548 



Fishery Bulletin 91(3). 1993 



Table 1 



Matrix of MULTIFAN inverse log-likelihood function values for alter- 

 native interpretations of the number of significant age classes under- 

 lying the North Carolina Division of Marine Fisheries 1986-1989 

 bluefish iPomatomus saltatrix) length-frequency test data. LISD = 

 length independent standard deviation in length at age, LDSD = 

 length dependent standard deviation in length at age, NOSEL = no 

 selectivity bias on the first age group. SEL = selectivity bias on the 

 first age group. Values in parentheses are the number of parameters 

 in model being tested (e.g., proportions at age, mean lengths at age, 

 A", LDSD, or SEL). Bold underlined value is combination of character- 

 istics selected for final evaluation as the best fitting model, based on 

 the significance of increases in value with added parameters. 



Ages LISD+NOSEL LISD+SEL LDSD+NOSEL LDSD+SEL 



10 



11 



12 



13 



growth follows the von Bertalanffy function. Other 

 growth functions such as the logistic or Gomphertz 

 may be better models of growth for the youngest 

 age classes of fish, or for species that experience 

 periods of rapid growth at intermediate ages fol- 

 lowed by slow growth as they approach asymp- 

 totic sizes (Moreau, 1987; Terceiro 4 ). 



The normal distribution of length at age as- 

 sumed in MULTIFAN is appropriate for many 

 fish species (Fournier and Breen, 1983; Fournier 

 et al., 1990; Terceiro et al., 1992). Other prob- 

 ability distributions might better describe the 

 variation in length at age for species with special 

 life-history characteristics. Species characterized 

 by multiple spawning events or extreme varia- 

 tion in growth among cohorts due to density de- 

 pendence often exhibit log-normal (long-tailed) 

 distributions of length at age. Consideration of 

 alternative probability distributions would be a 

 useful addition to the MULTIFAN model. For spe- 

 cies subject to a high degree of size selectivity 

 within age, or those experiencing very slow 

 growth at the oldest ages, the inclusion of pa- 

 rameters that account for departures from nor- 

 mality (skewness and kurtosis) could provide a 

 MULTIFAN model that better estimates age from 

 asymmetric distributions of length at age. 



4 Terceiro, M. 1991. Length composition analysis of Atlantic 

 sea scallop using the MULTIFAN method. In Report of the 

 Twelfth Northeast Regional Stock Assessment Workshop ( 12th 

 SAW), Spring 1991, Appendix 1. p. 1-29. U.S. Dep. Commer., 

 NOAA, Natl. Mar. Fish. Serv., Northeast Fish. Sci. Cent., 

 Woods Hole Lab. Ref. Doc. 91-03, 187 p. 



