FISHERY BULLETIN: VOL. 81, NO. 2 



changes less rapidly at moderate-high plankton 

 abundance, and in fact the constant preferred speed 

 of the Atlantic menhaden (41.3 cm/s) is sufficiently 

 close to s G 0PT that growth remains nearly maximal 

 over a very broad range of plankton abundance. Thus 

 there is no great "penalty" if the fish swim at constant 

 speed rather than exactly at s G 0PT within this region 

 of the curve. The choice of this preferred speed is 

 fairly exacting, however. As can be seen in Figure 11, 

 at speeds not greatly different from 41 cm/s (30 and 

 50 cm/s), growth will be suboptimal over much of the 

 plankton concentration range. 



How much of a sacrifice in growth efficiency is im- 

 plied if the fish swim at s COPT ? Figure 12 indicates 

 that K x K , though suboptimal, is still reasonably 

 high when the fish swim ats G 0PT . However, as the for- 

 aging speed increases above s G0PT , there is an in- 

 creasingly rapid decline in K 1 K , as can be seen in 

 Figure 12 where s = constant = 50 cm/s. 



In conclusion, the present results, which demon- 

 strate a very close agreement between the predicted 

 relationship between s G 0PT and food concentration, 

 and the observed relationship between foraging 

 speed and c, indicate that the foraging speeds of the 

 adult Atlantic menhaden have evolved over time 

 towards maximizing growth rate. This optimization 

 of growth rate has necessarily resulted in a submax- 

 imal growth efficiency. In his analysis of data for the 

 bleak, Ware (1975) showed that the observed forag- 

 ing speed when c ~ 0.000808 kcal/1 was also quite 

 close to the value of s G 0PT predicted from his model. 

 However, there was insufficient information in 

 Ivlev's (1960) original study to indicate whether the 

 bleak adjusts its foraging speed to remain near s G 0PT 

 at different plankton concentrations. Studies 



y 05 



o 



U. 04 

 UJ 



X 0.3 



I- 

 3 

 o 



<£ 02 

 e> 



</> 



in o i 

 o 

 cr 



4 8 12 16 20 24 



FORAGING TIME (h, hours/day) 



FIGURE 12. — A comparison of the gross growth efficiency of the 

 Atlantic menhaden as a function of foraging time, when the fish swim 

 according to s K qpt ; their actual voluntary speeds; and constant 

 speeds of 30 and 50 cm/s. Plankton concentration is 0.0030 

 kcal/1. 



demonstrating selective feeding in planktivores (e.g., 

 Brooks 1968; Leong and O'Connell 1969; O'Connell 

 1972; Werner 1974; Werner and Hall 1974; O'Brien 

 et al. 1976; Eggers 1977; Confer et al. 1978) indicate 

 that foraging strategies, which result in the max- 

 imization of energy intake, may be a more general 

 phenomenon among these fishes. However, it should 

 be pointed out that these feeding studies only con- 

 sider energy intake and not energy expenditures, so 

 that the extent to which these fishes are following op- 

 timal strategies for growth or growth efficiency can- 

 not really be determined. 



Extension of the Model to 

 Particles of Different Size 



Observations using several phytoplankton species 

 as food (Durbin and Durbin 1975) indicated that the 

 preferred (concentration independent) foraging 

 speeds were similar for these species. However these 

 estimates of swimming speed, made with a stop- 

 watch, were not sufficiently accurate to distinguish 

 the small changes in foraging speed that have been 

 found to be significant in the energy budget. Thus it 

 would be desirable to verify this observation using a 

 more precise method, such as video or cinema- 

 tography, to determine the swimming speeds. 



In the same study it was, however, clear that the 

 threshold concentration for the onset of feeding (c ( ) 

 and the concentration at which foraging speed 

 became approximately independent of food concen- 

 tration (c,) were quite different for plankton particles 

 of different size. The inverse nature of this relation- 

 ship is consistent with the fact that when an Atlantic 

 menhaden forages at a given speed, its energy expen- 

 diture is the same for all food types, yet its energy in- 

 take declines with decreasing food particle size 

 because of the declining efficiency of the gill rakers. 

 This means that a higher concentration of small par- 

 ticles is needed in order for a fish to satisfy its 

 minimum energy requirement, and thus we would ex- 

 pect an increase in c t and c, as particle size declines. 



The constants in the equations presented here have 

 been specified for Ditylum brightwelli, which is about 

 80 jiim long. A change in particle size will change the 

 filtration efficiency (e), which will necessitate recal- 

 culation of some of the constants in the equations for 

 R,E,G, s G0VT , and s K 0PT . This is a simple matter ex- 

 cept for the last two quantities, and for these we have 

 presented the steps in the integration of the equa- 

 tions in sufficient detail (Equations (33) to (45)) to 

 permit recomputation for different particle sizes. 



It is of particular interest to consider how s G0PT 

 changes with a change in food particle size. It has 



196 



