760 



Fishery Bulletin 101(4) 



Modeling approach 



In each annual time step for age classes one through six, 

 growth occurs to the mean shell length of the age class, 

 then natural mortality and harvest are imposed, and then 

 reproduction occurs (Fig. 1). Because Suminoe oysters 

 grow quickly in autumn (Cahn, 1950), the annual time 

 step begins in September Harvest occurs from October to 

 April. Natural mortality occurs at the greatest rates during 

 the summer months. Because an annual time step is being 

 used, the model is designed so that natural mortality and 

 harvest are imposed simultaneously. Reproduction occurs 

 during the summer months. The model simulates repro- 

 duction for fertile individuals in all mature age classes. 

 The final population size for a particular age class after 

 natural mortality and harvest becomes the starting value 

 for population size for the next age class in the next time 

 step. All individuals stocked each year are age-class zero 

 individuals. The starting population size for age-class one 

 in the next time step is equal to the sum of all individuals 

 less than one-year old produced by all age classes, plus the 

 number of individuals stocked. 



Model variables, parameters, and equations 



The initial conditions for the model are determined by the 

 user's choice of specific values for several variables (Tables 1 

 and 2). The key abiotic variable driving population growth 

 is salinity, because fecundity is highly dependent upon 

 salinity (Mann and Evans, 1998). Biotic variables of the 

 model include mean shell length for each age class, mor- 

 tality (natural and harvest) for each age class, disease 

 prevalence, total mortality of oysters less than one year 

 old, oyster population density, sex ratio for each age class, 

 and reproductively effective reversion rate for each age 

 class (Table 1). Other variable inputs are stocking rates, 

 harvest regulations, and management strategies. 



Stochasticity is programed into the model to incorporate 

 both the uncertainty involved in estimating variable values 

 and environmental variation. Some variables are regarded 

 as stochastic variables because they vary around some 

 mean value from year to year, whereas other variables 

 (such as salinity and sex ratio of the population for each age 

 class) are deterministic in the model because they fluctuate 

 over a longer period of time in the absence of a catastrophe 

 (Kennedy et al., 1996). Stochasticity affects shell length, 

 natural mortality, and reproductively effective reversion 

 rates at each age, and the degree of variance is set by the 

 user as a constant for each year At each time step, a mean 

 shell length, mortality rate, and reproductively effective 

 reversion rate for each age class is randomly drawn from a 

 log normal distribution around a mean with an associated 

 variance. 



We assume that the mean shell length of each age class 

 at the current time step does not affect the mean length of 

 the age class at a subsequent time step, because of large, 

 highly variable growth rates per year (Calvo et al., 2001). 

 Default mean shell length for each age-class values were 

 obtained from Cahn ( 1950). The user may, of course, specify 

 other mean shell lengths. Growth affects the potential for 



recruitment through the effect of shell length on fecundity 

 in Equation 1 below. 



An equation for individual size-specific fecundity pre- 

 sented by Mann and Evans (1998) was multiplied by the 

 numbers and mean sizes of females in each mature age 

 class in order to estimate total fecundity for a diploid 

 population: 



F,, = 39.06 X 10.000423 x lJ ,'"" |- '" x N, 



(1) 



where F, , = total fecundity (number of eggs produced) at 

 time t for age-class i greater than one; 



