DURBIN and DURBIN: ENERGY AND NITROGEN BUDGETS FOR ATLANTIC MENHADEN 



4 8 12 16 20 



FORAGING TIME (h, hours/day) 



FIGURE 4.— The relationship between foraging time and the foraging 

 speed which maximizes the Atlantic menhaden's gross growth 

 efficiency (s K 0FT ). s(s K 0PT ) is independent of plankton concentra- 

 tion (c). 



depends onh. Similarly, a fish feeding for 14 h/d will 

 maximize its growth efficiency if it swims at 23.8 cm/ 

 s; however the resulting values of K Y will depend 

 on c. 



The foregoing examples demonstrate that the rela- 

 tive size of each component in the energy budget {R K , 

 pR K , T K , E K , and G K ) will vary according to the values 

 of s, c, and h. Since the different elements retain no 

 fixed proportions within the overall energy balance, 

 there is no single "standard" energy budget which 

 can be described for the Atlantic menhaden. 



It can also be seen that in Model I, a change in either 

 food concentration or the duration of feeding has a 

 direct, proportional effect on the growth rate, 

 because total energy intake and expenditure are 

 linear functions of c and h, when s = constant. 

 However, a change ins has a nonlinear impact on the 

 growth rate. This is because the respiration rate is an 

 exponential function of swimming speed, and thus a 

 change in swimming speed causes a proportional 

 change in energy intake but a more-than-pro- 

 portional change in total energy output. 

 In the Model II energy budget, s is no longer an in- 

 dependent variable, but is a dependent function of 

 food concentration c, according to the experimental- 

 ly derived relationship in Equation (48). The foraging 

 speed is nearly constant at moderate to high concen- 

 trations, but is reduced at low plankton abundance. 

 The threshold concentration (0.0006 kcal/1) at which 

 the fish stop feeding on Ditylum is also included in 

 this model. The effect of reducing the foraging speed, 

 when plankton concentration is low, is illustrated in 

 Figure 5, which provides a comparison of Model LI 

 with Model I, where s = constant =41.3 cm/s. (This 

 foraging speed was chosen for the Model I example 

 because it provides the best overall fit to Model II, 

 facilitating the comparison between the two. The 



choice of another value for s would cause Model I to 

 depart further from the actual behavior of the fish 

 and would increase the difference between the two 

 models.) 



In Model I, we found that when s and h were con- 

 stant, the curves describing R K ,pR K , T K , E K , and G K 

 as a function of increasing c were all linear or constant 

 (Fig. 1, B1-B4; Fig. 5, A1-A4). In Model II, these curves 

 are nearly linear or constant at moderate to high 

 plankton concentrations, where s ~ constant. How- 

 ever, they become increasingly curvilinear at lower 

 concentrations, when s is changing rapidly (Fig. 5, 

 B 1 -B4). Thus we find that Model II is quite similar to 

 Model I where s = 41.3 cm/s, when the food concen- 

 tration is above c mm in the Model I example (-0.002 1 

 kcal/1 for h = 14 h/d). The models diverge signifi- 

 cantly as c declines below c min . If the Atlantic 

 menhaden were to continue to swim at their 

 "preferred" speed when the plankton concentration 

 is low, a significant deficit in the energy budget would 

 result (Fig. 5, A3). However, Model II shows that by 

 reducing their foraging speed when food concentra- 

 tion is low, the Atlantic menhaden act to regulate 

 their energy expenditure to remain close to their rate 

 of energy uptake (Fig. 5, B3). Reducing the foraging 

 speed has this effect, because of the exponential 

 relationship between respiration and swimming 

 speed. A reduction in foraging speed causes the res- 

 piration term to decline more rapidly than the inges- 

 tion term. The resulting change in the energy balance 

 enables the fish to obtain a maintenance ration in less 

 time, and at a lower concentration of food, than would 

 have been possible had they continued to forage at 

 the higher speed. The growth rate and growth ef- 

 ficiency are thereby enhanced at low concentrations 

 (compare Fig. 5, A4 and B4). This effect can also be 

 seen in Figure 2. 



At the threshold concentration (0.0006 kcal/1) 

 where Atlantic menhaden cease feeding on Ditylum, 

 it can be seen (Fig. 5, Bl and B2) that the routine 

 metabolic costs alone are greater than the energy 

 which could be derived from feeding. The behavior of 

 the fish apparently reflects the fact that it is not 

 bioenergetically profitable to feed at such a low 

 plankton density. 



Nitrogen Budget 



In the nitrogen budget there are three loss terms: 

 The endogenous excretion, which is a constant, and 

 the exogenous excretion and the fecal losses, which 

 are proportional to the nitrogen content of the daily 

 ration. The remaining nitrogen from the ration is 

 retained as growth. Thus we find that the nitrogen 



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