SWIMMING ENERGETICS OF THE LARVAL ANCHOVY, ENGRAULIS MORDAX

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 ti me 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 103 cal/h using known excursion rates. 0, consumption measurement of similar size larvae indicate a 2.19 x lo-'callh 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 l-cm 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 dian 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,