304 



Fishery Bulletin 88(2). 1990 



157" W 



- 57° 30' 



58°30N' 



- 56° 30 



155° 



153° 



Figure 1 



Typical locations of sampling stations (•) and the grid pat- 

 tern used for the computer simulation. The flux of larvae 

 through the solid lines is zero. The dashed lines are open 

 boundaries of the model that permit the loss of larvae. 



least a month after hatching (Incze et al. 1989). Assum- 

 ing no drift or dispersion of larvae away from the sam- 

 pling area, the instantaneous daily mortality was esti- 

 mated as 0.086 (Kim and Gunderson 1989). The effects 

 of advection and diffusion on the larval mass, however, 

 can cause errors in estimation of mortality and abun- 

 dance. Hence, the distribution and abundance of wall- 

 eye pollock larvae in Shelikof Strait should be recon- 

 sidered in the light of oceanic diffusion-advection 

 theory (McGurk 1989). 

 The main objectives of this paper are: 



1 Estimation of diffusion coefficients and advection 

 rates of walleye pollock larvae based on ichthyoplank- 

 ton distribution in Shelikof Strait; 



2 Description of expected larval distribution and 

 abundance with time from a computer simulation using 

 a diffusion-advection model; and 



3 Reestimation of larval mortality and expected lar- 

 val abundance reported in Kim and Gunderson (1989) 

 and comparison of these results with field observations. 



Background of theories and model 



In general, the simplest approach to the diffusion prob- 

 lem for particles in a fluid medium follows from the 



assumption that the rate of diffusion is directly pro- 

 portional to the local concentration gradient (Okubo 

 1980). Walleye pollock larvae in Shelikof Strait are 

 advected and diffused in the upper 60 m during early 

 larval stages (Kendall et al. 1987), and the swimming 

 ability of larvae less than 10 mm is assumed to be in- 

 consequential. Therefore, a horizontal two-dimensional 

 diffusion-advection model is applicable to changes in 

 the distribution and abundance of young walleye pol- 

 lock larvae in Shelikof Strait. Current speeds (ii and 

 v) and diffusion coefficients (K^ and A',J are set con- 

 stant, with the assumption of a homogeneous turbu- 

 lence field and negligible horizontal divergence. Newly 

 hatched larvae (i.e., the source material in the diffusion- 

 advection model) are assumed to be produced daily at 

 a fixed location near the center of Shelikof Strait (Kim 

 and Kendall 1989). Once larvae that dispersed from the 

 source point arrived at the Alaska Peninsula coast, they 

 were required to remain there, since the shallow coastal 

 region is considered a nursery area of young fish 

 (Walters et al. 1985). Since larvae grow as they drift, 

 the simulated distrilnition and abundance of larvae can 

 he divided into several size groups. The partial differen- 

 tial equation, with initial condition Ci{x,y, Ti ) = and 

 boundary conditions as described above, is 



