Bradford Recruitment predictions from early life stages of marine fishes 



447 



correlations nearly as strong as those predicted for 

 metamorphs might be possible. 



The correlations will be weaker if sampling errors 

 are included in the estimates of abundance. Preliminary 

 simulations with random sampling errors with a coef- 

 ficient of variation of 50% (untransformed abundances) 

 decreased R- values in Figures 2 and 3 by 0.10-0.15 

 (Bradford unpubl.). Biased estimates, e.g., due to gear 

 avoidance (Lo et al. 1989), will not affect correlations 

 between an early stage and recruitment, unless the 

 magnitude of the bias is correlated with the estimate. 

 Precision, through the use of consistent technique 

 across years, is more important for the purposes of 

 forecasting. Large-scale surveys of abundance of late 

 larvae or juveniles may be sufficiently accurate for the 

 forecasting of recruitment (Lo et al. 1989) if the stage 

 sampled is likely to be strongly correlated v, ith recruit- 

 ment (Fig. 5). 



An implicit, though infrequently stated, assumption 

 of research on early-life-history influences on recruit- 

 ment is that the mean and the interannual variance of 

 mortality rates are correlated. High mortality alone will 

 not cause recruitment variation; it must also be coupled 

 with high interannual variability. The data compiled in 

 Figure 1 provide evidence that this is generally true, 

 and that the interannual variability in the larval period 

 is proportionately no greater than that found for other 

 stages. In addition, my sensitivity analysis suggests 

 that the general conclusions of this paper are robust 

 to the sampling variability of this relationship. How- 

 ever, detailed investigation of the recruitment dynam- 

 ics of an individual species will require estimation of 

 the variance of stage-specific mortality rates, because 

 the predictive power of Figure 1 is still relatively low 

 for any particular case, and the biology of an individual 

 species may not result in rates that follow the overall 

 average pattern. Examples are provided by species 

 which spawn during periods of extreme climatic events 

 such as wind storms (e.g., capelin Mallotus villosus or 

 red drum Sciaenops ocellatus, reviewed by Taggart and 

 Frank 1990). In these cases, interannual variability in 

 the mortality of the earliest stages is probably larger 

 than predicted by the regression of Figure 1, and the 

 correlation between the early stages and recruitment 

 is likely to be stronger than I have predicted. In con- 

 trast, for the North Sea plaice a relationship {R^ 0.7) 

 was found between egg abundance and recruitment 

 (Zijlstra and Witte 1985), which is higher than my 

 model predicts for this species (although just within 

 the 95% range). This species has relatively low recruit- 

 ment variation, suggesting that larval and juvenile sur- 

 vival rates are not as variable as predicted by Figure 

 1, or that density-dependent mortality might be impor- 

 tant in regulating recruitment (Zijlstra and Witte 

 1985). 



The recruitment variances generated by various ver- 

 sions of the model tend to be higher than published 

 values (Tables 2, 3). These literature estimates will like- 

 ly be underestimates of the true variability in recruit- 

 ment, because errors in catch sampling and ageing can 

 greatly reduce recruitment variability estimated from 

 sequential population analysis (Rivard 1989, Bradford 

 1991). Alternatively, my recruitment variances could 

 be too high because I have either overestimated the 

 variances of mortality rates or underestimated the 

 severity of density-dependent mortality. Since the data 

 in Figure 1 include sampling error, all of the variances 

 in Tables 2 and 3 will be somewhat inflated. If sam- 

 pling error is proportional to the rate of mortality, the 

 sensitivity analysis suggests that removing sampling 

 error (i.e., lowering the intercept of Fig. 1) will have 

 only a slight effect on recruitment correlations. 



One additional source of variability not explicitly con- 

 sidered in my analysis is the effect of varying stage 

 duration, due to interannual variability in growth rates. 

 Houde (1987, 1989) has demonstrated through life-table 

 manipulation that small variations in larval growth may 

 have large effects on the number of metamorphs pro- 

 duced. The effect on recruitment will be buffered 

 somewhat as shortening the larval period will increase 

 the length and, therefore, the total mortality of the 

 juvenile stage. However, if the variation in growth 

 rates is due to temperature, Pepin (1991) suggests that 

 the offsetting effects of temperature on development 

 and mortality will result in no net effect of temperature 

 variation on cumulative mortality over the egg and lar- 

 val stages. In this case, by not including variation in 

 growth rates I will have overestimated the variability 

 in larval mortality. However, to some extent the ef- 

 fects of gi'owth-rate variation are already included in 

 my model because many of the estimates in Figure 1 

 are based on total stage length and will, therefore, in- 

 clude the effects of varying stage duration caused by 

 variation in growth rates in the calculation of the 

 average daily mortality rate. 



The sampling variability of correlations from short 

 datasets makes it difficult to draw inferences about the 

 causes of recruitment variability. This low precision 

 suggests that confidence limits around the sample 

 estimates, r or R~, should always be supplied, much 

 in the same way that standard errors are given for sam- 

 ple means. A population correlation from Figures 2 and 

 3 is a value that would be obtained from a very long 

 time-series of data, and is a true measure (in the con- 

 text of the model) of the contribution of an early life 

 stage to recruitment variation. However, there is a 

 good chance (e.g., >30% for early larvae in Fig. 5) that 

 a sample correlation between the abundance of an early 

 stage and recruitment may not be significantly dif- 

 ferent from 0. Even if the correlation is significant. 



