LO: EGG PRODUCTION OF NORTHERN ANCHOVY 



group). It was necessary to compute a weighted 

 mean of larval production (wPt) because the 

 number of net tows was not proportional to the 

 area size: The daily larval production [Ptj , tj ) was 

 estimated first for each of the three subareas {j - 

 1: inshore = regions 7 and 11; 7 = 2: nearshore = 

 regions 4, 8, and 13; and j = 3: offshore = regions 

 5, 9. and 14) (Fig. 1). The data set (u-Pt , t ) was used 

 for final fitting of the mortality curve where w Pt = 



S Ptj uj , and uj = 0.17, 0.31, and 0.52 for^ = 1, 2, 



and 3, the relative area sizes. The unweighted 

 average age t over three areas was used because 

 little variation exists among tj's (Fig. 2). 



P,= 1.364 (t/3.16)-2-2i' 



- 0.45 



30 



O 



3 



a 

 o 



cc 

 a. 



-I 



< 

 > 



< 



_i 0.15 - 



< 



00 



2.0 3.0 4.0 5.0 



AGE/3.16 (t/th) 



6.0 



FIGURE 2.— Weighted daily larval production (wPt) and age in 

 days (t) of northern anchovy and the fitted larval mortality curve 

 based upon Equation (8B) for larvae < 20 d old, 1979. 



MODEL 



If a cohort of eggs (larvae) is followed and Nt 

 is defined as the number of eggs (larvae) at age 

 t (days), then the ratio Nt/No measures the 

 survival probability at age t: Sit; zit)) = P(T 

 > t; z (t)). The sample ratio m/no estimates 

 the survival probability Sit) where zit), the in- 

 stantaneous mortality rate (IMR), is defined as 



lim PU:Si:^l±Al^:>i) If the sample data 

 At^O A^ 



{nt,t) are taken from a single cohort and the form 



of Sit) is known, both No and zit) can be esti- 

 mated through nt = no Siit); zit)). Assuming 

 that the standing stock of eggs and larvae repre- 

 sents a single cohort (with stable age distribution) 

 as it ages, then iNt , t ) can be estimated from the 

 number of eggs and larvae in various stages 

 (lengths) which are later converted to age in the 

 sample. Hewitt (1982) conducted a simulation 

 study to check for possible bias in larval mortality 

 rate caused by seasonal changes in the intensity of 

 spawning of northern anchovy which violates the 

 assumption of a stable age distribution. He found 

 that mortality was overestimated in the begin- 

 ning (January-February) of a season when spawn- 

 ing was increasing and underestimated at the end 

 (May-July) when spawning was decreasing. When 

 the larval numbers were accumulated over the 

 entire season, these two biases tended to cancel 

 out. Therefore, the stable age distribution is a 

 reasonable assumption if the egg and larval sam- 

 ple covers the entire season. To compute larval 

 mortality for each year, I chose larval data from 

 January to April to be consistent with the current 

 sampling scheme. According to Hewitt's study, 

 the larval mortality may be overestimated. How- 

 ever, because only young larvae (<8 mm pre- 

 served length) were considered in the model, the 

 upward bias is slight. The number of eggs and 

 larvae at various stages or length classes int, ), as 

 mentioned in a previous section, was further 

 adjusted for the duration in days that eggs ( larvae) 

 remained in a particular stage or length class (d; ), 

 i.e., Pt, = nt.ldi. The quantity Pt, is egg (larval) 

 production per day per unit area (e.g., 0.05 m^ ) at 

 age ti , the average age of eggs (larvae) in the iih 

 stage (length) class (Farris 1960; Saville 1964; 

 Harding and Talbot 1973; Ciechomski and Capez- 

 zani 1973). (In later sections, the subscript / is 

 dropped, thus iPt, t) is used in place of (P^, , ti).) 



The model is based on the form of the mortality 

 curves of northern anchovy eggs and those for 

 anchovy larvae, the form of the curve for eggs and 

 larvae being distinctly different. The daily egg 

 and larval production Pt is modeled by three 

 survivorship functions Si, S2, and S.3: 



141 



