Bradford: Recruitment predictions from early life stages of marine fishes 



445 



longer late-larval period. The recruitment-forecasting 

 threshold of 0.8 was never reached for correlations be- 

 tween recruitment and any larval mortality rate. 



A wide range of R'^ values can result from a short 

 time-series. For example, the 95% range of R- values 

 for the correlation of early cod larvae with recruitment 

 (10-yr time-series) in the density-independent model 

 that includes covariance in mortality rates extended 

 from 0.07 to 0.86 (Fig. 5). The 95% range decreases 

 if the true relationship between the variables is 

 stronger; for cod metamorphs the conclusion that this 

 stage can be used to describe the majority of recruit- 

 ment variation will nearly always be reached (Fig. 5). 



Sensitivity analysis 



Two sensitivity analyses were conducted to assess 

 dependence of the results on input parameters. First, 

 stage-specific variances in mortality were recalculated 

 with the slope of the variance-mean regression set at 



DI-COV 



DD-COV 



CO 



Dl 



DD DI-COV 



Model Version 



DD-COV 



Figure 4 



Predicted R'^ values for correlations between recruitment 

 and early- and late-larval mortality rates for cod (O). anchovy 

 (■), plaice (•), and herring (□). Axis labels refer to four ver- 

 sions of the model, incorporating density-independent (DI) or 

 -dependent (DD) juvenile mortality and covariances between 

 mortalities (GOV). 



its 95% confidence limits; the intercept was derived by 

 constraining the line through the mean of both vari- 

 ables. For the cod-DI model, increasing the slope to the 

 upper confidence limit increased the R~ for the cor- 

 relations between the abundance of recruits and early 

 larvae or metamorphs by about 0.05; decreasing the 

 slope lowered R^ values by similar amounts. There 

 was little effect on correlations involving the egg or 

 first-feeding stages. I also recalculated the correlations 

 with the intercept of the variance-mean regression at 

 its 95% confidence limits. With the intercept at its 

 lower limit, R'~ values increased by 0.01-0.04, and at 

 the upper limit the correlations decreased by a similar 

 amount. Thus, the overall results are not particularly 

 sensitive to the sampling error associated with the data 

 in Figure 1. 



I also varied the length of the early-larval period. In 

 the life tables (Table 2), I fixed the early-larval period 

 at 10 days and set the daily mortality rate at twice the 

 average for the whole larval period. In sensitivity runs 

 I varied this period from 5 to 15 days; duration and 

 mortality rate of the late-larval period were recalcu- 

 lated to keep the total mortality for the larval period 

 constant. The duration of this period of high larval mor- 

 tality had a strong effect on the strength of the cor- 

 relation between abundance of larvae sampled at the 

 end of the early period and recruitment. When the 

 early-larval period was increased by 5 days, the i?- in 

 the cod-DI model increased by 0.21 (Fig. 6). 



cr 



1.0 



0.6 



0.4 



0.2 



-0.2 



Egg F-feeding E-larvae Metamorphs 



Stage Sampled 



Figure 5 



Variability in sample R'^ values (10-yr series) for the correla- 

 tion between recruitment and abundances of early stages for 

 cod in the model, with density-independent juvenile mortal- 

 ity and mortality covariances. Shown are the median (bar), 

 interquartile (rectangle), and 95% ranges (line). Data are from 

 1000 runs; note that the criterion for significance {R->0. 

 a 0.05) is 0.40. 



