Sigler: Estimation of abundance of Anoplopoma fimbria off Alaska 



601 



Figure 11 



Coefficient of error (CE) of the exploitable biomass (thou- 

 sands metric tons) versus year: asymptotic selectivity, age 

 and length data (♦); asymptotic selectivity, age data (■): 

 asymptotic selectivity, length data (▲); and dome-shaped 

 selectivity, length data i#). 



age structure could be inferred from survey length 

 data for the several years where no age data were 

 available. This latter assumption may hold for sable- 

 fish, but would be conspicuously violated for other 

 species such as Pacific halibut, Hippoglossus 

 stenolepis, whose growth rate has changed over time. 

 Recent improvements in Alaskan sablefish data col- 

 lection eventually will lead to tests of these assump- 

 tions. Otoliths have been collected and read annu- 

 ally from longline surveys since 1995. Fishery lengths 

 have been collected annually since 1990. 



A measure of relative abundance, effort data, was 

 necessary to obtain reasonable estimates of absolute 

 abundance with an age-structured model of Pacific 

 halibut, as shown by comparison to cohort analysis 

 of historical data of year classes with complete catch 

 data (Deriso et al., 1985). The frequency and num- 

 ber of the relative abundance estimates can affect 

 abundance estimation. Absolute biomass was esti- 

 mated successfully for Alaskan sablefish in this pa- 

 per and for the simulated widow rockfish fishery 

 (Bence et al., 1993). Annual surveys were simulated 

 for 17 and 15 years, respectively. However, precise 

 abundance estimates may not always be possible 

 when survey effort is less. Three triennial surveys 

 were insufficient to estimate absolute abundance for 

 the eastern Bering Sea walleye pollock fishery with 

 useful precision (Kimura, 1989). Species-specific 

 simulations can help to determine the amount of 

 survey effort necessary to estimate absolute abun- 

 dance. For example, McAllister ( 1995 ) examined sur- 

 vey timing for assessments of the eastern Bering Sea 



Figure 12 



Estimates of exploitable biomass ( thousands metric tons ) 



by delay-difference analysis ( ) and age-structured 



analysis ( ). 



yellowfin sole fishery. A population dynamics model 

 was fitted to two survey time series, 1975-81 and 

 1982-94, then the population was projected forward 

 15 years and annual, versus triennial, trawl surveys 

 were compared. Net present value of the fishery was 

 less for more frequent sui'veys, primarily owing to 

 increased survey cost, but CV (ABC) was less for more 

 frequent surveys (28 versus 369^) when absolute 

 abundance was estimated. 



Parameter interactions with abundance estimates 



Abundance estimates are related to estimates of sev- 

 eral model parameters. Absolute abundance and sur- 

 vey catchability are inversely related because a given 

 observation of the survey abundance index can be 

 due to a small population that is easy to catch or to a 

 large population that is difficult to catch. Natural 

 mortality and catchability also are inversely related; 

 increasing q while decreasing M tends to give simi- 

 lar log-likelihood values (Table 2, panel 1). Absolute 

 abundance and natural mortality tend to be posi- 

 tively correlated (panel 2; Schnute and Richards, 

 1995). Given the obsei-ved abundance index, abso- 

 lute abundance estimates must be larger for the 

 population to sustain more natural mortality. Reduc- 

 ing the correlation and improving estimation of natu- 

 ral mortality is difficult because the number of natu- 

 ral deaths for marine fish species is usually unob- 

 servable; no data are available to estimate M directly. 

 For the sablefish age-structured analysis, the over- 

 all changes in the likelihood function with respect to 

 M were minor and not sufficient to allow estimation 

 of M as part of the model-fitting process. I had to fix 



