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Fishery Bulletin 104(3) 



Bioenergetics model 



Rates of anabolism, catabolism, and waste losses 

 (Table 1) were used to construct a bioenergetics model 

 that predicted daily energy consumption (C^, in joules 

 per day, J/d): 



Cr 



RMR„ + SDA + G„ + F +11. 



(1) 



The model used a daily time step, consistent with 

 the determination of daily energy ration. Due to the 

 reporting of the daily routine metabolic rate (RMRj^), 

 specific dynamic action (SDA), fecal losses (F). and 

 excretions (U) as fractions of consumption (see below), 

 we rearranged Equation 1 and solved for C,; to yield 

 the model: 



RMR^+G„ 

 a-SDA-U-F) 



(2) 



We set the immigration and emigration dates for the 

 simulation as May 15 and September 30, respectively 

 (VIMSi). 



We used the model to estimate daily energy ration for 

 average individuals within each of six age-classes us- 

 ing the Chesapeake Bay nursery (Musick et al., 1993). 

 In turn, we combined energetic requirements with diet 

 composition data to estimate rates of food consump- 

 tion (daily ration) and predatory impact of individual 

 sharks over the course of the summer for each age class. 

 Finally, these individual estimates were merged with 

 estimates of population size and age structure to esti- 

 mate the overall predatory demand of juvenile sandbar 

 sharks in the Chesapeake Bay nursery area. 



Model parameters 



Routine metabolic rate (RMR) Like a number of car- 

 charhiniform species, sandbar sharks are continuously 

 active, which leads to high daily metabolic expenditures 

 (e.g., Carlson et al., 1999). As a result, metabolic rate is 

 the largest and most variable component of the energy 

 budget for these active fish (Kerr, 1982; Boisclair and 

 Leggett, 1989). Unfortunately, because of a paucity of 

 available data, metabolic rate parameters are often 

 borrowed from other species (e.g., Schindler et al., 

 2002). Sensitivity analyses have shown that accurate 

 metabolic rate data are needed to construct realistic 

 bioenergetics models (Kitchell et al., 1977; Bartell et 

 al., 1986). 



The allometric (size-dependent) influence on standard 

 metabolic rate (SMR) in juvenile sandbar sharks was re- 

 cently determined over the entire size range (42-92 cm 

 PCL, 1-10 kg) characteristic of the Chesapeake Bay 

 nursery area in flow-through respirometers for sharks 

 treated with a neuromuscular blocker (Dowd et al., 

 2006). The best fitting allometric equation for SMR 

 {SMR=axMh for 33 sharks at 24°C was 



where M = mass in kilograms; and 

 SMR = mgOj consumed per hour. 



The values in parentheses are the standard errors of 

 the allometric intercept and the allometric exponent 

 estimates (hereafter SMRa and SMRb, respectively). 



Dowd et al. (2006) also determined the routine meta- 

 bolic rate (the average oxygen consumption rate of a 

 swimming shark) for 15 individual sandbar sharks at 

 24^C in an annular respirometer (diameter 1.67 m). The 

 ratio of routine metabolic rate to SMR, corrected for the 

 cost of swimming in a curved path in the respirometer 

 (Weihs. 1981), averaged 1.62 ±0.11 (Dowd et al., 2006). 

 This ratio was used in the model as a constant activ- 

 ity multiplier (ACT) to estimate field metabolic rate 

 (sensu Winberg, 1960; Kitchell et al., 1977; Schindler 

 et al., 2002). The ACT used is similar to those derived 

 from field data for subadult Negaprion hrevirostns (1.3; 

 Sundstrbm and Gruber, 1998) and juvenile Sphyrna 

 lewini (1.45; Lowe, 2002). The sandbar shark ACT was 

 assumed to remain constant for all age classes and over 

 all temperatures (Dowd et al., 2006). 



The effects of acute temperature changes (quantified 

 as Qj||) on SMR for juvenile sandbar sharks (mass 1 — 10 

 kg) between 18" and 28°C have also been measured 

 (Dowd et al., 2006). The overall mean Qj,, (the relative 

 increase in metabolic rate with temperature, scaled to 

 a 10° temperature range) was 2.89 ±0.16 (?! = 43), was 

 consistent over the size range of sharks tested, and 

 was statistically indistinguishable among three treat- 

 ments (18-24°C, 24-28°C, and 18-28°C). We assumed 

 that the SMR Qjq remained constant throughout the 

 simulation period. 



For each day of the simulation, the Q,q was used 

 to adjust the predicted SMR from Equation 3 to the 

 simulated daily temperature (T) (equation adapted from 

 Schmidt-Nielsen, 1997): 



SMRt, = W 



logSMB.,4+logQi 



' 10 J 



(4) 



SMR„. = 120.0 (±17.3)M0 788 (±o.o76). 



(3) 



SMRj, was then multiplied by the ACT and by 24 hours 

 to obtain the daily metabolic expenditure in mgO^/day. 

 Finally, this value was converted to daily metabolic 

 energy utilization (RMR^) by using the oxycalorific coef- 

 ficient 13.59 J/mgOj (Elliott and Davison, 1975). 



Specific dynamic action (SDA) Specific dynamic action 

 represents the energetic cost of incorporation of digested 

 amino acids into new proteins (Brown and Cameron, 

 1991). Although SDA varies with growth rate, or the 

 protein content of ingested food (e.g., Ross et al., 1992), 

 most bioenergetics models set SDA as a constant fraction 

 of consumed energy (e.g., Hewett and Johnson, 1992). 

 Fortunately, although SDA has been measured in only 

 a few elasmobranch species, it is typically a relatively 

 small fraction of consumed energy (DuPreez et al., 1988; 

 Sims and Davies, 1994; Duffy, 1999; Ferry-Graham and 

 Gibb, 2001). As an initial estimate, we assumed SDA to 

 be 10% of consumed energy (Schindler et al., 2002). 



