DURBIN and DURBIN: ENERGY AND NITROGEN BUDGETS FOR ATLANTIC MENHADEN 



with the experimental data, the budgets are de- 

 veloped for the case of an adult Atlantic menhaden, 

 26 cm FL (fork length) and weighing 302 g wet and 

 101 g dry, which feeds upon the diatom Ditylum 

 brightwelli. The temperature is 20°C. 



DERIVATION OF ENERGY AND 

 NITROGEN BUDGETS 



Energy Budget (Model I) 



The general equation for the energy budget is pre- 

 sented in Equation (1). 



Energy Intake 



TOTAL DAILY RATION, R K (KCAL/G DRY 

 WEIGHT PER DAY).— The daily ration, R K (kcal/ 

 fish per d) which is obtained by an Atlantic menhaden 

 will be equal to the volume searched (i\ 1/fish per h), 

 times the efficiency (e, dimensionless) with which 

 particles are removed from the volume searched, 

 times the concentration (c, kcal/1) of food particles in 

 the water, times the duration (h, h/d) of the 

 feeding period. 



F 



e = — 

 v 



(5) 



#„ 



v e c 



h (kcal/fish per d). 



(3) 



Volume searched (v).— During feeding, the mouth is 

 held continuously open and the fish swim in school 

 formation, travelling along a straight or curvilinear 

 path without changing course to pursue individual 

 prey. Thus each fish filters the column of water which 

 lies directly ahead. The volume searched is equal for 

 all prey types, and may be adequately described as a 

 cylinder, or, more accurately, an ellipsoid, with a 

 cross-sectional area equal to that of the fish's open 

 mouth and a length equal to the distance covered by 

 the fish per unit time, i.e., the foraging speed (s, cm/ 

 s) . For an Atlantic menhaden averaging 26 cm FL, the 

 gape was approximately elliptical, with major and 

 minor axes of 3.91 and 2.90 cm, respectively; the to- 

 tal cross-sectional area of the mouth was therefore 

 8.93 cm 2 (Durbin and Durbin 1975). Thus 



v= 32.148 s (1/fish per h). 



(4) 



In feeding experiments (Durbin and Durbin 1975) 

 the mean value of F for Ditylum brightwelli was 5.8 1/ 

 fish per min, while v was estimated to be 23.3 1/fish 

 per min. This gives a value of e = 0.25 for D. 



brightwelli. 



Filtration efficiencies for different-sized particles 

 may be calculated from an equation describing the 

 relationship between filtration efficiency and food 

 particle length (Durbin and Durbin 1975): 



F = 8.290 \og l0 L - 9.733 (1/fish per min). (6) 



In the experiments the fish were unable to filter par- 

 ticles smaller than about 13 /on. 



Incorporating the appropriate values for u and e into 

 Equation (3), the ingested ration, R K , for D. 

 brightwelli would be given by 



Filtration efficiency (e).— Filtration efficiency is the 

 efficiency with which the Atlantic menhaden filters 

 particles of a given size from the water and is equal to 

 the observed removal rate or volume swept clear, F 

 (1/fish per min) , divided by the total volume searched, 

 v (1/fish per min), i.e., 



p = 8.037 sc h (kcal/fish per d). 



(7) 



In the model the Atlantic menhaden weighed 302 g 

 wet = 101 g dry (Durbin and Durbin 1981). Thus 



r k = 0.079574 sch (kcal/g dry weight per d). (8) 



ASSIMILATED RATION, P R K (KCAL/G DRY 

 WEIGHT PER DAY).— If the fecal losses, F K , are 

 subtracted from the ingested ration, R K , a measure of 

 the assimilated ration is obtained. The assimilated 

 ration can also be determined by multiplying R K by 

 the assimilation efficiency, p, i.e.,pR K , where 







R K ' 



(9) 



In our experiments with the Atlantic menhaden, we 

 observed slight changes in the overall assimilation 

 efficiency of a meal, depending on meal size (Durbin 

 and Durbin 1981). However, because the observed 

 differences in overall assimilation efficiency were 

 small and because of the uncertainty about the 

 significance of these differences, we assumed a con- 

 stant assimilation efficiency for the model and took 

 the means of the experimentally determined values. 

 For Atlantic menhaden feeding onD. brightwelli, the 

 mean assimilation efficiency, p, equalled 0.8636 for 

 carbon, 0.9240 for nitrogen, and 0.8954 for calories 

 (Durbin and Durbin 1981). 



Substituting Equation (9) into Equation (1) we may 

 rewrite the general equation for the energy budget: 



G K = pR K -T K -E 1 



(10) 

 179 



