CLARKE: DIEL FEEDING PATTERNS OF MESOPELAGIC FISHES 



where S is stomach fullness as percentage of fish 

 weight; So and S,, the values at the beginning and 

 end of a period oft hours; and/?, the instantaneous 

 evacuation rate in per hour. 



For most of the species considered here, there is 

 no extended period of decline in stomach fullness 

 where the above assumptions are met, but a rough 

 estimate of /? is possible for//, prox^'mum and three 

 species of stomiatoids. Hygophum proximum ap- 

 parently ceases feeding early in the night, and 

 stomach fullness declines from N2 to SR under 

 essentially constant conditions, i.e., the fish re- 

 main in the upper layers. Stomach fullness de- 

 clines from SS to SR in Vinciguerria nimbaria, 

 Valenciennelliis tripunctulatus, and Danaphos 

 oculatus, and except for relatively brief periods of 

 migration in the first two species, they remain at 

 the same temperature, etc., for this period. 



The values of ^ for these four species were calcu- 

 lated by simply using the integral form of Equa- 

 tion (1) and the median values of S for the begin- 

 ning and end of the periods mentioned above 

 (Table 4). (Other fitting procedures, such as least 

 square methods, require that a number of ques- 

 tionable statistical assumptions be made.) The 

 values of k are inversely correlated with night 

 depth and thus positively with temperature being 

 lowest for D. oculatus, highest for Vinciguerria 

 nimbaria and H. proximum, and intermediate for 

 Valencienellus tripunctulatus. 



For each of the four species, prey concentration 

 and temperature, pressure, etc., were essentially 

 constant throughout the period when feeding oc- 

 curred (SS to N2 for H. proximum and SR to SS for 

 the stomiatoids). It is not unreasonable to assume, 

 as a first approximation, that feeding rate was 

 constant during the periods of increasing stomach 

 fullness. Changes in fullness would then be de- 

 scribed by: 



dS/dt ^ F - k'S 



(2) 



where /j ' is the instantaneous evacuation rate dur- 

 ing the period of feeding, andF is the feeding rate 

 in percentage bodily weight per hour. Integrating 

 and rearranging gives an equation forF in terms 

 of ^', the duration of the feeding period /' in 

 hours, and median fullness at the beginning (Sq ' ) 

 and end (S, ') of the feeding period: 



F = 



k' (S/ X S„'e-''-' 



1 



-*'t' 



(3) 



(In some cases, there were a few relatively high 

 values of stomach fullness among the data for a 

 given period; consequently, the feeding rate of 

 some individuals may have been lowered due to 

 satiation. Such values had little effect on the me- 

 dian, and thus the assumption of constant feeding 

 rate is probably not seriously violated as long as 

 medians are used in the calculations.) 



Estimates of feeding rate and daily ration ( = 

 Ft') were calculated (Table 4) using median values 

 of stomach fullness at SR and SS as So' and S,', 

 respectively, for the stomiatoids and, similarly, SS 

 and N2 for H. proximum. Since both D. oculatus 

 and H. proximum feed at the same temperatures 

 as those under which the instantaneous evacua- 

 tion rates were estimated above, /? ' in Equation (3) 

 was assumed equal to/? calculated from Equation 

 ( 1 ). The daytime or "feeding" temperatures of Vin- 

 ciguerria nimbaria and Valenciennellus tripunc- 

 tulatus are lower than those under which k was 

 estimated from Equation (1). During the day both 

 species occur at nearly the same temperature as 

 does D. oculatus both day and night. Con- 

 sequently, for each of the two migrating 

 stomiatoids, two values of feeding rate and daily 

 ration are given in Table 4 — one calculated using 



Table 4. — Estimates of instantaneous stomach evacuation rates, feeding rates, and daily rations for four species of mesopelagic fishes 

 based on changes in median stomach fullness over the dial cycle. The first three columns give the sampling periods (Table 1 ) between 

 which feeding rate was assumed to be zero, the duration of this interval it), and the calculated instantaneous stomach evacuation rate 

 ik). The last five columns give the sampling periods between which feeding rate was assumed constant and positive, the duration of this 

 interval (f), the instantaneous stomach evacuation rate assumed for the feeding periods (k '), and calculated feeding rate (F in % of 

 bodily weight per hour) and daily ration (/? = Ft' in '7c of bodily weight per day). For both Valenciennellus tripunctulatus and 

 Vinciguerria nimbaria, two values of /e ', F, and R are given: the higher values under the assumption of constant stomach evacuation 

 rate night and day ik' = k), the lower under the assumption that stomach evacuation rate during the feeding period was lower and equal 

 to that estimated for the nonmigrating, deep-living, Danaphos oculatus. See text for formulae and further explanation. 



Species 



Nonfeeding period 



t (h) 



k (h-') 



Feeding period 



r (h) 



k' (h- 



F(%h) 



,;d) 



511 



