Heifetz et al.: Age validation and analysis of ageing error for Anoplopoma fimbria 



259 



•■ab 



(*) 



^r£-ii*£iMii' 



■2 ai6. 



^2no{b) 



(5) 



To estimate the classification matrix defined by Equa- 

 tion 2, maximum likelihood was used to estimate the 

 parameters of the model. The likelihood (L) of the 

 observed ages A given the true ages B is 



/ .] 



L(A\B) = WY\q(a^j\b„<S», 



(6) 



,=1 j=i 



where a - the age assigned to fish / by reader 7; 

 and 

 6, = the true age of fish j. 



In practice, the inference function -2 log L(A | B) is 

 minimized to obtain parameter estimates. Given the 

 number of parameters A'^, the Akaike information 

 criteria (AIC) (Akaike, 1974; Richards et al., 1992), 



A/C = -2 log L(A|B) + 2N, 



(7) 



was used in the model identification process. A model 

 with a low AIC value in relation to other models is con- 

 sidered the best-fit model with the fewest parameters. 

 Six alternative representations (cases) of ageing 

 error were considered in the analysis. The different 

 cases represented the two different data sets, full 

 models, and models reduced by parameter con- 

 straints (Table 1). Although not within the scope of 

 our study, we recognize other alternative model speci- 

 fications may be appropriate for these data sets. For 

 example, a classification matrix with skewed distri- 

 butions of the probability of assigning an age to a 

 fish of a given true age may be appropriate. 



Results and discussion 



Comparison of reader ages to known ages 



The primary reader ages agreed with the known ages 

 in 35.4'7f of the cases (Fig. 1). Of the 49 known-age 

 sablefish otoliths, the primary reader chose not to 

 age one specimen because of the poor condition of its 

 otoliths. Of the 31 misaged fish, the primary reader 

 misaged most (80.6%) by 1 year: 17 of the 18 

 underaged fish and 8 of the 13 overaged fish. In three 

 cases (known ages=4, 6, and 6 years), the primary- 

 reader ages differed substantially at 8, 11, and 12 years. 

 Results for the tester were generally similar to 

 those of the primary reader The tester age agreed 

 with the known age in 38.6% of the 44 total otoliths 

 that the tester aged (Fig. 1), and 5 otoliths were con- 



14 

 13- 

 12 • 

 11 

 10 - 

 9 - 

 « 8- 



ra 7 - 

 to I 



^ 5- 

 4 

 3 



2 ( 

 1 

 

 -1 : 



1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 



Individual otoliths 



Figure 1 



Comparison of known age with ages obtained by two age 

 readers for 49 sablefish. A value of-1 for a age denotes the 

 reader chose not to age the given sample. The .r-axis has 

 been sorted by known age from youngest to oldest. 



sidered unreadable. Of the testers's misaged fish, 

 most (70.1%) were misaged by 1 year: 10 of the 13 

 underaged fish and 9 of the 14 overaged fish. The 

 largest discrepancy was 4 years; known age was 9 

 years and tester age was 13 years. 



Agreement between primary reader and tester ages 

 was much greater than between the known and pri- 

 mary-reader ages or the known and tester ages (Fig. 

 1). Primary reader and tester matched ages in 24 of 

 the 44 (54.5%) specimens compared, indicating that 

 they interpreted annuli similarly. Most discrepan- 

 cies {n-12\ 60.0%) were discrepancies of one year. 

 The primary reader tended to age the fish younger 

 than the tester: 12 less than tester ages and 8 greater 

 Only once did their ages differ by more than two years 

 (known age=9; primary reader=9; tester=13). 



