442 



Fishery Bulletin 90(3), 1992 



over the number of years of data available, and the 

 variance calculated. Both variates were log-trans- 

 formed, and a least-squares regression was fitted to 

 the data. 



I used the variance-mean relationship to calculate the 

 interannual variance in mortality from mean daily mor- 

 tality rates extracted from published life tables (Table 

 1). I split the larval period and defined the first 10 days 

 of feeding as the early stage. This period corresponds 

 to the usual definition of the 'critical period' for first- 

 feeding larvae (Leggett 1986): few marine larvae can 

 survive more than 10 days without feeding (Miller et 

 al. 1988). Except for anchovy, where values were taken 

 directly from Smith (1985), the daily mortality rate for 

 the early period was set at twice the average rate for 

 the whole larval period. Mortality rates for the late 

 period were adjusted so that the mortality for the total 

 larval period matched the published life tables. The 

 result of these calculations was that the daily mortal- 

 ity rates of the early-larval interval were about 2.5 

 times those for the late-larval period. It is difficult to 

 assess whether this decline is realistic, because there 

 is considerable variability in the decline in mortality 

 over time in empirical studies; in many cases mortal- 

 ity has been found to be nearly constant over much of 

 the larval period (Dahlberg 1979), while there are other 

 cases where significant declines have been observed 

 (i.e., Savoy and Crecco 1988). Declines in mortality wath 

 larval age may be accentuated by a possible bias due 

 to sampling interval (Taggart and Frank 1990). The 

 variance in mortality over the duration of a particular 

 interval was then calculated as the product of the 

 square of the interval's duration (in days), and the 

 variance of the daily mortality rate predicted from the 

 variance-mean relationship. 



Covariation in mortality rates 



Two scenarios were developed concerning the effects 

 of covariation between mortality rates. In the inde- 

 pendent case, all mortality rates were varied in- 

 dependently of one another, while for the 'covariance' 

 version, mortality rates of adjacent stages were as- 

 sumed to be correlated across years. Few data are 

 available to estimate the strength of these correlations, 

 so I assumed p values for the correlations between ad- 

 jacent M|( based on the likelihood of common agents 

 of mortality. I assigned a relatively low p value of 

 0.25 for the correlation between the egg/yolksac period 

 and the early-larval mortality because early-larval mor- 

 tality is thought to be strongly affected by feeding suc- 

 cess, which does not affect egg survival. Nonetheless, 

 predation pressures are probably similar for both 

 stages, causing some covariation in mortality rates. 

 A p value of 0.5 was used between the early- and late- 



Table 2 



Interannual variability in log-transformed egg production and 

 recruitment, compiled from literature values. All egg esti- 

 mates are residuals from linear regressions of log abundance 

 on time, except for cod where an intermediate value between 

 herring and plaice was used. 



Species 



Var(NJ 



Var(N,) 



Cod 



Herring 

 Anchovy 

 Plaice 



0.075 

 0.081 

 0.282 

 0.055 



0.40 

 1,92 

 1.91 

 0.14 



Data sources 



Cod: mean of 5 northwest Atlantic stocks in Koslow et al, 



(1987). 

 Herring: mean of 7 northwest Atlantic stocks in Winters and 



Wheeler (1987), 

 Anchovy: eggs— Peterman et al. (1988), recruitment— Methot 



(1989). 

 Plaice: Bannister (1978). 



larval intervals because of the similarity of habitat 

 between these two periods. For the pelagic species, 

 anchovy and herring, p = 0.25 was used for the correla- 

 tion between the late-larval and juvenile intervals, 

 while for the demersal species, cod and plaice, I set 

 p = 0, reflecting the major habitat shifts associated wath 

 metamorphosis. 



Density-dependence 



To explore the effects of density-dependence on cor- 

 relations, I ran the model with b= 1.0, the density- 

 independent case, or b = 0.7, simulating moderately 

 strong density-dependent mortality. The variance of 

 juvenile mortality predicted from Figure 1 is in fact 

 the sum of both the density-independent and density- 

 dependent sources of mortality. To estimate the 

 density -independent component of mortality (Mj) re- 

 quired for Eq. (2), I had to remove the density- 

 dependent mortality from the total juvenile mortality 

 predicted by Figure 1. Rearranging Eq. (2) and solv- 

 ing for the total juvenile mortality (Mjto,) yields 



M 



■jtot 



N„,-N, = (l-b)N„, + Mj. 



In the models without covariances between mortality 

 rates, and in the covariance model for cod and plaice 

 where there is no covariation in mortality across meta- 

 morphosis, taking variances yields 



Var(Mj) = Var(Mju„) - (1 - b)^Var(N„,). 

 In these cases, to find Var(Mj) I ran the stochastic 



