FISHERY BULLETIN: VOL. 83, NO. 2 



Zit) ={z2it) 

 Zzit) 



t< tc 



tc<t<20d 



tk < t 



where 52^; zit) \T>tc)-= PiT > t; zit) \T >tc), 

 tc is the age when the form of IMR changes, 

 tk is max ti for ti < 20 d where ti is the average 

 age for the iih. length class. 



The quality of larval data for larvae older than 20 

 d is questionable because older larvae avoid the 

 net (Hewitt 1982). The forms ofzz{t) and Szit) for 

 ^ > 20 d are unknown at the present time. 

 Therefore, only the mortality of eggs and larvae 

 < 20 d old was assessed. 



The IMR, zU), relates to the survivorship func- 

 tion S{t), by definition, in the form of 



-I z\(u)du 



(4) 



-Si(0 t^tc 



-Jo-(" 



)du 



rtc 



-I zi(u)du 

 •'0 



•'tc 



Z2(u)du 



tc<t<20 



= Siitc)S2(t\T> tc) 

 = S2it). 



The critical age tc was defined as the age before 



which z{t) = ziit), after which zit) = Z2it). Pt 

 and t from larval data were used to estimate both 

 Ptc and Z2(t) through Equation (3B) after Sit) is 

 specified. Both larval production iPt^ ) and the 

 standing stocks of eggs and larvae up to age tc 

 imtf) were then used to estimate Po and ziit) 

 through Equation (3A) as below: 



and 



mt,= r Pf dt = f^' Po Slit; Ziit)) dt (5A) 



*'0 •'0 



Pt, = PoSiitc;zi{t)). 



(5B) 



Now I have two Equations (5 A) and (5B) to be 

 solved simultaneously for the unknowns Po and 

 the parameters in ziit). An iterative procedure 

 was used to obtain estimates of Po and ziit). 

 Clearly, the selection of the function forms of 21 it) 

 and Z2it) are important in obtaining accurate 

 estimates of Po and Ptc  



Anchovy Mortality Curves and 

 Estimation of Egg Production 



Daily egg and larval production per 0.05 m^ and 

 their ages iPt , t) were estimated for 1979-81 

 to model the mortality curves Po Siit) and Pt^ 

 S2it\T > tc) (Equation (3)). The egg data were 

 collected in vertical net tows from 70 m with the 



Table L — Daily egg and larval production per 0.05 m^ (Pt) at various ages in days 

 ( t ) sampled from Cal VET and bongo tows, and the estimates of five parameters: egg 

 production at age zero (Po *. egg mortality id), larval mortality coefficient (/3 ), larval 

 production at hatching (P/ ) and incubation time in days ( </ ) in CalCOFI regions 4, 

 7, 8, and 11, January-April 1979-81. 



' Not weighted by area size 



^For both 1980 and 1981 larval data. 



^Asymptotic standard error in parentheses. 



142 



