596 



Fishery Bulletin 97(3), 1999 



egorized as |2, 3, ..., 15, 16+) . For inaccurate age or 

 length data, 50% were correctly assigned to the true 

 age, 'ZOVc to -1 year, 20% to +1 year, 5% to -2 years, 

 and 5% to +2 years, then categorized as 12, 3, ..., 8, 

 9+). 



Survey selectivity may affect parameter estima- 

 tion. Bence et al. ( 1993 ) found that biomass estimates 

 were more accurate and precise for a population 

 model with data from a survey with asymptotic se- 

 lectivity than from one with dome-shaped selectiv- 

 ity. Therefore, both asymptotic and dome-shaped se- 

 lectivity were compared. The dome-shape was cho- 

 sen such that the availability of the last age group 

 was 0.5. 



A measure of the variability of biomass estimated 

 in the simulations is the MSE computed from pa- 

 rameter estimates and their "true" values. Mean 

 square error (MSE I was converted to coefficient of 

 error (CE), defined as the "true" value divided into 

 the square root of MSE (Kimura, 1990). Twenty-five 

 to fifty replicate simulations were completed for each 

 scenario. 



Results 



Model results for the original data 



The model fitted all the original data well: abundance 

 index ( Fig. 4 ), age data ( Fig. 5 ), and length data ( Fig. 

 6 ). The estimate of survey catchability appears good; 

 the likelihood profiled over a range of catchabilities 

 shows a distinct, regular curvature (Fig. 7). Esti- 

 mated exploitable biomass for 1995 was 181,000 t 

 (Fig. 8), and projected ABCgg was 19,600 t. Estimated 

 biomass decreased from a peak in the mid-1980s. The 



peak is attributed to strong recruitment in the late 

 1970s; recruitment has decreased in recent years 

 (Fig. 9). Estimates of recent exploitation rates for 

 fully selected ages average 107f (Fig. 8), which is near 

 the exploitation rate equivalent to F^^y., the current 

 reference point for sablefish management in Alaska. 

 The shape of the estimated selectivity curve was as- 

 ymptotic (i.e. Y=0). 



The estimate of natural mortality for sablefish is 

 uncertain; therefore its effect on abundance estima- 

 tion was examined. An important part of this exami- 

 nation was to analyze the interaction between M and 

 other key parameters. Model parameters were esti- 

 mated for several fixed values of natural mortality 

 around M = 0.10 (Table 2). The log-likelihood is not 

 maximized at M = 0. 10, and there is a slightly higher 

 value for M = 0.12 (panel 1). Catchability was smaller 

 and exploitable biomass was larger for larger M ( panel 

 2); biomass was larger to account for more natural 

 deaths. The fishable fraction of the total population 



.N. 



/I^vo 



V a 



was smaller for larger M (panel 3) because the fish 

 recruited later (panel 4). Asymptotic selectivity was 

 estimated whatever the value of M (panel 5). A5Cgg 

 was larger for larger M( panel 6) because exploitable 

 biomass was larger and the fishing rate, F^^^., in- 

 creases with M. 



Natural mortality and survey catchability can af- 

 fect abundance estimates; therefore their effect was 

 examined. Model parameters were estimated for sev- 

 eral fixed values of g and M (Table 2). For each fixed 

 M, the approach was to fix q at values near the esti- 

 mated q. The results are likelihood profiles of q for 

 each fixed M (panel 1). Given M, exploitable biomass 

 was smaller for larger q (panel 2). The effect of g on 

 the fishable fraction was more complicated. Given 

 M, the fishable fraction was smaller for the fixed q 

 that was less than the estimated q (panel 3) because 

 older fish were less vulnerable to the fishery (panel 

 5). Given M, the fishable fraction was less for the 

 fixed q that was greater than the estimated q be- 

 cause fish recruited later (panel 4). Selectivity was 

 asymptotic and could not increase above 1.0, forcing 

 the decreased fishable fraction to occur by means of 

 a later recruitment age. ABCgg was larger for smaller 

 values of g (panel 6) because exploitable biomass was 

 larger (panel 2). 



Model results for the simulated data 



Biomass estimates were unbiased for simulations 

 based on a survey with asymptotic selectivity, when 



