Bradford: Recruitment predictions from early life stages of marine fishes 



443 



model up to the metamorph stage and calculated the 

 median Var(Nn,). Var(Mj) was then found by subtrac- 

 tion using Var(Mjtot) predicted from Figure 1 (Table 

 3). For herring and anchovy in the covariance model, 

 the equation above should include a term for the covar- 

 iance between Mjtot and N,,,. In these cases, Var(Mj) 

 was found by trial by running the model with different 

 values of Var(Mj) and matching the median Mjtot with 

 the value predicted from the regression equation of 

 Figure 1. 



To provide objective criteria for evaluating recruit- 

 ment hypotheses, I defined two performance criteria 

 for the correlations with recruitment. Recruitment 

 research is commonly cast as a search for the stage 

 when "year-class strength is determined" or "recruit- 

 ment is fixed." I define such a stage as having an 

 i?2>0.50 with recruitment, i.e., being able to account 

 for at least half of the variability in year-class strength. 

 A more rigorous standard of i?->0.80 was set for cor- 

 relations to be used for management purposes (Walters 

 1989). 



(D 

 O 



c 

 m 



'\— 



CO 



> 



O 



-10 



-15 



-20 



-8 -6 -4 -2 



Log Daily Mortality 

 Figure 1 



Relationship between interannual variance in daily mortal- 

 ity rates and mean daily mortality from published values. Sym- 

 bols indicate eggs (•). larvae (<>). juveniles (■), and adults 

 (D). Equation of the line: ln{Var(M)} = 2.231 ln(M) - 1.893 

 (7?" 0.90, P<0.0001). Regression uses the square root of 

 number of years comprising each data point as weights. 



Table 3 



Variances of juvenile mortality rates V(Mj) used in the four versions of 

 the model and the variance of log recruitment, V(N,), generated by the 

 model. Model versions include density-dependent (DD) or independent (DI) 

 juvenile mortality and, in some cases, covariance between stage-specific 

 mortality rates (COV). Variances for M^ in the DD models are for the 

 density-independent component only, and were found by simulation. 



DI 



DI-COV 



DD 



DD-COV 



Species V(Mj) V(N,) YiM,) V(N,) V(Mj) V(N,) V{M-,) V(N,) 



Cod 0.45 



Herring 0.91 



Anchovy 0.58 



Plaice 0.22 



1.49 

 1.49 

 2.54 

 1.64 



0.45 

 0.91 

 0.58 

 0.22 



2.04 

 2.08 

 3.91 

 2.46 



0.35 

 0.85 

 0.40 

 0.09 



0.87 

 1.14 

 1.36 

 0.79 



0.34 

 0.92 

 0.45 

 0.09 



Results 



Variance-mean relationship 



There was a highly significant relationship {R~ 0.90. 

 P<0.0001, n 97) between the log of mean daily stage- 

 specific mortality and the log of the interannual vari- 

 ance in the daily mortality rate (Fig. 1). The variance 

 in mortality rate was independent of the number of 

 years of data comprising each point (multiple regres- 

 sion with mean mortality, P 0.81 for sample size). The 

 square root of sample size was used as a weight in all 

 analyses. There was no significant effect of life history 

 (freshwater, marine, or anadramous) on the variance- 

 mean relationship (ANCOVAR; for slopes and adjusted 

 means, all P>0.20). There was no difference in the rela- 

 tionship between the variance and mean of mortality 

 among the egg, juvenile, and adult stages (P>0.5), but 

 the slope for the larval stage was significantly differ- 

 ent from the other three stages (intercept P 0.10, slope 

 P 0.010). Because there were a number of studies on 

 the same species, I also averaged the data across both 

 species and stage to decrease the non-independence of 

 the data due to common phylogeny. The variance-mean 

 regression for this averaged dataset was almost iden- 

 tical to the full set (P2o.92, P<0.0001, 

 n 53); the regression parameters differed 

 by <2%. In this case, the regression for the 

 larvae was not different than for the other 

 three stages (intercept P 0.28, slope P 0.11), 

 suggesting the significant effect found for 

 the full dataset may have been due to the 

 overrepresentation of some species. I there- 

 fore used the overall regression (Fig. 1) to 

 predict the variance of mortality of all 

 stages, rather than using a separate regres- 

 sion for larvae. This is a conservative pro- 

 cedure for rejecting Hjort's hypothesis, 

 because the single regression predicts a 

 more variable mortality for the early-larval 

 stage than does the separate larval re- 

 gression; the single regression produces 

 stronger correlations between abundance of 



1.15 

 1.59 

 2.16 

 1.04 



