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Fishery Bulletin 92(2). 1994 



owing to levee building for instance (Mackin and 

 Hopkins, 1962), population recovery rates appear 

 to be more rapid at lower latitudes (compare 

 Owen, 1953; Hofstetter, 1983; Stanley and Sell- 

 ers, 1986; Mackenzie, 1989). 

 3 Major population crashes resulting in long-term 

 loss or decline of the C. virginica fishery have oc- 

 curred almost exclusively along the northeast 

 coast of North America. Moreover, significant 

 population declines occurred earlier in the century 

 at higher latitudes (viz. Canada, 1910s, Mid-Atlan- 

 tic area, 1950s; Delaware and Chesapeake Bays, 

 1980s) (Stanley and Sellers, 1986; Mountford and 

 Reynolds, 1988; Mackenzie, 1989; and others refer- 

 enced previously), although more than one signifi- 

 cant population has declined in some areas. 



These trends in oyster population dynamics 

 gleaned from the literature are not well documented. 

 Much literature is anecdotal and significant excep- 

 tions do exist. Nevertheless, taken as a whole, these 

 trends suggest two hypotheses: 1) a latitudinal gra- 

 dient in susceptibility to population crashes exists 

 in oyster populations; and 2) as temperature varies 

 both latitudinally and seasonally, temperature, 

 through its effect on oyster physiology (e.g. Koehn 

 and Bayne, 1989), may determine the susceptibility 

 of oyster populations to potentially destabilizing 

 episodes of mortality. 



In this study, we tested these hypotheses using a 

 population dynamics model. The results of the mod- 

 eling exercise were then used to examine some ba- 

 sic decisions required for fishery management; viz. 

 the timing and length of the fishing seasons and the 

 size limits set for the fishery to obtain a maximum 

 sustainable yield (e.g. Glude, 1966; Hofstetter and 

 Ray, 1988; Young and Martin, 1989). 



The model 



Perspective and basic characteristics 



The oyster population model shown in Figure 1 is 

 designed to investigate the dynamics of the post- 

 settlement phase of the American eastern oyster's, 

 Crassostrea virginica, life from newly settled juve- 

 nile through adulthood. The model consists of a sys- 

 tem of ten coupled ordinary differential equations, 

 with each equation representing a size class of oys- 

 ter; however, the ten size classes are not evenly di- 

 vided across the length or biomass spectrum (Table 1). 

 Size class 1 includes newly settled juveniles (Dupuy 

 et al., 1977). Size class 10 corresponds to oysters that 

 are larger than those normally found in natural popu- 

 lations. The boundaries between size classes 4 and 5, 

 5 and 6, and 6 and 7 represent size limits that have 



been used or considered for market-size oysters: 2.5 

 in; 3.0 in and 3.5 in, respectively. We define adults, 

 individuals capable of spawning, as individuals 

 weighing more than 0.65 g ash-free dry weight, 

 about 50 mm in length (Hayes and Menzel, 1981). 

 Therefore, size classes 1 to 3 are juveniles. 



All calculations were done in terms of energy in 

 calm 2 . When necessary, oyster energy is converted 

 to oyster biomass by using a caloric conversion of 

 6100 cal-g dry wt -1 for oysters (Cummins and 

 Wuycheck, 1971) and biomass to an approximate 

 length by using White et al.'s (1988) biomass-length 

 conversion. To calculate any gain, loss, or transfer 

 of energy (or biomass) between size classes, an ad- 

 ditional conversion was made to express the gain, 

 loss or transfer in terms of a specific rate (day -1 ) 

 which was then multiplied by the caloric quantity 

 in a size class. Transfers between size classes were 

 scaled by the ratio of the average weight of the cur- 

 rent size class (in g dry wt or cal) to that of the size 

 class from which energy was gained or to which en- 

 ergy was lost. This ensured that the total number of 

 individuals in the model was conserved, in the absence 

 of recruitment and mortality. Because, the size classes 

 in the model are not equivalent in dimension, each 

 specific rate for each transfer between size classes was 

 scaled by the ratio between the two size classes: 



for transfers up : Wj/(Wj +1 -Wj) 

 for transfers down : W /(Wj -W J _ l )> 



where W is the median biomass (in g dry wt) in size 

 class j. For simplicity, we will not include any of 

 these conversions and scaling factors in the equa- 

 tions given subsequently. 



