FISHERY BULLETIN: VOL. 81, NO. 2 



tration. These results reflect basic differences in the 

 ingestion process between filter- and particulate- 

 feeding planktivores. Since a filter feeder like the 

 Atlantic menhaden removes a constant proportion of 

 the particles in the water per unit of time, without the 

 necessity to capture and handle each item of prey in- 

 dividually, the ingestion rate increases linearly with 

 increasing food concentration and swimming speed. 

 In contrast, with the particulate planktivore, feeding 

 is a series of discrete events and there will be a max- 

 imum ingestion rate set by the time required to cap- 

 ture and handle each prey. Thus, as Ivlev has shown 

 experimentally (Ivlev 1960, 1961), ingestion rate in- 

 creases asymptotically with increasing food concen- 

 tration. This causes an asymptotic growth curve. 

 There does not appear to be any information avail- 

 able to describe the ingestion pattern of a particulate 

 feeder as a function of swimming speed. However, 

 based on Holling's predation model (Holling 1966), 

 an increase in the swimming speed of a particulate 

 planktivore will increase the encounter frequency 

 and hence the feeding rate. Based on this model we 

 could expect that with increasing swimming speed, 

 the ingestion rate will increase asymptotically towards 

 a maximum rate set by the handling time. 



In most laboratory studies of the relation between 

 feeding and growth, the fish are given a fixed ration 

 for a specified period, after which the amount of 

 growth is determined. The food is made readily avail- 

 able to the fish, and hence the time and energy 

 expended for feeding is presumably small. In the 

 majority of these studies, growth was linearly related 

 to ration size, which implies that assimilation efficien- 

 cy and the increment in metabolism and growth per 

 unit of ration remained constant at all ration levels 

 (Pandian 1967; Birkett 1969; Gerking 1971; Jones 

 and Hislop 1972, 1978; Niimi and Beamish 1974; 

 Staples and Nomura 1976; Stirling 1977). Where 

 reported, growth efficiency increased asymptotically 

 with increasing ration size; this is a consequence of 

 the observed linear growth-ration relation. 



In several studies the relationship between growth 

 and meal size appeared to be slightly curvilinear, 

 however, with the growth rate somewhat depressed 

 at high rations (Carline and Hall 1973; Elliott 1975; 

 Wurtsbaugh and Davis 1977). Under these con- 

 ditions, growth efficiency increased curvilinearly 

 from zero at the maintenance ration to a maximum 

 value, and thereafter declined curvilinearly. Warren 

 and Doudoroff (1971) suggested that such a phe- 

 nomenon could be caused either by a reduction in 

 assimilation efficiency at high rations, or by a change 

 in the energy balance within the fish, in which the 

 metabolic component increased (higher SDA, or 



greater spontaneous activity) at the expense of the 

 energy available for growth. Another possible cause 

 of departure from linearity could arise from changes 

 in the wet weight: dry weight ratios (Staples and 

 Nomura 1976). These investigators found that fish at 

 high ration levels increased in percent of dry weight 

 relative to fish on low rations. Thus measurements of 

 growth based on wet weight will overestimate the 

 true growth of fish at low rations, and underestimate 

 growth at high rations, which can lead to an apparent 

 curvilinearity in the growth-ration relationship. 



The growth of sockeye salmon on fixed rations in- 

 creased nearly linearly with increasing ration size, in 

 keeping with results from other similar studies (Brett 

 et al. 1969; Brett and Shelbourn 1975). However the 

 latter investigators found that if they included growth 

 data from fish fed "excess rations," where voluntary 

 food intake continually declined as the fish grew, the 

 overall relationship between growth and increasing 

 ration size was asymptotic, making the growth ef- 

 ficiency curve convex upwards. 



The Model I prediction of a linear relation between 

 ration size and growth in the Atlantic menhaden, 

 when swimming speed is constant (i.e., activity = 

 constant), and the slight departure from linearity by 

 Model II, is therefore supported by most experimen- 

 tal studies of feeding and growth in other fish species. 

 It should be noted that if assimilation efficiency in 

 Atlantic menhaden were to decline at high feeding 

 rates beyond the range of the experimental data, we 

 would expect that growth rate will approach an 

 asymptote, and growth efficiency will decline with 

 further increases in ration size. However since the ex- 

 periments covered the range of plankton concen- 

 trations which the fish might be expected to encounter 

 in nature (Durbin and Durbin 1981), the possible 

 decline in assimilation at very high feeding rates 

 would not appear to be meaningful for Atlantic 

 menhaden under most circumstances in the wild. 



It should also be noted that since the foraging costs 

 of obtaining a ration of a particular size will vary ac- 

 cording to s, c, and h, there will not be a single 

 (unique) relationship between ration size, growth 

 rate, and growth efficiency in Atlantic menhaden. 



The models predict that over most of the range of 

 plankton concentrations where growth is possible, 

 growth efficiency will be higher for calories than for 

 nitrogen. These findings are consistent with field ob- 

 servations that the fat and caloric composition of the 

 menhaden increases relative to protein during its 

 season of growth (Dahlberg 1969; Dubrow et al. 

 1 976) . At low plankton concentrations the fish forage 

 at speeds such that growth in nitrogen is possible 

 even when there is an overall net energy deficit. This 



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