310 



Fishery Bulletin 88(2), 1990 



Reed et al. (1989) estimated parameters based on cur- 

 rent measurement and larval patch in Shelikof Strait. 

 By examining the abundance in small areas around the 

 densest larval patches found in April and May surveys, 

 they estimated an instantaneous mortality rate of 

 0.063/day and an advection rate of 4.3 km/day (Table 

 2), which are in excellent agreement with our esti- 

 mates. Also, the estimation of eddy diffusivity in the 

 along-strait direction of 43.2 km^/day by Reed et al. 

 (1989) did not differ greatly from our mean value of 

 65.2 km^ (Table 2), even though the former was de- 

 rived from moored current meter data in the surface 

 layer (56 m) and the latter from larval distribution. 

 These estimates are realistic only in a mean sense, 

 because they vary in both time and space. 



The diffusion process tends to destroy larval aggre- 

 gation until larvae reach a certain size, so that patch- 

 iness will decrease with time. The Lloyd Patchiness 

 Index (LPI) has been frequently used for describing ag- 

 gregations of organisms (Lloyd 1967), and Kim (1987) 

 discussed changes in LPI of walleye pollock larvae as 

 they grew. The smaller size groups of larvae usually 

 had a higher LPI, but it decreased until a size of about 

 10 mm because of dispersal of the larval patch. For 

 sizes greater than 10 mm, although their contribution 

 to the total larval abundance was very small, the LPI 

 increased with length, perhaps because of reaggrega- 

 tion of the larvae as their swimming ability increased. 

 If a larval retention mechanism worked for large lar- 

 vae (10-12 mm) in Shelikof Strait due to increased 

 swimming ability, that might explain the higher larval 

 abundance from field samplings than that from the 

 simulation shown in Figure 3. Similar examples of lar- 

 val aggregation (i.e., initially patchy, dispersing until 

 a larval size of around 10 mm, and then patchy again) 

 were reported for northern anchovy and jack mackerel 

 off California (Hewitt 1982). 



The expected total larval abundance from the first 

 simulation was almost identical to that in Kim and 

 Gunderson (1989) because the same parameter values 

 were used. By adding the concept of diffusion and 

 advection to their model, elaborations on mortality and 

 expected abundance of walleye pollock larvae were 

 made. Based upon good agreement between observed 

 and simulated results, this paper has emphasized that 

 dispersion (or emigration) of organisms is important 

 in the field of population dynamics. 



Acknowledgments 



We are indebted to many people for helping us com- 

 plete this manuscript. We would like to thank P. Sta- 

 beno, R. Reed, and J. Schumacher at the NOAA Pacific 

 Marine Environmental Laboratory and A. Okubo at 



State University of New York at Stony Brook for their 

 comments and advice. Also we are greatful to all FOCI 

 (Fisheries Oceanography Coordinated Investigation) 

 members of AFSC (Alaska Fisheries Science Center) 

 who have prepared and provided us the necessary data. 

 Special thanks is given to A. Kendall (AFSC) who 

 funded this project and gave us valuable comments. 



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