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Fishery Bulletin 91(3), 1993 



ter length-frequency distributions. The third set of 

 catch-at-age estimates was based on quarterly age- 

 length keys but included data from haddock sampled 

 in the commercial catch and from the NEFSC bottom 

 trawl surveys. The final set of age-length keys con- 

 tained data from haddock caught both commercially 

 and in trawl surveys but combined all data for the 

 first half of the year. 



I treated length-frequency samples as simple ran- 

 dom samples from the entire stock area in the compu- 

 tation of the variance of catch at age. Following Gavaris 

 and Gavaris (1983), the proportion of catch at age for 

 unpooled samples was estimated as 



Ac - 2. L P.,, 



where, 



A iq = Estimated proportion at age i in quarter q 



L iq - Proportion of total individuals at length j in 



quarter q 

 P IJq = Proportion of age i individuals at length j in 



quarter q. 



For samples where age-length keys were pooled across 

 quarters, the proportion of catch at age was estimated 

 as 



A,, = 2-, L jq P ljq 



j 



where P', iq is the proportion of age i individuals at length 

 j for the pooled quarters, and L* q is the pooled propor- 

 tion at length j in the pooled quarters. These propor- 

 tions were calculated as 



p, _ n llt + n lj2 



(L^N. + iL^N, 



N i+ N 2 



where, 



n lj: = # of age i fish at length j> in first time period 

 n lj2 = # of age i fish at length./ in second time period 

 n,, - # offish at length/ in first time period 

 n j2 = # offish at length,/ in second time period 



n\ 



N, 



total # offish landed in first time period 

 total # offish landed in second time period. 



This method of pooling age-length keys treats each 

 observation as a random sample from a single popula- 

 tion. No weighting factors were applied when age- 

 length keys were pooled. A pooled proportion of total 

 individuals at length was computed as a stratified ran- 



dom sample where the weighting for each quarter was 

 the total number of individuals landed during that 

 period. This allows for the possibility that the length 

 composition of landings differed between quarters. 



Estimates of the variance of proportion at age for 

 unpooled data were computed following Gavaris and 

 Gavaris (1983): 



Var(A„)= X 



LIPu 



lk^> 



w 



Where n q is the number offish aged in quarter q. 



Estimates of the variance of proportion at age when 

 age-length keys were pooled were computed with the 

 above formulae, except P] n was substituted for P, jq . 

 Catch at age and variance for each quarter were com- 

 puted following Gavaris and Gavaris (1983). Because 

 these computations do not depend on whether pooled 

 or unpooled age-length keys are used, the formulae 

 are not repeated. 



Results and discussion 



Seasonal growth and comparison of 

 age-length keys 



Most of the annual growth of Georges Bank haddock 

 takes place during the third quarter, from June through 

 September (Fig. 1). From this pattern of annual growth, 

 age-length keys would not be significantly different 

 between the first and second quarters, but would dif- 

 fer significantly betweens the second and third quar- 

 ters, and the third and fourth quarters. Accordingly, 

 tests were conducted between these pairs of quarters 

 to determine if age-length keys could be pooled across 

 any adjacent quarters. Summary statistics of these 

 tests are presented in Tables 2 through 4. Although 

 little growth takes place between the fourth quarter 

 and the first quarter in the following year, landings 

 data are usually finalized on an annual basis; pooling 

 between years is therefore of limited use. 



Comparisons between the first and second quarters 

 yielded 9 of 94 tests exceeding the 0.05 level (Table 2). 

 None of these tests exceeded the adjusted significance 

 level (a*=0. 00054) needed to maintain an error rate of 

 0.05 for this set of comparisons. The number of results 

 exceeding 0.05 is not substantially greater than the 

 number of significant results that would be expected 

 based on random chance; further, these differences oc- 

 curred sporadically among the length classes (Table 2). 

 Thus, based on these tests, first and second quarter 

 age-length keys within each year can be treated as 

 samples drawn from the same population and can be 

 pooled. 



