564 



Fishery Bulletin 89(4). 1991 



were similar to the estimate of Q M in the present 



study. 



Swimming metabolism Standard metabolism (Q„ = 

 12.1 cal • g' 1 -day -1 ) subtracted from the Q M esti- 

 mates for fish at the two speeds left 3.7 and 13.3 

 cal • g" ' • day " : , respectively, for the metabolic cost of 

 swimming (Q v ) for 12 hours a day at 8.7 and 21.1 

 cm/s. On an hourly basis, Q v amounted to 0.308 and 

 1.11 cal-g _1 -h _1 , respectively. A linear fit to log- 

 transformed estimates of Qv versus log-transformed 

 V indicated that 



Qv = (0.0137 V 144 )cal-g" 1 h- 



(10) 



For extrapolating beyond the range of measurements, 

 a power function makes a good model for swimming 

 metabolism, because mechanical principles and em- 

 pirical evidence (Ware 1978, Wu and Yates 1978) in- 

 dicate that thrust and drag in swimming fish are power 

 functions of speed. 



Effect of fish size Fish size was not manipulated in 

 the present study, so size effects could not be quan- 

 tified from the results. However, reviews (Winberg 

 1956, Brett and Groves 1979) of results from a large 

 number of studies have led to the generalization that 

 the mass exponent of standard metabolism in fishes is 

 close to 0.8. The corresponding mass-specific exponent 

 (-0.2) combined with the estimate of Qo from the 

 present study results in this model, 



Q„ = 18.8 M-" 2 cal -g" 1 day 1 



= 0.783 M~ - 2 cal-g^-h" 1 , (11) 



where M is anchovy wet mass (~9g in the present 

 study). 



The effect of fish size on the cost of swimming can 

 be modeled by expressing speed relative to length so 

 that the cost of swimming at the normalized speed is 

 the same for any size of fish. The cost of swimming in 

 sockeye salmon Oncorhynchus nerka, obtained by sub- 

 tracting standard metabolism from total metabolism 

 of 8-54 cm salmon swimming at speeds of 13-143 cm/s 

 (Brett 1965), can be accurately described by a power 

 function of the Reynolds number (Wu and Yates 1978). 

 The Reynolds number combines fish length, speed, and 

 kinematic viscosity. A similar way of expressing this 

 relationship, which matches Brett's (1965) results (at 

 15°C) extremely closely, is 



Qv = 8.7934 



V 



L 0.64 



1.71 



mg (V'kg- 1 -h" 



(12) 



Thus, for different sizes of sockeye salmon, the cost 

 of swimming is the same when speed (V) divided by fish 

 length (L in cm) to the 0.64 power is the same. This 

 relationship is also reflected in length exponents 

 (0.5-0.7) for endurance speed in fishes (Bainbridge 

 1962, Hunter 1971). Note that dividing V by L (body 

 lengths/second) does not normalize speed with respect 

 to swimming cost or endurance. For anchovy, the 

 present study assumed that the length exponent for 

 normalized speed was 0.6. Then, from Equation (10) 



Qv = 0.095 



L 0.6 



1.44 



cal • g~ !  hr 



(13) 



and the cost of swimming in anchovy can be estimated 

 for any size and swimming speed. 



Effect of temperature Anchovy metabolic rates 

 were estimated at only one temperature (17 °C) in the 

 present study, but the effect of temperature on en- 

 graulid anchovy metabolism was estimated for Peru- 

 vian anchoveta (Villavicencio 1981) at 14-20°C. These 

 data indicated an increase of 78% in total respiration 

 rate over a change of 6°C. Applying this intensity of 

 temperature effect to the model would amount to 



Q' = 2.046 Q e 



0.0959 T 



(in any units), 



(14) 



where Q is the metabolic rate (in any units) at 17°C, 

 and T is the ambient temperature (°C). However, short- 

 term temperature acclimation periods in the laboratory 

 (Villavicencio 1981) may result in greater metabolic 

 rate changes than in the long term in nature. Estimates 

 from Equation (14) should be viewed skeptically, until 

 better estimates of the effect of temperature on an- 

 chovy metabolism can be found. 



Evaluation of the model 



Estimates of maintenance metabolism (Qm = Qo + Qv) 

 from the model (Equations 11 and 13) for 4, 10, and 

 25 g northern anchovy at 17°C were compared with 

 other data on erigraulids (Fig. 5), assuming an oxy- 

 calorific equivalent of 3.24 cal/mg 2 (Elliott and 

 Davison 1975). Oxygen consumption of northern an- 

 chovy swimming at about 9 cm/s in an annular respir- 

 ometer was 0.38 mg 2 • g~ '  h - ' (Kaupp et al. unpubl. 

 data). The rate of energy loss in fasting northern an- 

 chovy swimming in a flume at about 9 cm/s was 29.3 

 cal • g" 1 • day -1 or 0.34 mg 2 • g" 1 • h ~ ] (Kaupp et al. 

 unpubl. data, energy loss multiplied by 0.9, the metab- 

 olizable fraction). These data were about twice as high 

 as the tunnel respirometry data on anchoveta (Villa- 

 vicencio 1981) swimming at 9cm/s (Fig. 5). The model 



