FISHERY BULLETIN: VOL. 81, NO. 2 



tion (46)), is expressed in units of nitrogen through 

 the following relationship: 



Thuss 



1 jug chlorophyll a = 0.00984 mg N. (56) 

 3,010.2 n - 29.62 



101.63 n - 0.604 



+ 12.2 cm/s (57) 



where n is the plankton concentration in mg N/1. 



The nitrogen budget can then be expressed solely in 

 terms of plankton concentration, n (mg N/1), and 

 foraging time, h (h/d), by substituting Equation (57) 

 into Equations (50), (51), (27), (52), and (53) to com- 

 pute R N ,pR N , E N , G N , and X liN (mg N/g dry weight 

 per d), respectively 



If the food ration or the plankton concentration is 

 expressed in kilocalories rather than units of ni- 

 trogen, Equation (48) is substituted into Equation (8), 

 and then Equation (8) into Equations (54) and (55) 

 for the calculations of G N and /f liN> respectively. 



The Model II nitrogen budget, like energy budget II, 

 is thus controlled by only two variables, c and h. 



RESULTS 

 Energy Budget 



The energy budget is presented in two forms, a 

 general model (Model I) and a special case of this 

 model which incorporates information on the swim- 

 ming and feeding behavior of the fish in response to 

 plankton concentration (Model II). Model I, which 

 defines the range of values which the energy budget 

 could theoretically assume, is a function of the forag- 

 ing speed (s), the concentration of plankton in the 

 water (c) , and the foraging time (h ) . In Model II, forag- 

 ing speed is a dependent function of plankton con- 

 centration, and the energy budget is defined simply 

 in terms of the variables c and h. Thus the two models 

 describe the potential, and the actual, bioenergetic 

 ranges within which the menhaden operate. 



In the following examples to illustrate the models, 

 the variables s, c, and h assume values from to 50 

 cm/s, to 0.0090 kcal/1, and to 24 h/d, respectively, 

 which should encompass the range of these variables 

 in nature. In examples where s is assumed to be con- 

 stant, a value of 41.3 cm/s was selected, because in 

 the experiments this was the average foraging speed 

 of the Atlantic menhaden at moderate to high plankton 

 concentrations, where s was nearly independent of 

 food level. Where c = constant, a value of 0.0030 

 kcal/1 was used, which is slightly above the threshold 

 value of c at which s becomes food-concentration 

 independent. We lack information on the foraging 

 time of adult Atlantic menhaden in the wild. However, 



184 



since they feed continuously in the laboratory when 

 food is present, when h — constant, we assigned it a 

 value of 14 h, which is approximately equal to the 

 number of daylight hours during the summer at the 

 latitude of Narragansett Bay. 



In the experimental studies from which the budgets 

 were derived, the variables s,c, and h took the follow- 

 ing values: /i = 7h,c- 0.0010 to 0.0065 kcal/1, and 

 s = 29.3 to 43.3 cm/s (1.1 to 1.7 body lengths/s). 

 Within this relatively narrow range in foraging speed, 

 the respiration rate increased from 2.2- to 5.4-fold 

 over the routine rate. Slower foraging speeds (<29 

 cm/s) were observed during the transition period of 

 declining phytoplankton concentration, after the in- 

 put of food was terminated. The minimum foraging 

 speed was greater than the routine swimming speed 

 (12.2 cm/s), but was not closely determined in this 

 study. The total ration ranged from 0.015 to 0.147 

 kcal/g dry weight, which corresponded to a feeding 

 rate of 0.00217 to 0.02065 kcal/g dry weight per h. 



Using Model I we have described how foraging 

 speed, food concentration, and the duration of feed- 

 ing affect the menhaden energy budget (Fig. 1). 



InFigure 1, Al-A4,s increases, whilec and/7 remain 

 constant. The total and the assimilated daily food in- 

 take {R K and pR K ) increase linearly with increasing 

 values of s (Fig. 1, Al). Among the energy expendi- 

 ture terms, the exogenous nitrogen excretion (E f K ) 

 increases linearly, the endogenous nitrogen excre- 

 tion (E b K ) and the routine metabolic rate (T r A ) re- 

 main constant, and the respiration during feeding 

 {T f K ) increases exponentially with increasing s (Fig. 1, 

 A2). Thus the assimilated daily ration increases 

 linearly, whereas the total energy expended in- 

 creases curvilinearly. If these two curves are drawn 

 on the same axes, we find that they intersect twice, at 

 a low and a high foraging speed (here, about 7 and 5 1 

 cm/s) (Fig. 1, A3). These intersections, where the en- 

 ergy intake is balanced by the output and G = 0, 

 define a range of foraging speeds within which the en- 

 ergy intake exceeds expenditure, and positive growth 

 takes place. At foraging speeds outside this range, 

 the energy expenditures exceed the energy intake 

 and the fish must draw upon stored energy reserves, 

 thus undergoing negative growth. Within the defined 

 range of foraging speeds, the growth curve (G K ) is 

 convex upwards, increasing curvilinearly from zero 

 to reach a maximum value at an intermediate swim- 

 ming speed, then declining back to zero (Fig. 1, A4). 

 The growth efficiency curve (K l K ) shows a similar 

 pattern, but reaches its maximum value at a different 

 foraging speed than that for maximum growth. 



InFigure 1, Bl-B4,c increases, whiles and/j remain 

 constant. The energy intake (R and pR) increases 



