662 



Fishery Bulletin 93(4). 1995 



cod 



20 2.5 



Herring 



Anchovies 



I 



00 0.5 



Plaice 



_ 



0.0 5 10 15 2.0 



SD of log Ricker residuals 



B 



Cod 



00 05 



2 2.5 



Herring 



■III. 



00 05 10 15 20 



Anchovies 



5 10 15 2 



Plaice 



1 



00 05 10 15 20 



SD of log recruitment 



Figure 3 



(A) Histograms of the standard deviation of the log-recruitment residuals from a Ricker fit to the 

 stock-recruit relation for four species of marine fish. (B) Histograms of the standard deviation of log 

 recruitment (without adjustment for stock size) for four species of marine fish. 



Predictability of recruitment: density 

 dependence 



It is evident from Equation 15 that the effect of posi- 

 tive a is to reduce a lnfl , which is desirable here, be- 

 cause the formulation with a = overestimated o ]nB 

 for cod and plaice (Table 1). 



We now select cod for closer examination, since 

 there are reliable estimates for the strength of den- 

 sity dependence in this species (Myers and Cadigan 

 [1993a]). Our parameter a corresponds to 1-A, in 

 Myers and Cadigan (1993a). They found that X, was 

 typically about 0.5 for a cod stock, suggesting a = 

 0.5. With this specification we find from Equation 

 15 that o lnfl = 0.58, which is in good agreement with 

 Figure 3A. For this case, a = 0.5, the correlation be- 

 tween AC 4 and Aln/V 3 is 0.6, so that about 36% of the 

 variance in juvenile mortality is related to larval 

 abundance (see Eq. 13). 



With a fixed we have recalculated, r cl and r ni , for 

 cod using the equations above, and have displayed 

 them in Table 2 along with their counterparts calcu- 



lated for Table 1 (for which a = was assumed). It is 

 apparent that the prescribed density dependence has 

 appreciably lowered the correlation coefficients. 

 There is a particularly large reduction in r c4 , stem- 

 ming from the fact that the juvenile mortality has 

 two components which tend to offset one another (in 

 the limit £ - 0, in Equation 13, juvenile mortality 

 will actually be positively correlated with recruit- 

 ment). Thus, realistic levels of density dependence 

 (Myers and Cadigan, 1993a) have the effect of sub- 

 stantially reducing the predictability of log-recruit- 

 ment from prerecruit mortalities or abundances. 



Predictability of raw recruitment 



For o laR = 0.5 we find from Equation 21, r' n lr a = 

 0.94 and for o lnR = 1.0 we have r^/r ei = 0.76. It is 

 evident that the predictability of raw recruitment 

 ( r' ci ) declines relative to the predictability of log re- 

 cruitment (r„) as o lnfi increases. 



In Table 3 we have completed the presentation for 

 the cod case, showing the r' ci ,r' ni ,r^ in comparison to 



