Mertz and Myers. Estimating the predictability of recruitment 



663 



the r ci , r m . It is clear in these examples that predict- 

 ability is lost when one works with the untrans- 

 formed recruitment or abundance. 



Peterman et al. (1988) have investigated the pre- 

 dictability of recruitment from surveys of prerecruit 

 abundances. Equations 22 and 23 shed some light 

 on how predictability is influenced by log transform- 

 ing the prerecruit abundances. Recall that when 

 cx ln(m) «l, then r n " = r' ni , i.e. the raw recruitment is 

 predicted equally well by abundance or log abun- 

 dance. However, if o ln(ni -, is considerably larger than 

 a lnfi , then r' m > r£ (e.g. for o lnfl = 1.0, o^ = 2.0, r ni = 

 0.5, then /•„',■ = 0.38, whereas r n " = 0.18). Conversely, 

 ifo lnfi is considerably larger than a ln(ni> then, r," t > r' m 

 (e.g. for a ]nR = 2.0, a ln(n ,, = 1.0, r m = 0.5, then r,' u = 

 0.14 and r£ = 0.18). This implies that whether or 

 not one will achieve a better correlation between re- 

 cruitment and log abundance (of pre recruits) than 

 between recruitment and abundance depends on the 

 relative magnitudes of o lnR and o ln(m) . 



Discussion 



CV for mortality 



The incorporation of estimates of 

 measurement error into the relation- 

 ship between variability of mortality 

 and mean mortality indicates that 

 the slope coefficient (see Eq. 27), 

 which is the mortality CV, may be 

 substantially altered by measure- 

 ment error. However, removal of the 

 error component does not destroy the 

 intuitively appealing approximate 

 proportionality between variability of 

 mortality and its mean. 



In the presence or absence of den- 

 sity dependence the slope parameter 

 in Equation 27 does not affect the 

 predictability of log recruitment; see 

 Equations 11, 12, 16, and 17. Increas- 

 ing this parameter inflates o ]n(nh and 

 o c , but it also increases o lnfl by the 

 same proportion, leaving the corre- 

 lation coefficients r ni and r ci un- 

 changed. This invariance of the cor- 

 relation coefficients with respect to 

 the mortality CV is a useful result 

 stemming from our treatment of the 

 predictability problem. The predict- 

 ability of raw recruitment is influenced 

 by the mortality CV, because a ]nR de- 

 pends on this CV and because a lnB af- 

 fects the correlation coefficients for raw 

 recruitment (Eqs. 21 and 22). 

 The true size of the mortality CV cannot be deter- 

 mined with certainty, because the degree of inflation 

 of the true CV by measurement error cannot be ac- 

 curately ascertained. However, Equation 27, which 

 specifies a mortality CV of only 0.2, gives reasonable 

 estimates for the magnitude of the recruitment vari- 

 ability (a lnff ). Comparison of Table 1 and Figure 3A 

 shows that Equation 27 (with Equation 10) over- 

 predicts the median o lnE in three cases (cod, ancho- 

 vies, and plaice). Underestimation of recruitment 

 variability due to ageing errors by 20-30% (Bradford, 

 1991; Bradford 1 ) could rectify this discrepancy. For 

 cod and plaice it is likely that density dependence is 

 in part responsible for the discrepancy between cal- 

 culated (from Equation 27) and empirical values 

 of o laR (see Myers and Cadigan, 1993, a and b). In 

 any case, the approximate agreement between cal- 

 culated and observed values of o laff is powerful veri- 

 fication for the general validity of Bradford's (1992) 

 regressions. 



