DURBIN and DURBIN: ASSIMILATION EFFICIENCY OF ATLANTIC MENHADEN 



With the Atlantic menhaden the exponential 

 model seems appropriate since fecal elimination 

 rates showed an exponential decline after the fish 

 stopped feeding. This exponential fecal elimina- 

 tion rate (/?'), determined from the decrease in 

 fecal silicon elimination rate with time, is dif- 

 ferent from the exponential rate of gastric 

 (stomach) evacuation (i?), which is the factor mea- 

 sured in most studies. However, if the time re- 

 quired for food to travel the length of the intestine 

 is constant, then the estimate of/? ' based on mea- 

 surements of fecal elimination will be the same as 

 R determined directly from measurements of the 

 decline in stomach contents with time. In order to 

 more fully investigate this, and to understand the 

 patterns of change in feces elimination by Atlantic 

 menhaden, especially during feeding, we have fit 

 the data to a modified version of a model proposed 

 by Elliott and Persson (1978). This theoretical 

 model was then compared with our observed 

 elimination rate data. A good agreement between 

 the two would indicate that stomach evacuation is 

 exponential, that R ' is a good estimator of/?, and 

 that stomach evacuation is the principal factor 

 governing the fecal elimination rate. Such an 

 analysis may also serve to indicate whether sys- 

 tematic deviations between predicted and ob- 

 served data occur as ration size changes. 



The model of Elliott and Persson (1978) assumes 

 that the fish feed at a constant rate, and that the 

 gastric evacuation rate R is exponential. Thus the 

 rate of change in stomach content (S) is given by: 



the onset of feeding, whereas St is the instantane- 

 ous amount present in the stomach at time t. For 

 the present analysis we assumed that R ' = /?, and 

 substituted R ' into Equation (13). From values of 

 R ', F , and Ct for each experiment we then calcu- 

 lated St and SEt for hourly intervals during and 

 after feeding. All calculations were in terms of 

 silicon, since this was not digested by the fish. 



Curves illustrating Ci, St, and SE/ for the 12 

 fish are shown in Figure 13 for Experiment 7. The 

 value of /? ' was 0.406/h and F was 0.241 mg Si/g 

 dry weight per h. Since the ingestion rate was 

 constant, Ct increased linearly with time. The 

 amount of Si present in the stomach (St) increased 

 curvilinearly during the feeding period, then de- 

 clined exponentially after feeding stopped. The 

 cumulative Si evacuated iSEt) increased sigmoi- 

 dally, with the inflection point at the time the fish 

 stopped feeding. While most of the Si had been 

 evacuated from the stomach within 5 h after the 

 end of feeding, small amounts continued to be 

 evacuated for many hours as the evacuation rates 

 declined exponentially to very low levels. 



(dSldt) = F-RS. 



(12) 



The actual amount of food iSt, milligrams/gram 

 dry weight) present in the stomach after t hours is 

 given by: 



F 

 Soe-^«'+— (1 

 R 



Rt 



(13) 



where So is the initial amount of food in the 

 stomach and F is the amount of food consumed per 

 hour. AsF -*0,St^ Soe'^'. The amount of food 

 (SEt, milligrams/gram dry weight) which has 

 been evacuated from the stomach by time t is 

 simply: 



SE, = Cf 



(14) 



where Ct is the total amount of food (milligrams/ 

 gram dry weight) consumed in t hours. Thus SEt 

 and Ct are cumulative quantities measured since 



Figure L3. — Experiment 7. Cumulative ingestion of silicon (CtL 

 and model calculations of the instantaneous amounts of silicon 

 present in the stomach (St) and the cumulative amounts of sili- 

 con which have been evacuated from the stomach (SEt) during 

 and after a 7-h feeding period. 



The time lag between the ingestion of a particle 

 and its elimination in the feces is the digestive 

 tract residence time for that particle. Similarly 

 the stomach residence time is the time lag be- 

 tween the ingestion and the gastric evacuation of a 

 particle. The total digestive tract residence time 

 was determined by subtracting the time required 

 for the fish to ingest a given amount of Si, from the 

 observed time when that same amount of Si was 

 eliminated in the feces. The gastric residence time 

 was similarly calculated from the observed feed- 

 ing rate and the predicted values of SEt. In each 

 experiment the calculated gastric residence time 

 followed a pattern similar to the digestive tract 

 residence time (Figure 14). The two curves were 



611 



