DURBIN and DURBIN: ENERGY AND NITROGEN BUDGETS FOR ATLANTIC MENHADEN 



time (/?). Model I describes the potential interactions 

 among these three variables, and their effects on 

 menhaden energy intake, energy expenditure, 

 growth, and growth efficiency. 



Energy Budget (Model II) 



Model II is a special case of Model I which incor- 

 porates information on the swimming and feeding 

 behavior of the Atlantic menhaden in response to 

 plankton concentration. Laboratory observations 

 have shown that Atlantic menhaden adjust their 

 foraging speed according to the concentration of food 

 in the water. When D. brightwelli was the food, the 

 threshold concentration for the onset of feeding was 

 about 1 jig chlorophyll a/1. Between about 1 and 4 ju.g 

 chlorophyll a/1, the menhaden increased their forag- 

 ing speed roughly in proportion to increasing 

 plankton concentration. Above 4 /xg chlorophyll a/1, 

 however, swimming speed remained nearly constant 

 at about 4 1.3 cm/s(1.6 body lengths/s), independent 

 of further increases in plankton concentration. Thus 

 the relationship between the Atlantic menhaden 

 foraging speed and Ditylum chlorophyll a (a, ju.g/1) 

 was approximately asymptotic, where 



29.62 (a - 1) 

 0.396 + (a - 1) 



+ 12.2 (cm/s) 



(46) 



(Durbin et al. 1981). The equation includes the feed- 

 ing threshold for Ditylum (1 jug chlorophyll a/1) and 

 the routine (nonfeeding) swimming speed of the fish 

 (12.2 cm/s), which represents the lower limit of the 

 foraging speed. 



The chlorophyll a content of D. brightwelli may be 

 converted to kilocalories according to the following 

 relationship: 



1 jug chlorophyll a = 6.06 X 10" 4 kcal . (47) 



Thus Equation (46) becomes 

 48,873 c - 29.62 



s = 



1,650 c - 0.604 



+ 12.2 (cm/s) 



(48) 



where c (kcal/1) is the plankton concentration. 



By substituting Equation (48) fors in Equations (8), 

 (12), (19), (29), (30), and (32) for R K ,pR K , T K ,E K ,G K , 

 and A', K , respectively, we are able to eliminate as 

 a variable and rewrite the menhaden energy budget 

 solely in terms of food concentration (c, kcal/1) and 

 foraging time (h, h/d). This is Model II. 



Nitrogen Budget (Model I) 



The general equation for the nitrogen budget pre- 



sented in Equation (2) may be rewritten: 

 G N = pR N — £ N 



(49) 



where p is the assimilation efficiency for nitrogen = 

 0.9240 (Durbin and Durbin 1981). The nitrogen 

 budget is controlled by the same three variables as 

 the energy budget: The foraging speed (s), the food 

 concentrations (c or n), and the foraging time (h). 



The total dialy ration, R N (mg N/g dry weight per 

 d), equals 



R s = 0.79574 s n h (mg N/g dry weight per d) (50) 



where n is the plankton concentration (mg N/1). 



The assimilated daily nitrogen ration, pR N , 

 equals 



pR N = 0.073526 s n h (mg N/g dry weight 



perd). (51) 



The endogenous, exogenous, and total daily nitro- 

 gen excretion rates, E b _ N , E f _ N , and E N (mg N/g dry 

 weight per d) are presented in Equations (21), (23), 

 and (27), respectively. 



Substituting Equation (27) into Equation (49), we 

 obtain the following expression for the daily growth 

 rate, G N : 



G N = 0.308 R N - 0.237 (mg N/g dry weight 



per d). (52) 



Gross growth efficiency, K lN , equals 

 0.308 i? N - 0.237 



^l.N 



R, 



(mg N/g dry weight 



per d) 



(53) 



where i? N is calculated according to Equation (50). 

 If the ration is converted from units of nitrogen to 

 kilocalories (Equation (25)), then Equations (52) and 

 (53) become 



G N = 5.0016 R K - 0.237 



(mg N/g dry weight per d) 



^l.N — 



5.0016 R k - 0.237 



(54) 

 (55) 



16.239 R K 

 where R K is calculated according to Equation (8). 



Nitrogen Budget (Model II) 



The empirical relationship between foraging speed, 

 s (cm/s), and plankton concentration, a(pig/l) (Equa- 



183 



