Dew et a\ Model for assessing populations of Crassostrea anakensis in Cfiespeake Bay 



763 



certainty in obtaining a 100% harvest rate 

 would be lower. 



Population size for the current year is 

 determined from the previous year's popu- 

 lation size, harvest rate, natural mortal- 

 ity, and certainty in obtaining the desired 

 harvest rate. Thus, the next year's starting 

 population for the next age class greater 

 than one is 



N.. 



= N,,xe 



■((H,xC)+M,, 



(8) 



where H^ = harvest rate for age-class i 

 greater than one; 

 C = certainty in obtaining the 

 desired harvest rate; and 

 M, , = natural mortality rate at time 

 t for age-class i greater than 

 one. 



Total population size is determined by the 

 summation of all individuals across all age 

 classes: 



. 76 6 mm 

 Minimum 

 shell lengtfi- 

 at-harvest 



-66 7 mm 

 Minimum 

 shell length- 

 at-harvest 



9.5 11.5 



Salinity (ppt) 



Figure 2 



Relationship between salinity at deployment site and probability of a C. 

 ariakensis population becoming self-sustaining, when area is set at 100 m^, 

 stocking size is set at 20,000 oyster, and when all other variables are set at 

 default values. The solid line represents the relationship when the minimum 

 shell length-at-harvest is 77.6 mm. The dashed line represents the relation- 

 ship when the minimum shell length-at-harvest is 66.7 mm. 



Ntntal,=^N,,. 



(9) 



where Ntotalf = the total population size at 

 time t for all age classes. 



Model simulations and output 



The model provides two options for output to the user. 

 The first option shows results of one run of the simulation 

 model. The output is a graph showing population size over 

 time. The other output option shows the distribution of out- 

 comes resulting from running the same scenario (i.e. the 

 same input parameter and variable values) a set number 

 of times. This output option shows the probability of the 

 population becoming self-sustaining given the specified set 

 of input conditions and yields probability profiles for risk 

 assessment (Rosenburg and Restrepo, 1994). Probabilities 

 range from 0%, meaning there is a zero probability of a 

 population becoming self-sustaining given a set of input 

 conditions, to 100%, meaning that this outcome will occur 

 every time under the given set of input conditions. 



Self-sustainability of a population is tested by running 

 the simulation for a specified number of years with stock- 

 ing, and then continuing to calculate population size for 

 a specified number of additional years without stocking. 

 Should the population size become zero, then the popu- 

 lation is supported solely by stocking. However, should 

 population size prove greater than the number stocked in 

 earlier years, then the population is self-sustaining. The 

 default setting for the simulation is to continue running 

 the simulation twenty years without stocking, reflecting a 

 maximum longevity of 20 years for Suminoe oyster (Cahn, 

 1950). 



To understand the effects of changes in key variables 

 on model predictions, we performed a sensitivity analysis. 



A first set of model runs changed the value of only one vari- 

 able at a time, while keeping all other variables constant 

 at default values. The variables that were changed were 

 salinity, certainty of obtaining the desired harvest rate, 

 minimum shell length-at-harvest, and stocking density. 

 The second set of model runs was similar to the first, except 

 changes were made to the values of two variables at a time 

 while all other variables remained constant at default val- 

 ues. Salinity was varied from 8.5 ppt to 13.5 ppt. Certainty 

 of obtaining the desired harvest rate was varied from 0.5 to 

 1.0. Minimum shell length-at-harvest was varied from 60 

 mm to 100 mm. To determine stocking density, the number 

 of oysters stocked was varied from 100 to 1,000,000 oysters, 

 but the area was set at 300 m^. 



All simulation results reported below were obtained by 

 using default values for all variables (Table 2), unless noted 

 otherwise. 



Results 



Effects of four major variables on the probability of a 

 Suminoe oyster population becoming self-sustaining were 

 examined by using the simulation model. These variables 

 were salinity, certainty of obtaining the desired harvest rate, 

 minimum shell length-at-harvest, and stocking density. 



Salinity 



Salinity between 8 ppt and 13.5 ppt affected the likelihood 

 of developing self-sustaining populations because when 

 salinity decreases, fecundity decreases (Fig. 2). However, 

 this trend can be altered or masked by the effects of other 

 variables on the probability of a population becoming self- 



