FISHERY BULLETIN: VOL. 86, NO. 3 



and 4) 29-80 mm TL, corresponding to the juvenile 

 stage and the onset of scale development (Marcy 

 1976). These four groups are hereafter referred to 

 as early larval, midlarval, late larval, and juvenile 

 stages, respectively. 



We used otolith increment counts (Savoy and 

 Crecco 1987) to age a subsample of 100-400 Ameri- 

 can shad larvae and 80-200 juveniles annually from 

 1979 to 1987. The age-length relationship for lar- 

 vae and juveniles in all years was well described by 

 the Gompertz growth equation (Crecco et al. 1983; 

 Crecco and Savoy 1985b) so we used a pooled 

 Gompertz equation to describe larval and juvenile 

 growth. The average age (t) of each of the four 

 length groups was estimated by rearranging the 

 Gompertz equation: 



t = logAKIK - log,(L,(Lo))]/a 



(5) 



where L( = total length (mm); Lq = length at 

 hatching (8.0 mm); K = growth rate at the inflec- 

 tion point; and a = rate of exponential decay. 



The daily instantaneous mortality rates (d) for 

 each stage and their standard errors from 1979 

 through 1987 were estimated by an exponential 

 model, 



Nt = A exp{-dt), 



(6) 



that related abundance (A^^) and age (t) by non- 

 linear regression methods (SAS 1982). The total 

 instantaneous mortality rates of early (ZELf), mid 

 (ZMLf), and late (ZLLt) larvae and juveniles (ZJf) 

 were estimated by multiplying the corresponding 

 daily mortality rate (d) by the average duration (Ds 

 = days) within each stage. Previous studies (Crecco 

 and Savoy 1985a; Savoy and Crecco 1987) found 

 that the growth rates of early (10-13 mm) and mid- 

 larvae (14-19 mm) were positively correlated with 

 June water temperatures, whereas the growth of 

 late larvae and juveniles were independent of river 

 temperatures. As a result, we adjusted the stage 

 duration {Ds ) of early and midlarvae with the mean 

 June temperatures (U.S. Geological Survey 1979- 

 87) from 1979 through 1987 and the larval growth- 



subtracting the sum of larval {ZEL, , ZMLf , ZLL,), 

 juvenile (ZJ^) and postjuvenile (ZA^) mortality rates 

 from the total prerecruitment mortality rate 

 (ZTotal,): 



ZEt = ZTotalt - [ZELi + ZML, + ZLLt 



+ ZJt + ZAt), (7) 



where ZTotal^ = -logp(/2,/Eggs,). However, since 

 the 1983 through 1987 year classes have not been 

 fully recruited to the spawning population, we esti- 

 mated total adult recruitment {Rp^ ) for those year 

 classes by the following environment-dependent 

 stock-recruitment model: 



Rpt = 24.29 (PARt) exp(- 0.0052 • P,,) 



exp(- 0.0032 • PJ 

 exp(- 0.0025 • JFLOW() 



(8) 



Adult recruitment was estimated independently 

 of the juvenile indices by substituting each 

 year's parent stock size (PAR^), mean June flow 

 (e/FLOW), female parent stock lifted over the Hol- 

 yoke Dam (P„ ), and female parent stock below the 

 Holyoke Dam (P^) (Table 1) into the model. This 

 nonlinear model was shown (Lorda and Crecco 1987) 

 to be a good predictor (r^ = 0.81, P < 0.001) of 

 adult recruitment (P^) for the 1966 through 1982 

 year classes. Moreover, the predicted recruitment 

 levels (P() of the 1983 through 1987 year classes 

 from Equation (8) were closely correlated (r = 0.92, 

 P < 0.01) with the corresponding juvenile abundance 

 (J() for those years (Table 4) which is consistent 

 with the positive correlation (r = 0.78, P < 0.01) 

 between adult recruitment and the 1967-82 juvenile 

 indices (Fig. 2). This justifies the use of Equation 

 (8) to predict adult recruitment, total mortality, and 

 postjuvenile mortality rates for the 1983-87 year 

 classes. 



The standard errors about the egg mortality rates 

 (ZEt) were derived as the sum of the variances of 

 all other terms (Cochran 1965): 



SEze' = ^SEzel' + SE^ml' + S^zll' + ZJ^ + SE^/ + SE^xotai' 0) 



temperature equations (Crecco and Savoy 1985b: 

 table 7). 



We estimated total egg and prolarval mortality 

 rates (ZE^) indirectly from 1979 through 1987 by 



The standard errors about the total prerecruitment 

 (ZTotal,) and postjuvenile (ZA^) mortality rates 

 (Table 5) were based on the same principle as Equa- 

 tion (9) (App. 1). 



474 



