interval taken in the j th haul (i = 



1 q; j = 1 r), 



number of P. borealis in the ith size 



interval sampled from the jth haul, 



weight of P. borealis in the jth haul, 



and 



sampled weight in the jth haul. 



Estimates of abundance for each size 

 group were summed for all tows annually 

 to form length-frequency distributions (Fig. 

 2). The technique of Macdonald and Pitcher 

 (1979) was then used to separate and quan- 

 tify year-class modes. Length was assumed 

 to be normally distributed for a given year- 

 class. The computer algorithm (Macdonald 

 1980) requires starting values of parameters 

 (mean, standard deviation, proportion) for 

 each component (year-class). Starting values 

 for parameters were visually determined 

 and the program iteratively computed max- 

 imum-likelihood parameters. 



The estimated number of shrimp of a 

 given year-class (N k ) was calculated as 



Nk = P k N.. B/£Cj, (3) 



j=i 



letting 



P k = estimated proportion of the kth 

 year-class in the sample popula- 

 tion N. ., 

 N . . = estimated total number of shrimp 

 captured in a survey period, and 



