Dowd et al Consumption rates of Carcharchmus plumbeus in Chesapeake Bay 



337 



Model calculations 



For each daily time step of the model and for each age 

 class, RMRp and G^ were calculated as described above. 

 These estimates were used to solve for daily consump- 

 tion in joules in Equation 2, where SDA, U, and F are 

 the fractions of consumption described above. These 

 daily energy consumption estimates were summed to 

 determine total energy consumption for an average 

 individual of each age class during the entire stay in 

 the Chesapeake Bay nursery. Mean daily energy ration 

 (DERl was calculated in kJ/d. The daily energy ration 

 was also expressed as a percentage of the average total 

 energy content (%DER) for each day: 



%DER = 100 



Cd 



(10) 



' Mg+M^^^ 



5400 I 



Finally, gross conversion efficiency (i^T, ), the fraction 

 of consumed energy that is devoted to growth, was cal- 

 culated for each day: 





(11) 



This value was used as a general test of the model 

 outputs. 



Error analysis 



Static models were run by using the initial parameter 

 estimates described above to determine point estimates 

 of consumption. SDA and energy losses in U and F 

 were modeled as constant fractions of consumption. The 

 initial choices of these values, therefore, had a direct 

 effect on the predicted consumption rates. Further, a 

 number of the model parameters were measured with 

 some uncertainty. A stochastic, Monte Carlo simulation 

 routine (Crystal Ball'- 2000 Academic Edition, vers. 

 5.2.2, Decisioneering, Inc., Denver, CO) was used to 

 assess this uncertainty with error analysis (Bartell et 

 al., 1986). Error analysis is particularly useful for evalu- 

 ating model sensitivity to parameters that enter the 

 model in a nonlinear fashion (Bartell et al., 1986), such 

 as the SMR allometric exponent (SMRb) and allometric 

 constant (SMRa) and the Qj,,. The simulation randomly 

 drew values from probability distributions for each model 

 parameter (Table 1) for each of the 2000 Monte Carlo 

 iterations. The model parameters were ranked in impor- 

 tance by their relative contribution to the variance of the 

 stochastic model outputs (Bartell et al., 1986). 



Results 



Consumption rates 



The model predicted mean daily energy rations (DER) 

 increasing from 233 ±5 kJ/d (%DER = 1.95 ±0.03%) 

 for young-of-the-year to 784 ±16 kJ/d (%DER = 1.20 



Table 4 



Gross conversion efficiency (Kj), daily energy ration 

 (DER), daily ration (DR), and total seasonal prey con- 

 sumption (C(^,) for individuals of each age-class of the 

 sandbar shark iCarcharhinus plumbeus) in the bioener- 

 getics model. DER and DR were averaged over the 138 

 days of the simulation (mean ±SEl. 



Age class K, DER(kJ/d) DR(7rBM/di Ct„t(kg) 



±0.02%) for an age-5 juvenile. These values correspond 

 to prey consumption rates of 2.17 ±0.03%BM/d and 

 1.30 ±0.02%BM/d, respectively (Table 4). The predicted 

 daily rations for a given age class over the course of the 

 simulation period fluctuated with temperature because 

 of the thermal influence on metabolic rate. 



During the 4.5-month stay in the Chesapeake Bay 

 nursery area, the static model predicted total energy con- 

 sumption of 269% of the total energy content for an age-0 

 shark (-32,000 kJ), declining to 165% (-108,000 kJ) for 

 age-5 sharks. When merged with diet composition data, 

 the model predicted that an age-0 shark would consume 

 6.6 kg (300% average BM) of prey per summer, and an 

 age-5 juvenile would consume 21.8 kg (180% average 

 BM). Therefore, the total sandbar shark population would 

 consume 124,400 kg of prey over the course of the sum- 

 mer in the Chesapeake Bay nursery area (Table 3). 



The average Kj declined quickly with age from 16.3 

 ±0.3% of consumed energy for age-0 sharks to 10.0 ±0.2% 

 of consumed energy by age five. Because growth plus rou- 

 tine metabolism comprised a constant proportion of the 

 total energy budget in the static model, the proportion 

 of consumption devoted to metabolism increased with 

 age. Metabolism for age-0 sandbar sharks accounted for 

 roughly 46% of ingested energy, increasing to 53% of 

 the energy budget for age-5 juveniles. When growth was 

 set to zero, we calculated the maintenance rations to be 

 63-80% of the rations when growth was included. 



Error analysis 



The relative contributions of each of the input param- 

 eters to the variance of the model outputs exhibited 

 similar patterns for all age classes (Fig. 1). The von 

 Bertalanffy parameters predicting size at age (L^, K) 

 had consistently high ranks for their contribution to 

 model variance, as did those describing the allometric 

 scaling of standard metabolic rate {SMRa, SMRb). F also 

 contributed significantly to the variance of the model 

 outputs for all age classes (Fig. 1). The contributions 



