770 



Fishery Bulletin 88(4), 1990 



Figure 13 



Response surface of the SRLCA score function for the northern 

 shrimp survey 1984-88 length-frequency distribution. 



Values from the primary ridge tended to treat the 

 assumed first and second observed age-groups, up to 

 21 mm, as a single mode, with animals greater than 

 21.5 mm classified as age 2. Values from the secondary 

 ridge accurately interpreted the assumed age-group 1, 

 but lumped the assumed second and third age-groups 

 as a single mode, with shrimp >25 mm classified as 

 age 3. Values from the tertiary ridge also correctly 

 characterized the first age group and failed to resolve 

 the second and third modes to distinct age classes, but 

 split shrimp >24 mm into age-groups 3 and 4. It is in- 

 teresting to note that the two sets of previously derived 

 von Bertalanffy parameters for this stock noted earlier 

 (see Methods: A Priori Assumptions) fell within this 

 tertiary ridge of scores. This indicated that growth 

 rates based on those parameters were too fast to pro- 

 vide an interjjretation of length distributions consistent 

 with visual inspection of the length modes. 



Quaternary ridge values successfully classified the 

 first-fourth assumed age-groups in line with prior 

 assumptions. These parameters also provided an age- 

 group 5 for CL >27.5 mm. The quaternary ridge non- 

 Ixiundary maximum score parameters (L,„f = 33 mm, 

 K = 0.32) were selected for final SRLCA evaluation of 

 the pooled length frequency, as these values provided 

 the characterization of the pooled distribution closest 



o 



CD 



=) 

 Z 



Z 

 < 



< 



1984-88 



X 



o 



o 



o 



LJ 



> 



_1 



o 



15 20 25 3D 



CARAPACE LENGTH (mm) 



35 



Figure 14 



Northern shrimp survey 1;)<X4-.S,S |>cH)led length-frequency distribu- 

 tion (Tiistogram) and pattern of SRLCA scores (solid curve) for growth 

 parameters selected for final evaluation (L|„( = 33 mm, K = 0.32). 



to the assumed age structure (Fig. 14). The growth 

 curve defined by these parameters indicates a slower 

 rate compared with previously estimated growth 

 curves (data from Haynes and Wigley 1969, Mclnnes 

 1986), a result of the influence, or "bias," of the abun- 

 dant, apparently slower-growing, 1982 cohort on the 

 score function (Fig. 15). 



We derived annual age frequencies by slicing annual 

 length frequencies to age-groups according to the max- 

 imum-scoring growth parameters provided by the four 

 score ridges of the pooled analysis (Table 6). Since 

 shrimp of age-group 2 and older are assumed fully 

 recruited to the survey trawl gear, total instantaneous 

 mortality estimates (Z) were derived from: 



In (^ age 2 + for Year^ / X '^>^'^ ^ + f"*" Yearx + 1 ). 



These values were then compared with jireviously 

 calculated estimates of total mortality from the length- 

 frequency data (NSTC 1985, 1986, "l987, 1988). 



Table 7 shows the widely divergent age frequencies 

 and subsequent Z estimates provided by the four 

 different pairs of growth parameters, which again illus- 

 trate a necessity for some external source of informa- 

 tion to interpret SRLCA results in a manner consis- 

 tent with a priori assumptions. We note that for the 

 1987 distribution, the quaternary ridge parameters and 

 NSTC visual inspection sliced the length-frequency 

 distribution at the same length intervals, resulting in 

 identical age frequencies for 1987. As expected, use 

 of the quaternary SRLCA score ridge parameters to 



