594 



Fishery Bulletin 97(3), 1999 



l l I f I I I I M I M ' I I M ri -i 

 40 46 52 58 64 70 85 



40 46 52 58 64 70 85 



0,0 



40 46 52 58 64 70 85 



40 46 52 58 64 70 85 



0.3 -I 



40 46 52 58 64 70 85 



0.3 1 



0.2 



0.1 



0.0 -I M ^ t 



40 46 52 58 64 70 85 



Length class (cm) 



Figure 3 



Survey ( ) and fishery t ) length compositions for females. Male lengths also 



are available, but only female lengths are displayed for brevity. Alaska-wide fishery 

 length data were available only since 1990. 



age and length samples are independent, then the 

 log-likelihood is 



Pxl 



^ = X Py log ^^ + X Py' ^°^ 



ya Pya yi Pyl 



-^'Y\].og{Iy)-\Qg(qN^)\ + constant, 



where A is the ratio of the effective multinomial 

 sample sizes, either age or length, to the variance of 

 the log-transformed abundance index (Deriso et al., 

 1985). Thus A is a weighting factor that adjusts the 

 relative influence of the abundance index and age 



and length components of the likelihood. The range 

 of A from 0.02 to 10 was tested. The value A = 1 ap- 

 peared the most reasonable and is used henceforth. 

 This value was chosen on the basis of fit of each data 

 type and the effect on the estimated recruitment 

 values as A was varied. As A increased from 0.02 to 

 10, the fit of the index data improved only at the 

 expense of the fit of the length data, but the relative 

 sizes of the annual recruitment estimates were un- 

 affected for A < 2. Increasing A substantially improved 

 the fit of the index data until A was from 1 to 2, when 

 improvement slowed. Thus a value of A between 1 

 and 2 seems reasonable, with A = 1 chosen because 

 the fit of the age data was best at that point. In prac- 



