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Fishery Bulletin 92(2). 1994 



Model solution 



The model described by Equation 3 was solved nu- 

 merically by using an implicit (Crank-Nicolson) 

 tridiagonal solution technique. The time step for 

 model integration was one day. Simulations were 

 run for six years which is sufficient time for the 

 model solutions to adjust so that trends in popula- 

 tion levels could be identified in the simulations. 



Results 



Model initialization 



The system of equations given by Equation 3 re- 

 quires that an initial oyster population size-fre- 

 quency distribution be specified. The simulations 

 described in the following sections are designed to 

 investigate seasonal and latitudinal mortality effects 

 on oyster population size frequency and stability. 

 Therefore, it proved useful to begin the simulations 

 with a size-frequency distribution representative of 

 a crowded population; that is, one suffering little 

 mortality. In this way, changes in the simulated 

 oyster populations will be the result of mortality 

 only. Also, using the same initial population distri- 

 bution allows for comparison between simulations 

 throughout the entire 6-year simulated time period. 

 The initial oyster size-frequency distribution was 

 obtained from a simulation that was started with 10 



individualsm -2 in size-class 7 on 1 January. The 

 food time series for this simulation contained two 

 phytoplankton blooms of two months duration 

 (March/April, August/September) with intervening 

 summer months and winter months as detailed in 

 Figure 2. Dense bivalve populations can deplete the 

 surrounding water column of food (Frechette et al., 

 1991 ). We used Lund's ( 1957) low flow conditions to 

 simulate the effect of oyster density on food supply. 

 Such conditions might be typical of an enclosed or 

 sheltered reef (Powell et al., 1987). No mortality was 

 allowed in any size class. 



The time development of the simulated population 

 (Fig. 3A) shows that the mean size of the popula- 

 tion slowly declines from size class 7 to size class 3, 

 as population density increases about 3 orders of 

 magnitude. These trends are characteristic of a 

 crowded population: high population density and 

 reduced adult size. Reproduction continues through- 

 out the simulation (Fig. 3, A and C) with a strong 

 fall spawning pulse (Fig. 3B) occurring in response 

 to the fall phytoplankton bloom (Hofmann et al., 

 1992). Therefore, food limitation is not sufficient 

 to cap population growth; however, the rate of popu- 

 lation increase has dramatically declined over the 

 6-year simulation. It is the population size- 

 frequency distribution at the end of the 6-year simu- 

 lation (Fig. 3D) that is used to initialize the 

 mortality simulations described in the following 

 sections. 



