FISHERY BULLETIN: VOL. 81, NO. 3 



jective of defining the spawning areas of the Euro- 

 pean eel (Tesch et al. 1979; Schoth and Tesch 1981) 

 and the American eel (McCleave and Kleckner 3 ). 

 Kleckner and McCleave 4 have obtained evidence 

 that recently hatched American eel leptocephali are 

 associated with a thermal front in the Sargasso Sea. 



Also, little is known regarding the time course of the 

 leptocephalus drift migration. Following Schmidt's 

 (1925) summary, several authors have compiled in- 

 formation on the spatiotemporal distribution of 

 anguillid leptocephali, including Smith (1968), 

 Vladykov and March (1975), Tesch (1980), and 

 Kleckner and McCleave (1980). These studies only 

 provide a broad outline of the course of the lep- 

 tocephalus drift migration, as the number of iden- 

 tified leptocephali collected is still small, considering 

 the scale of the migration in terms of distance and 

 probable numbers. The available data are difficult to 

 interpret and may better represent the distribution 

 of sampling effort than the distribution of lep- 

 tocephali (Kleckner and McCleave 1980). Unless 

 sampling at a particular location was done sys- 

 tematically, the absence of leptocephali from collec- 

 tions can only be interpreted as negative evidence 

 concerning the presence of leptocephali at that loca- 

 tion. It is still not known how leptocephali are trans- 

 ported in the Florida Current-Gulf Stream system. 

 How do American eel leptocephali cross the Gulf 

 Stream to approach the North American coast, and 

 why are substantial numbers of these leptocephali 

 not transported across the Atlantic to populate Eu- 

 rope? Are any behavioral components necessary in 

 the leptocephalus drift migration? In summary, 

 where and when are leptocephali most likely to be 

 found, and what implications does this distribution 

 have for the eel's life history and migration 

 patterns? 



To answer some of these questions a simulation 

 model of leptocephali drift in the North Atlantic sur- 

 face currents was developed. The intent was to im- 

 plement the simulation so that leptocephali started 

 at points in the presumed Sargasso Sea spawning 

 area would be transported in a way realistically ap- 

 proximating actual surface current transport. The 

 objectives of the research were to generate patterns 

 of distribution representing the likely time course of 

 a passive drift migration and to compare and inter- 



'J. D. McCleave, Professor of Zoology, and R. C. Kleckner, 

 Research Associate in Zoology, Department of Zoology, Murray 

 Hall, University of Maine at Orono, Orono, ME 04469, pers. com- 

 mun. July 1981. 



4 R. C. Kleckner, Research Associate in Zoology, and J. D. 

 McCleave, Professor of Zoology, Department of Zoology, Murray 

 Hall, University of Maine at Orono, Orono, ME 04469, pers. com- 

 mun. July 1981. 



pret these distributional patterns with information 

 about the actual leptocephalus distribution and the 

 eel's life history. In this way the model serves an ex- 

 planatory role, highlighting the factors important in 

 generating a distribution of leptocephali, and also 

 provides a framework for future research on the lep- 

 tocephalus drift migration. Distributional patterns 

 that developed during some of the simulations are 

 presented here, with emphasis on the American eel; 

 limited results for the European eel are also given. 



MATERIALS AND METHODS 



Anguilla leptocephali are found in the top few hun- 

 dred meters of the water column (Kleckner and 

 McCleave 1980; Schoth and Tesch 1981), and 

 therefore the model was developed with only two 

 horizontal spatial dimensions. The model was based 

 upon the time-dependent, two dimensional form of 

 the advection- diffusion equation: 



dP + d_ 

 dt dx 



( 



— *.fH(-f .£)- 



o 



where P = concentration of leptocephali; 



u and v = velocities in the respective x and y 

 directions; and 



K x and K y = diffusivity coefficients for the respec- 

 tive directions. 



Leptocephali were not assumed to have any directed 

 swimming capability, so the velocities in the above 

 equation represent simple water current velocities. 

 The diffusivity coefficients express the dispersion of 

 leptocephali by turbulence, eddies, and other 

 phenomena not expressed by the advective terms 

 (Okubo 1980). 



The derivatives in the above continuous equation 

 were approximated by finite differences. For exam- 

 ple, to approximate the time derivative the following 

 relation was used: 



dP 



dt 



K+l _ 



/" 



A; 



where pt 

 pt+i 



At 



concentration of leptocephali at the 



present time t; 



concentration of leptocephali at time 



t + At; and 



duration of the time step. 



The derivatives with respect to thex andy directions 

 were approximated by weighted finite differences. 

 The method developed by Fiadeiro and Veronis 



484 



