542 



Fishery Bulletin 9 1 (3), 1993 



Discussion 



Cohort slicing, standard application of the CNN ALK, 

 the IALK method, and MULTIFAN are increasingly 

 complex solutions to the problem of estimating ages 

 from length data when appropriate age-length keys 

 are not available. All four methods provided reason- 

 able interpretations of the NCDMF bluefish data by 

 accurately reflecting the dominance of age-0 and age-1 

 fish in the length distributions. Cohort slicing using 

 the NOAA (1989) parameters generally provided the 

 poorest match with the NCDMF proportions at age, 

 because the method fails to account for the variability 

 in length at age owing to multiple spawning events 

 and the variation in growth among cohorts. 



The CNN ALK and IALK provided satisfactory reso- 

 lution of bluefish lengths to age, nearly matching those 

 estimated by the best MULTIFAN fit for the combined 

 NCDMF 1986-1989 data. Performance of the CNNALK 

 and IALK was poorest for those bluefish ages with a 

 high degree of overlap in the NCDMF length distribu- 

 tions (usually ages 4 and 5) because of the inability of 

 these methods to accurately portray the variation in 

 growth among cohorts. However, the CNN ALK and 

 IALK provided the most accurate estimates of mean 

 length at age for very large bluefish (age 7 and older) 

 which often may not be sufficiently abundant in length- 

 frequency sample distributions to form significant 

 modes. 



We note that with the IALK method, the length-age 

 data would usually be applied to a length distribution 

 of unknown age composition, in which case the alter- 

 native method we used for selecting the best IALK 

 solution would not be an option. Kimura and Chikuni 

 < 1987) suggested the IALK method should reduce bias 

 in the resulting age distribution if an age-length key 



is applied to length-frequency data with potentially 

 different underlying growth or selectivity patterns. Our 

 work confirmed that the IALK algorithm achieves the 

 goal of reducing the differences in underlying age dis- 

 tribution of the length-age data used as a key and the 

 length frequency to be aged. However, when these dif- 

 ferences are so large that even the less restrictive as- 

 sumptions of the IALK method are violated, the IALK 

 method provides little improvement over standard ap- 

 plication of the age-length key. 



MULTIFAN performed well in resolving the under- 

 lying age structure of bluefish length frequency 

 samples, given the reasonable number (e.g., through 

 age 5 or 6) of age groups that were apparent in the 

 NCDMF 1986-1989 length samples. MULTIFAN was 

 the only method to correctly estimate the relative pro- 

 portions at ages 4 and 5, by accurately reflecting the 

 variation in length at age of fish from the length fre- 

 quency mode at 65-75 cm. 



Key attributes of the MULTIFAN model which con- 

 tributed to good performance in this exercise with blue- 

 fish data include 1) the large number of parameters 

 estimated by the model, and consideration of variation 

 of mean length at age and selectivity bias on the first 

 age class, 2) use of the entire NCDMF length data 

 series to estimate the growth pattern, and 3) the hy- 

 pothesis testing approach to model evaluation. Based 

 on qualitative evaluation of the estimates of mean 

 lengths at age and the quantitative comparison of es- 

 timated proportions at age with the Kolmogorov- 

 Smirnov cumulative distribution test, we believe that 

 MULTIFAN was the best current alternative to a time 

 series of fishery-specific age-length keys for the esti- 

 mation of bluefish ages from lengths data. 



The MULTIFAN model is a good starting point for 

 future method development. MULTIFAN assumes 



