Powell et al.: Modeling oyster populations 



351 



for January to June and 



R eff] = 0.047T - 0.809 



(14) 



for July to December. Equations 13 and 14 were 

 derived empirically from the field observations of 

 Soniat and Ray (1985) and may not hold north of 

 Delaware Bay (Hofmann et al., in press). 



The portion of net productivity going into repro- 

 duction is given by 



P rj =R efS NP J , for j = 4,10. 



(15) 



Somatic growth is the remaining fraction. In cases 

 where NP- < 0, we assume preferential resorption 

 of gonadal tissue to cover the debt. For juveniles and 

 adults with no gonadal tissue, resorption of somatic 

 tissue occurs. We assume that reduced reproduction 

 at low salinity (Engle, 1947; Butler, 1949) results 

 from decreased filtration rate and increased respi- 

 ratory rate and so include no specific relationship 

 for this effect. 



Spawning of the oyster population occurs when 

 the total cumulative reproductive biomass of the 

 population exceeds 20% of the total oyster biomass 

 (Choi et al., 1993). This value is lower than the es- 

 timates of Galtsoff (1964) and Deslous-Paoli and 

 Heral (1988), but comes from direct measurements 

 of egg content. Once spawning occurs, the total re- 

 productive biomass is apportioned into male and 

 female biomass according to Kennedy (1982) 



L 



0.02 1L. -0.62. 



(16) 



where f ti is the ratio of females to males and L h 

 is shell length in mm obtained from biomass (White 

 et al., 1988). Oysters can change their sex, and 

 Kennedy (1982) suggested that the ratio of males to 

 females is affected by oyster density, salinity, and 

 stress. While perhaps important in some situations, 

 no data exist to parameterize these relationships 

 adequately. They are not included in the model. 



The female portion of reproductive biomass (R,) is 

 converted into eggs spawned by 



Number of eggs spawned 



R f 1/6133 l/W egg 



(17) 



where 6133 is the egg's caloric content (cal g dry 



wt^MKlincketal. 



tained from 



1992) and W is egg weight ob- 



W egg = 2.14x10 



it 



V 



egg 



IS 



where oyster egg volume (V ) is from Gallager and 

 Mann (1986). The factor 2.14X10" 14 represents con- 



versions for density, dry wt to wet wt, and um 3 to 

 cm 3 . The egg weight, 13 ng dry wt, calculated from 

 Equation 18 is close to experimentally determined 

 egg weights (Lee and Heffernan, 1991; Choi et al., 

 1993). 



Larval recruitment and mortality 



Larval growth rate, which determines the time 

 spent in the plankton, is controlled by ambient food 

 concentration, temperature, salinity, and turbidity. 

 Therefore, larval life span can range from twenty to 

 sixty days (Dekshenieks et al., in press). For the 

 purposes of this modeling study, larval life span was 

 assumed to be twenty days, which may be an un- 

 derestimate for some environmental conditions, but 

 is in general agreement with observations 

 (Prytherch, 1929; Dupuy et al., 1977; Bahr and 

 Lanier, 1981). We allow an additional 10 days for the 

 larvae to grow to the mean biomass represented by 

 size class one in the post-settlement model. Thus, 

 thirty days after spawning, larvae appear in the 

 simulated post-settlement oyster population as new 

 recruits to the first size class (/=1). 



While in the plankton, oyster larvae undergo con- 

 siderable mortality from a variety of sources. Lar- 

 val mortality is included in the model by using a 

 simple linear relationship of the form 



Number of larvae recruited spawn l 

 s( Number of eggs spawned) 



(20) 



where s determines the rate at which individuals are 

 lost per spawn (in spawn -1 ). No attempt is made to 

 differentiate among sources of oyster larval mortality. 



Post-settlement population mortality 



Post-settlement oyster populations undergo natural 

 mortality from diseases and predators and man-in- 

 duced mortality through fishing. Both natural and 

 man-induced mortality vary with season and size of 

 individual. Adult mortality was modeled by using a 

 linear mortality relationship of the form 



Number dying time : = 

 k d ( Number living), for./' = k,l 



(21) 



d determines the daily mortality rate (in 

 and k and / are the inclusive size classes 



where k 

 day 1 ) 



being affected by mortality. As with larval mortal- 

 ity, this approach does not differentiate among the 

 many sources of oyster mortality. However, the ef- 



