Modeling and Simulations of the Migration of Pelagic Fish Alethea Barbaroy{ Baldvin Einarssonyz{ Björn Birniryz{ Sven Sigurðssonz Héðinn Valdimarsson§ Ólafur Karvel Pálsson§ Sveinn Sveinbjörnsson§ Þorsteinn Sigurðsson§ June 16, 2008 Abstract We model the spawning migration of the Icelandic capelin stock using an interacting particle model with added environmental fields. Without an artificial forcing terms or a homing instinct, we qualitatively reproduce several observed spawning migrations using available temperature data and approximated cur- rents. The simulations include orders of magnitude more particles than many similar models, affecting the global behaviour of the system. Without environmental fields, we discuss how various parameters scale with respect to one another. In particular, we present scaling behaviour between the size of the time step, radii of the sensory zones and the number of particles in the system. We then discuss how environmental data are incorporated into the model. y Department of Mathematics, University of California, Santa Barbara, USA. z Department of Mathematics, University of Iceland, Reykjavík, Iceland. z Department of Computer Science, University of Iceland, Reykjavík, Iceland. § Marine Research Institute of Iceland. { Center for Complex and Nonlinear Science, University of California, Santa Barbara, USA. Keywords: Collective motion, Fish migration, Icelandic capelin (Mallotus villosus), Interacting particle model. Corresponding author: Baldvin Einarssson,
[email protected] 1 Introduction take can be observed, as can the approximate tim- ing, the surrounding environment and other char- acteristic factors. There are year-to-year variations Many species of marine animals travel great dis- which could be influenced by a number of variables tances between feeding and spawning grounds, in- including temperature and other environmental fac- cluding pelagic species of fish like the capelin (Mal- tors such as food density, salinity, bottom topography lotus villosus) and herring (Clupea harengus) (Vil- and oceanic currents.