LAURENCE: BIOENERGETIC MODEL FOR WINTER FLOUNDER LARVAE 



ing rest is represented by the standard metabolic 

 rate (Q s ) and active metabolism by the active rate 

 (Q). Thus, if it is assumed that a fish actively feeds 

 for a given number (a) of hours, the total daily 

 expenditure of energy for metabolism can be de- 

 fined as: 



Q_ =a(Q -Q s ) + 24Q S . (5) 



The basic Equation (4) can then be rewritten as: 



0.7Q + = Q' + a(Q - Q s ) + 24Q s . (6) 



Also, the energy of food consumed (Q + ) can be 

 equal to the sum of the hourly rations, r (see Prey 

 Density and Intensity of Feeding), or Q + = ar, and 

 thus: 



Q + = aR(l - e~ aP ). 



(7) 



Solving Equations (6) and (7) simultaneously by 

 equating the Q: 



Q' + a(Q - Q s ) + 24Q, 

 0.7 



is obtained. Thus: 



aR(l - e~ aP ) (8) 



a 



Q' + 24Q S 



0.7i?(l - e~« p ) - (Q -Q s 



(9) 



Deriving the value of a, a number of different 

 parameters can be computed. They are: 1) critical 

 plankton density below which growth, metab- 

 olism and subsequent survival would be adversely 

 affected, 2) food intake, 3) energy expenditure, 

 4) nonassimilated energy, 5) growth efficiency, 

 6) percent body weight eaten, and 7) the number 

 of a given plankton species and life stages eaten 

 per day. The following is a step by step explana- 

 tion of the modifications used to compute these 

 parameters at 8°C for larval dry weight from 10 

 to 1,000 ixg (corresponding to the time period 

 hatching to metamorphosis), for plankton concen- 

 trations from 0.5 to 21.7 cal/liter (approximately 

 0.1-3.0 nauplii/ml), and for growth, metabolic 

 and digestion rates observed in laboratory exper- 

 iments at 8°C. 



1. Stomach contents weight in micrograms of 

 planktonic prey eaten by a given size larva was 

 computed from the regression equation presented 

 in Figure 1. 



2. The stomach contents weight per hour, or 

 weight of food consumed per hour, was calculated 

 from a modification of Bajkov's (1936) digestion 

 equation. The modified equation is: 



ST 

 H 



(10) 



where F = weight of food consumed per hour 



S = average weight of food in the stomach 



at the time of sacrifice 

 T = feeding time in hours 

 H = number of hours necessary for food to 

 be evacuated from the stomach at a 

 given temperature = 6.6 h at 8°C for 

 actively feeding winter flounder 

 larvae. 



Unpublished experiments indicated that winter 

 flounder larvae fed only in daylight hours. There- 

 fore, it was assumed that T was equal to 12.0 h 

 in these experiments, or the approximate number 

 of mean daylight hours in the period mid-Feb- 

 ruary to mid-April, when winter flounder spawn. 

 Also, F was considered to represent the maximum 

 ration of a larva, or R (Prey Density and Intensity 

 of Feeding section, Equations (7)-(9)). 



3. R was converted to a caloric value by multi- 

 plying by 0.0052519 cal, or the average caloric 

 value/microgram of the copepod species inhabit- 

 ing Narragansett Bay and serving as potential 

 prey for winter flounder (Laurence 1976). 



4. The coefficient of proportionality (a) in Equa- 

 tion (9) was found to change linearly in a negative 

 manner with increasing larval size (see Prey Den- 

 sity and Intensity of Feeding) and was correspond- 

 ingly adjusted. 



5. The growth increment, Q', was computed by 

 multiplying the weight of a larva by the specific 

 growth rate at 8°C for the specified plankton den- 

 sity (see Effects of Prey Density on Growth and 

 Survival). This was converted to calories by mul- 

 tiplying by 0.0050026, or the caloric value for 

 winter flounder tissue as determined in labora- 

 tory combustion experiments with a bomb calo- 

 rimeter. 



6. Metabolism for a larva of given weight was 

 calculated from the regression equations for 

 oxygen consumption and weight (Laurence 1975; 

 Figure 5) and converted to calories by multiplying 

 by 0.005 which represents the caloric equivalent 

 of 1 ix\ of oxygen for the full range of respiratory 

 quotients associated with the utilization of fats, 



535 



