664 



Fishery Bulletin 93(4), 1995 



Research needs 



For research purposes one may seek correlations 

 between recruitment and an environmental variable 

 assumed to be a proxy for mortality during some 

 prerecruit stage. It is apparent that there is no mean- 

 ingful distinction between log recruitment and raw 

 recruitment for the purposes of correlation analysis 

 provided o lnfi < 0.4. For the optimal case of minimal 

 density dependence, correlations between log recruit- 

 ment and mortality seldom exceed 0.6 to 0.7 (Table 

 1). This implies that any environmental variable that 

 is to serve as a proxy for mortality must be very tightly 

 correlated with mortality if there is to be a significant 

 correlation between the proxy variable and recruitment. 

 Similar results were found by Bradford ( 1992). 



Management needs 



The criterion for successful recruitment prediction 

 for stock management suggested by Walters (1989) 

 requires that the proxy should explain 80% of the 

 variance in log recruitment, or, equivalently, r ci , r ni = 

 0.9. Equations 11 and 12 allow a ready appraisal of 

 the likelihood of meeting this criterion; the applica- 

 tion of these equations yields the results in Table 1, 

 indicating that this criterion is never fulfilled un- 

 less one samples late in the juvenile phase. The in- 

 clusion of density dependence (Eqs. 16 and 17) gen- 

 erally reduces the correlation coefficients r cl and r m . 

 These findings agree with those of Bradford (1992). 



A management strategy requiring predictions of 

 recruitment (rather than log recruitment) is not 

 likely to be viable if the stock under consideration 

 has high recruitment variability. For a stock with 

 a lrLff = 1.0, if 80% of the log recruitment variance can 

 be explained by a proxy, only 46% (Eq. 21 or 22) of 



the variance of recruitment itself will be explained 

 by this proxy. For a o inR of 1.5, appropriate to some 

 herring stocks, only 21% of recruitment variance 

 could be explained by a proxy accounting for 80% of 

 log recruitment variance. These calculations bear on 

 the question of whether or not large year classes can 

 be predicted (Bradford and Cabana, in press; Ander- 

 son, 1988). Capturing the size of a large year class 

 requires an estimate of raw (rather than log-trans- 

 formed) recruitment; however, those stocks which 

 produce the most notable year classes (those with 

 large o lnR ) are the least predictable. 



Summary 



The analysis presented here complements that of 

 Bradford (1992). We have shown that correction for 

 measurement error can appreciably reduce the CV 

 for mortality, while not destroying the appealing pro- 

 portionality between variability of mortality and 

 mean mortality. We have demonstrated that in many 

 cases the predictability of recruitment can be deter- 

 mined analytically. It is evident from our treatment 

 that raw recruitment is considerably less predictable 

 than log recruitment for stocks with high recruitment 

 variability. Our results concur with those of Bradford, 

 suggesting that the prospects of predicting recruit- 

 ment from egg or larval surveys or from environmen- 

 tal variables are quite poor. However, it must be borne 

 in mind that some fish stocks will deviate from the 

 general pattern, and thus it is quite conceivable that 

 there will be fish stocks for which a critical stage 

 exists, allowing recruitment predictions from (say) 

 larval abundances. 



