Zenitani and Yamada: The relation between spawning area and biomass of Japanese pilchard, Sardinops melanostictus 



843 



Zenitani at al., 1995). Among these surveys, 

 two governmental institutions, the National 

 Research Institute of Fisheries Science and 

 the Nansei National Fisheries Research Insti- 

 tute, have collaborated on surveys covering the 

 inshore and offshore waters between 128-143°E 

 and 28-36°N since 1978 (Fig. 2). We used data 

 from these surveys covering the waters along 

 the Pacific coast of Japan between 130-142°E 

 and 28-36°N (Fig. 3). In the census, from 149 

 to 344 ichthyoplankton samples were collected 

 each year by towing two types of conical or 

 cylindrical-conical nets (inside mouth diame- 

 ter: 45 or 60 cm; mesh aperture: 0.335 mm). 

 Each net was retrieved vertically at 1 m/s from 

 150 m depth or from the bottom at stations 

 shallower than 150 m. 



We calculated two kinds of pilchard spawn- 

 ing area (A, and A.,). Pilchard spawning is 

 concentrated into two months, February and 

 March (Watanabe et al., 1996). Therefore, A, 

 in any given year was calculated by summing 

 the areas of 1° longitude x 1° latitude squares 

 where early developmental A-stage eggs, as 

 categorized by Nakai (1962), were collected 

 during February and March. A,, was calculated 

 by summing the areas of 1° longitude x 1° lati- 

 tude squares where eggs of any stage were col- 

 lected during February and March. The length 

 of time elapsing from fertilization to the end 

 of the A stage at the different temperatures, 

 15.2°, 17.5°, and 20.3°C, are 25, 16, and 10 

 hours, respectively. The length of time elapsing 

 from fertilization to hatching at the different 

 temperatures, 15.2°, 17.5°, and 20.3°C, are 85. 

 56, and 34 hours, respectively (Nakai, 1962). 



We used the pilchard biomass estimated 

 along the Pacific coast of Japan from 1977 to 

 1995 by Wada and Jacobson (1998). Biomass 

 estimation was conducted by virtual popula- 

 tion analysis (VPA) with the catch-at-age data 

 of the purse-seine fishery. The biomass esti- 

 mate was for the middle of June, the end of 

 the major spawning season for Japanese pil- 

 chard. During the main spawning season, most 

 spawning is done by age-l-i- pilchards and a 

 small amount is done by age-1 pilchards (Hira- 

 moto, 1981). The biomass of age-l-i- pilchards in 

 was assumed to be the spawning biomass (B) in 



100,000 



10,000 



1,000 



100 



 Biomass 

 Catch 

 - Egg abundance 



8000 



6000 (u 



4000 



2000 



r--r^cooocococoa>ijicD 

 cncr)CT)(j)C7)cr>CTicr)cr)c7i 



Year 



Figure 1 



Catch, spawning biomass, and egg abundance of Japanese pilchard 

 along the Pacific coast of Japan from 1978 to 1995 (after Wada and 

 Jacobson, 1998). 



35° N 



30° N 



■•—■■ H iWIII M 





Pacific Ocean 



130° E 



135° E 



140° E 



year y - 1 

 year y. 



Figure 2 



An example of station allocation for the spawning survey of Japanese 

 pilchard in February and March 1994. 



TV f\B)=u,exp{u,B), and 



V /tB)=AJl-|;/7'"; + "25'l"'l 



Model 



where u^, u., and A^ were parameters. 



To test whether spawning area could be correlated with 

 spawning biomass, statistical analyses were performed. 

 We used five relationships between A (=A, or A,, ) and B: 

 A=f\B) 



I 



II 



III 



flB)=u,B. 



f\B}=u,B+u.„ 



f\B)=UjB"'^,' 



Relationship V was obtained by a modification of Mangel 

 and Smiths (1990) model. They used the negative binomial 

 model to describe the contagion of pilchard eggs. It is commonly 

 used in ecological modeling (Pielou. 1977; Zweifel and Smith, 

 1981; Mangel and Smith, 1990; Zenitani et al.. 1998). Mangel 

 and Smith (1990) extended the negative binomial model to 

 include the possibility of failure to detect eggs which are pres- 

 ent at a station. According to Mangel and Smith ( 1990), 



