VLYMEN: SWIMMING ENERGETICS OF THE LARVAL ANCHOVY 



only such wave parameter available for 

 modification and incorporation into the energy 

 formulation is the wave amplitude. 



Hunter (1972) measured the relationship be- 

 tween tail-beat amplitude and larval length for 

 intermittent swimming and found the relation- 

 ship, 



A = 0.112 + 0.170L 



where L and A are in centimeters. Since minimal 

 amplitude dependence on length exists because of 

 the exaggerated whiplike motion of the tail, 

 Hunter's amplitude value is greater than my 

 value for the maximum wave amplitude of 1.4-cm 

 larvae. This is because amplitudes used in this 

 study are measured as the wave crest progresses 

 caudally at each successive time unit, whereas at 

 the tail, wave progression ceases along the body 

 and may even become retrograde due to the whip- 

 like motion. The important point is the intercept 

 at zero length where both measurements must be 

 consistent, i.e., equal. Thus, admitting equality of 

 the interception point at L = and adjusting the 

 first order coefficient in Hunter's equation to yield 

 the correct value for maximum amplitudes at L = 

 1.4 cm we get, 



An,ax= 0.112 + 0.094 L 



This value was substituted for A^^^ = 0.026 L 

 in the amplitude function A(t) = 0.206 L exp 

 [-0.044 (t -7.19)^] and its first two derivatives 

 used in the L = 1.4 cm formulation. The work 

 integrals were then recomputed at the three 

 new points L = 0.4 cm, L = 0.7 cm, and L = 

 2.0 cm. Because the A, nax values coincided at L 

 = 1.4 for both treatments this value was not 

 used again in the integration procedure. The 

 values obtained are shown in Table 2. Least 

 squares regression of the data assuming the 

 functional form E = aL^ where E is 



Table 2.— Excursion energies for five larval anchovy lengths 

 using Hunter's modified intercept amplitude function (see text 

 for complete discussion) for extension to larval lengths other 

 than 1.4 cm. 



Length 

 (cm) 



Energy/ 



excursion 



(ergs) 



2.0 



1.4 



1.0 



0.70 



0.40 



881,4 



144.8 



16.3 



3.6 



0.76 



energy/excursion in ergs and L length in cen- 

 timeters yielded E = 21 .b L ^ *^ The 

 energy/excursion calculated for the four addi- 

 tional lengths was then converted to hourly 

 energy rates using the excursion frequencies 

 cited earlier. The results obtained were plotted 

 with scales of calories per hour vs. length in 

 centimeters. For comparison, another curve of 



the form 4Q2_= f[L) was computed and plotted 



dt 

 along with the curve formed using the addi- 

 tional model points above (Figure 9). The line 

 shown connecting these points is fitted by eye. 

 The comparison curve was based on the respira- 

 tion value of 0.0218 cal/mg dry wt/h and the 

 following relationship between dry weight in 

 milligrams and length in millimeters, log W = 

 3.3237 log L - 3.8205 (Lasker et al., 1971). 

 This comparison curve is isomorphic to the 

 length-weight curve with no allowance being 

 made for specific respiration changes with in- 

 creasing weight. Therefore the curve is to be 

 regarded as the best approximation to the total 

 O2 consumption rate for swimming larval an- 

 chovies. It provides only a means of judging the 

 physiological reliability of the energy summa- 

 tion method employed here. However, because 

 the changes in specific respiration as a function 

 of weight would not change this comparison 

 curve appreciably, it can probably be regarded 

 as sufficiently reliable. With this understanding 

 some comparison of these curves can be made. 



From laboratory observation of larvae it 

 seems apparent that nondimensional amplitude 

 and wavelength do not remain constant but de- 

 crease in absolute value as length is increased. 

 That is, functions descriptive of these non- 

 dimensional parameters do not remain descrip- 

 tive of animals of all lengths. That is exactly 

 what is observed as we deviate from the origi- 

 nal L = 1.4 cm point where the nondimensional 

 wave parameters are fitted. Even with 

 modification of A max used to compute the origi- 

 nal curve this effect is still observable. Part of 

 the deviation is, however, due to the behavior of 

 the larvae as age increases. Very small larvae 

 float 907f of the time with occasional bursts of 

 intensive activity (Hunter, 1972) which, as I 

 pointed out earlier, is quite inefficient. As the 

 larvae get older, however, intermittent, more 

 efficient swimming becomes the dominant mode 

 of locomotion. This trend is partially reflected 

 in these two curves. As the larvae get older and 



897 



