Powell et al.: Modeling oyster populations 



349 



Governing equation 



The change in oyster standing stock with time in 

 each size class (O ) is the result of changes in net 

 production (NPj), taken to be the sum of the produc- 

 tion of somatic (P ) and reproductive (P r ) tissue, 

 and the addition of individuals from the previous 



size class or loss to the next largest size class by 

 growth. Following White et al. (1988), net produc- 

 tivity is assumed to be the difference between as- 

 similation (Aj) and respiration (R ), 



Oyster density/ 

 flowflsld 



Salinity 



Temp«ratur« 



-e 



' Particulate Load 



Food Supply 



Rltratlon Rata 



Ingestion 



//knlmllatkMiS 

 I Efflclancy ) 



AeslmllarJon 



Respiration 



Spawning 



/ Larval \ 



I Mortality J 



Rscrultment 



Figure 1 



Schematic diagram of the energy flow model. 



NP =P +P 



J gj rj 



R, 



(1) 



Accordingly, 



dOj 



dt 



Pgj + P rj + (gain from.;' - 1)  

 (loss to 7 + 1) 



(2) 



for j = 1,10 recognizing P r = forj = 1,3. 



Resorption of either gonadal or somatic 

 tissue results in loss of biomass. When 

 NP<0, oysters lose biomass and transfer 

 into the next lower size class. This is an im- 

 portant difference between our size class 

 model and a size class model based on lin- 

 ear dimensions; shell size does not change, 

 however biomass does during periods of 

 negative scope for growth. This is the basis 

 for the use of condition index as a measure 

 of health in oysters (e.g. Newell, 1985; Wright 

 and Hetzel, 1985). To allow for this, equation 

 2 must be modified as 



dO 



, - = Pgj+ P r j + (gain from J - 1) - 



( loss to 7' + 1) + (gain from 7 + 1) 

 -(loss to j — 1) 



(3) 



for j - 1,10. The last two terms on the right 

 side of Equation 3 represent the individuals 

 losing biomass and, thus, translating down 

 to the next lower size class. 



The relationships used to parameterize 

 the processes in Equation 3 are described in 

 the following sections. More details and a 

 discussion of the assumptions and support- 

 ing data for the model were presented by 

 Klinck et al. ( 1992), Powell et al. (1992) and 

 Hofmann et al. (1992). Accordingly, the ba- 

 sic oyster size class model is outlined only 

 briefly. However, calculations of spawning 

 size and recruitment, mortality, and the ef- 

 fect of oyster density on feeding are specific to 

 this study and are described in more detail. 



Feeding and assimilation 



Ingestion rate depends upon the filtration 

 rate and the ambient food concentration. We 

 adapted Doering and Oviatt's (1986) equa- 



