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



489 



A multivariate model, using the complete data se- 

 ries and incorporating April SLH. the natural loga- 

 rithm of the spawner index, and the April catch of 

 egg-bearing shrimp from the year of larval release, 

 was also highly significant (P<0.005) and explained 

 809c of the variation in log recruitment (Table 2, 

 model 4). As expected, the coefficients for SLH and 

 the catch of egg-bearing shrimp in April of the re- 

 lease year were both negative, whereas the coeffi- 

 cient for the natural logarithm of spawners was posi- 

 tive. Fitting this three-variable model, with the 1990 

 year class excluded, resulted in the catch of egg-bear- 

 ing shrimp not contributing significantly to the over- 

 all model fit, suggesting that this variable does not 

 have general predictive value for the recruitment 

 time series but is useful only in explaining the very 

 low recruitment in 1990. 



Despite efforts to de-emphasize the importance of 

 age-1 catches in the recruitment series by indexing 

 the stock at an earlier age, these early catches still 

 represented a large component of the index (Fig. 7). 

 This finding suggests that the assumption of con- 

 stant natural mortality could still be inducing errors 



in the recruitment index. However, when the analy- 

 ses discussed above were conducted on the recruit- 

 ment index excluding the April-July age-1 catches, 

 the results were very similar. This similarity argues 

 that the findings of this study are not sensitive to 

 failure of the assumption of constant natural mor- 

 tality, as it is employed in calculating the recruit- 

 ment index. The results were also insensitive to the 

 assumed level of elemental trawl efficiency (Table 3, 

 models 5 and 6). 



The data in Figure 4 suggest that if shrimp 

 spawner abundance could be maintained above some 

 threshold (about 1.3 billion shrimp for an assump- 

 tion of 0.50 for elemental trawl efficiency), the abil- 

 ity to produce large shrnnp year classes in favorable 

 environmental conditions could be preserved in all 

 years. A similar threshold could also be identified in 

 terms of egg production (Fig. 5). Examination of the 

 relationship between age-1 spawners, older spawn- 

 ers, and the recruitment index from the same calen- 

 dar year (Fig. 8 ), suggests a strong recruitment-stock 

 relationship for ocean shrimp and a minor role for 

 the fishery in determining spawner abundance. In 



