592 



Fishery Bulletin 97(3), 1999 



age or length data. The additional information al- 

 lows explicit tracking of cohorts, but many more pa- 

 rameters must be estimated. 



Fitting population models to survey and fishery 

 data has long been used to estimate absolute abun- 

 dance (Pope and Shepherd, 1985; Deriso et al., 1985) 

 and is one method of estimating absolute abundance 

 along with direct surveys, mark-recapture experi- 

 ments and depletion experiments. Abundance esti- 

 'mation with a population model works by tracking 

 population additions and losses and inferring abso- 

 lute abundance from the manner in which catch af- 



40 



o 10 



1979 1981 1983 1985 



1987 

 Year 



1989 1991 1993 1995 



Figure 1 



Reported fishery catches (thousands metric tons) from 1979 

 to 1995. 



fects the survey index and age and length composi- 

 tions. In simple terms and aside from other losses, if 

 harvesting 500 individuals decreases a cohort's in- 

 dex 10%, then the cohort's initial abundance was 

 5000 individuals. Estimation depends on having an 

 abundance index precise enough to detect cohort re- 

 ductions by the fishery. 



The population model presented here takes into 

 account the following unusual attributes of the avail- 

 able data. Length compositions are available from 

 the longline surveys for all years analyzed, compared 

 with infrequently available age compositions (Table 

 1). Not many Alaska-wide sablefish fishery data are 

 available, consisting only of total catches and five 

 years of fishery lengths, but no ages (Table 1) . 



Methods 



Model structure and estimation method 



The analysis generally follows the approach de- 

 scribed by Kimura ( 1990 ) for a separable age-struc- 

 tured population model. Let y, a , and / be the year, 

 age, and length indices, respectively. 



c , = observed fishery catch in numbers; 

 /, = observed survey abundance index in 

 numbers; 

 p = obsei"ved survey proportion at age; 

 p ,1 = observed survey proportion at length; 

 jj = Ij s = the exploitation fraction of age-a fish 

 during yeary which is separable into 

 s , the selectivity for age-a fish, and 

 jj ,, the exploitation fraction for fully 

 vulnerable ages; 



A^ 



A^. 



.A^. 



X<=^v 



the total number at age; 



the exploitable (fishable) 

 number at age; and 



the exploitable number. 



Figure 2 



Map of southern Alaskan waters. Adult sablefish inhabit the upper 

 continental slope seaward of the 200-m depth contour. 



Starting with initial cohort size, N^,^^, 

 natural deaths and observed catch were 

 removed to compute next year's cohort size, 

 A^ , , = ( 1-t/ ) N e-^. A discrete fish- 



v+l.a + l ^ \(i ya 



ery was modeled, c'y = ilyN\, because the 

 fishery was short for recent years except 

 1995. The modeled discrete fishery gener- 

 ally matches the timing of the observed dis- 

 crete fishery and occurs near the mid-point 

 of the earlier year-round fishery 



