SWIMMING ENERGETICS OF THE LARVAL ANCHOVY, 



ENGRAULIS MORDAX 



William J. Vlymen in* 



ABSTRACT 



A modification of Gray and Hancock's theoretical method for studying propulsion of spermatozoa was 

 used to estimate the energy expenditure of swimming anchovy, Engraulis mordax, larvae. Wave 

 parameters obtained from photographs of feeding anchovy larvae were incorporated into a time 

 dependent sinusoidal body displacement function which is used in the iterated energy integrals of the 

 model. The integrals were numerically evaluated by 2-dimensional 16-point Gaussian-Legendre 

 quadrature. The results for the mean larval length of 1.4 cm was 144.8 ergs/swimming excursion or 

 4.91 X lO'^^cal/Ti using known excursion rates. O2 consumption measurement of similar size larvae 

 indicate a 2.19 x IQ-^cal/h requirement. Extension to other larval sizes can be made using this model 

 with certain qualifications. The relationships of swimming energetics to larval fish behavior are 

 discussed. Current theories of large amplitude intermittent swimming are also discussed in light of 

 the high swimming efficiencies encountered in this study. 



The theoretical evaluation of swimming fish 

 energetics by hydrodynamic analysis has been an 

 extensively treated subject in recent years. Most 

 of these treatments however have concentrated 

 on calculation of thrust and thrust efficiencies 

 with the exception of Lighthill (1970, 1971) who 

 gave direct estimates for the mean swimming 

 work rate and has drawn attention to the impor- 

 tance of the accelerative, virtual mass contribu- 

 tions in estimates of mean swimming work rate. 

 Most expositions, however, deal with situations 

 where inertial effects predominate with all sub- 

 sequent derivations being consistent with that 

 assumption (Taylor, 1952a). The low Reynolds 

 number range of swimming energetics primarily 

 of spermatozoa, has also been extensively treated 

 (Taylor, 1951, 1952b; Gray and Hancock, 1955; 

 Carlson, 1959; Holwill and Miles, 1971). All these 

 treatments disregard inertial and accelerative ef- 

 fects in comparison with viscous effects in their 

 treatment. Also, both viscous and inertial treat- 

 ments calculate or estimate the mean swimming 

 work rate after steady motion has been estab- 

 lished. 



The problem attacked in this paper is a syn- 

 thesis and extension of the two classes of treat- 

 ments discussed above, specifically to determine 

 the energy expended per excursion by the 1-cm 



'Southwest Fisheries Center, National Marine Fisheries Ser- 

 vice, NOAA, P.O. BOX 271, La Jolla, CA 92037 and Scripps 

 Institution of Oceanography, University of California, San 

 Diego, La Jolla, CA 92037. 



larval anchovy, Engraulis mordax. The term ex- 

 cursion as used here requires some elaboration. 

 Larval anchovies have a peculiar swimming be- 

 havior because they do not continuously propa- 

 gate caudally directed waves. In the adult form 

 this behavior is noticeable by observing the tail, 

 i.e., it does not beat continuously even though the 

 fish appears to maintain constant forward mo- 

 tion. In the larval stages, however, this behavior 

 results in an obvious discontinuous motion. The 

 result is a series of bursts of motion from rest to 

 rest which hereafter I refer to as excursions. 



The estimation of excursion energetics by a 

 theoretical model rather than indirect metabolic 

 estimators during excursions is demanded be- 

 cause of the small size of the organisms consid- 

 ered, their discontinuous motion, and the inves- 

 tigator's inability to determine which fraction of 

 the total energy consumption is due to swimming 

 alone. 



The parameters used in the model to calculate 

 the excursion energy are taken from photographs 

 of a larval anchovy of a specified size executing 

 excursions in search of prey organisms. Since the 

 search for prey constitutes a large proportion of 

 the larva's activity, following Kerr ( 1971) we can 

 write the total metabolism of the larva as, 



where T j = total metabolism 



= cost of search for prey 



Manuscript accepted January 1974. 

 FISHERY BULLETIN: VOL. 72, NO. 4, 1974. 



885- 



