Hannah: A new method for indexing spawning stock and recruitment for Pandalus jordanl 



485 



age of total catch from these areas landed in Oregon 

 from 1980 to 1992 was 92.57f (Hannah et al., 1997). 

 Second, the components of the new indices, with one 

 exception, did not depend on a complete accounting 

 of catch and effort from the study area but simply on 

 a good estimate of average CPUE at age and accu- 

 rate estimates of stock area. The one component of 

 the recruitment index that was somewhat influenced 

 by the missing catch data was the added age-1 shrimp 

 catch from the months of April-July. A correction for 

 this potential source of error is not available; how- 

 ever, I believe the magnitude of error introduced is 

 likely to be small in relation to the interannual varia- 

 tion in the index itself.The use of CPUE as a direct 

 index of density is equivalent to assuming that el- 

 emental efficiency, p in Equation 2 above, equals 

 100%. This is clearly not reasonable, however; se- 

 lecting a value for p is problematic. The principal 

 importance of selecting a value for p is to obtain a 

 proper scaling between the two components of the 

 recruitment index: one based on CPUE and stock 

 area; the other based on the early-season catch of 

 age-1 shrimp. Proper scaling of these two components 

 is less critical than it seems at first examination be- 

 cause the two index components are actually closely 

 correlated (/■=0.774 atp=0.5). Accordingly, a change 

 in the scaling between the two components is ex- 

 pected to have little influence on the pattern of time 

 series variation in the resulting index. As a check on 

 this assumption, all indices using CPUE as a den- 

 sity index in this study were calculated with a range 

 of p-values, and the results were then examined to 

 see if they were sensitive to assumptions about p. 

 For the primary analysis, I chose a p-value of 0.5 

 and for the sensitivity analysis I used values of 0.25 

 and 0.75. forp, following my earlier examination of 

 shrimp mortality rates (Hannah, 1995). 



Commercial logbook data were used to generate 

 estimates of stock area for each shrimp year class. 

 The methods used to estimate stock area, including 

 the correction of estimates for variation in sampling 

 rates, are described in detail in Hannah ( 1997 ). Stock 

 area was estimated by using logbook data from June 

 of the recruit year through May of the following year, 

 the time period during v/hich age-1 shrimp contrib- 

 ute most heavily and reliably to the catch. For a few 

 of the years in the 1980-96 time series, the fishery 

 failed to target age-1 shrimp adequately, and har- 

 vested primarily the remaining age-2 and older 

 shrimp from prior year classes. For those years, stock 

 area was estimated from a linear regression of stock 

 area on a simple virtual population estimate for that 

 year class, as described in Hannah (1997). 



To index the ocean shrimp spawning stock, I used 

 an approach similar to that used for the recruitment 



index. For each spawning year, I used the average 

 age-specific CPUE in September-October as an in- 

 dex of age-specific density. Once again, these esti- 

 mates of density were expanded by using assumed 

 levels of elemental trawl efficiency ranging from 0.25 

 to 0.75, as discussed above. I then multiplied each 

 density index by the stock-area estimate for that year 

 class, as calculated in the year of recruitment. In 

 using this approach I assumed that the geographic 

 distribution of each newly recruited year class was 

 established at settlement and was persistent, and 

 that local shrimp density was modified by fishing and 

 natural mortality. This assumption is supported by 

 several observations, including the obvious auto- 

 correlation in stock area estimates noted previously 

 (Hannah, 1995), the lack of any evidence for migra- 

 tion in this species and the approximately linear rela- 

 tionship between stock area and abundance. There is 

 some evidence fi'om sea bed drifter recoveries ( ODFW^ ) 

 that suggests slow gyres in bottom currents may help 

 retain or concentrate shrimp in some of the major 

 shrimp beds. However, it is unknown whether this ef- 

 fect is sufficiently large to actually alter the areal 

 extent of a shrimp year class after settlement. 



An egg production index for ocean shrimp was cal- 

 culated by expanding the spawner index with avail- 

 able shrimp biological data (ODFWM. The biological 

 data used included the mean percentage of females 

 and mean female shrimp carapace length, by age, 

 from samples of the fishery in October. For a few 

 years, October samples were unavailable and Sep- 

 tember samples were used. I used a pooled length- 

 fecundity relationship from Hannah et al. ( 1995) to 

 estimate mean fecundity for each age group of fe- 

 male shrimp based on mean carapace length data. 



The April harvest of egg-bearing females was esti- 

 mated for the years 1979-95 in a straightforward 

 manner. April shrimp catch, expressed as numbers 

 of shrimp, for each PSMFC statistical area, was ob- 

 tained from Hannah et al. ( 1997). Catch in numbers 

 was multiplied by the average percentage of egg-bear- 

 ing shrimp estimated for each PSMFC area from bio- 

 logical samples of the April catch (ODFWM. The catch 

 of egg-bearing shrimp from each of the four areas 

 (Fig. 1) was then summed. 



Because the percentage of egg-bearing shrimp de- 

 clined throughout April, a time-stratified approach 

 was used to estimate the average percentage of egg- 

 bearing shrimp. One problem with this approach is 

 variation in sample coverage. Although the total 

 number of shrimp examined from the April catch has 

 been fairly consistent, averaging about 2900 shrimp 

 from 1980 to 1996, the early and late portions of April 

 have not always been sampled evenly. For example, 

 some years that had excellent sample coverage in 



