Model I 



FISHERY BULLETIN: VOL. 81, NO. 2 



Model H 



Figure 5.— A comparison of the Model I 

 energy budget, where foraging speed and 

 foraging time are constant while plankton 

 concentration increases, with the Model 

 II budget incorporating the actual volun- 

 tary swimming speed of the Atlantic 

 menhaden at each concentration of plank- 

 ton. Panels numbered 1, 2, 3, 4 are as in 

 Figure 1. 



0.0030 0.0060 0.0030 0.0060 0.0090 



PLANKTON CONCENTRATION (c.kcal/i) 



budget, though functionally simpler than the energy 

 budget, is controlled by the same three variables: 

 The foraging speed (s, cm/s), the concentration of 

 food (c, kcal or mg N/1), and the foraging time {h, h/d). 

 In the Model I nitrogen budget, R N , pR N , E fN , and G N 

 all increase linearly, E bN remains constant, and K 1N 

 increases asymptotically with increasing values of s, 

 c, and h (Fig. 6). However, as we found in the energy 

 budget, these curves in the Model II nitrogen budget 

 are nearly linear at plankton concentrations suf- 

 ficiently high that s ~ constant, but become in- 

 creasingly curvilinear at low plankton concentrations 

 because of the decline in the foraging speed (Fig. 7). 

 Here, also, the reduction in foraging speed enables 

 the Atlantic menhaden to obtain a maintenance ra- 

 tion in less time and at a lower concentration of 

 188 



plankton, and to increase their growth rate and 

 growth efficiency, relative to the case in Model I 

 where foraging speed was assumed to remain con- 

 stant at 41.3 cm/s. 

 The nitrogen and energy budgets differ in some im- 

 portant ways. First, we have seen that in the energy 

 budget, with an increase in swimming speed (s), the 

 growth rate and growth efficiency increase from zero, 

 reach a maximum, then decline back to zero (Fig. 1, 

 A4). However, in the nitrogen budget, growth in ni- 

 trogen increases linearly (i.e., indefinitely), and 

 growth efficiency increases asymptotically (Fig. 6, 

 A4) with increasing swimming speed. Second, for any 

 given s, c, and h, the predicted growth efficiency in 

 calories is usually significantly different from that in 

 nitrogen (Fig. 8). Figure 8 shows that differences ex- 



