Our research is motivated by a desire to track the annual migration of the capelin from the north of Iceland to their feeding ground in the Arctic Ocean near Jan Mayen and then back and around to their spawning ground south of Iceland. The capelin are extremely valuable to Iceland's fishing industry both economically and ecologically. The capelin plays a large role in the ecology of the whole North Atlantic and North Pacific region, with Canadian and Norwegian capelin species executing similar migrations. Our aim is to create a model of these migration cycles which can be used to estimate the location of the capelin stock during their feeding and spawning migration.

Many environmental factors can affect the migration, such as temperature, availability of food, size of the capelin population, and oceanic currents. While some studies are being performed incorporating some of these data, for example see [35] and [36] which build ocean temperature and currents into the model, these studies use forcing which models a homing instinct to reproduce the migration. Our goal is to model the migration using the physical factors mentioned above with no such preferred direction affecting the route.

In Chapter 1, we give an overview of our work and summarize our results. In Chapter 2, we discuss the biological background necessary to understand the work herein and give an overview of the history behind our model and previous work on our problem. We detail our model in Chapter 3. In Chapter 4, we give Birnir's derivation of coupled ordinary differential equations (ODEs) derived from the discrete model and an overview of the solutions which he found. We then numerically confirm these solutions. In Chapter 5, we confirm the existence of the solutions to the discrete system which the ODE analysis indicates we should find. We also find several additional solutions motivated by the addition of different zones of interaction and the presence of noise.

We then move on to discuss the implementation in C++ and the application of our model to the migration of the capelin. In Chapter 6, we discuss the architecture of our code. In Chapter 7, we discuss the parallelization of our algorithm and the associated challenges. In Chapter 8, we address the addition of environmental data to our algorithm. In Chapter 9, we discuss the parameters in our model and the challenge of calibrating the model to our particular biological system. Chapter 10 compares the results of our simulations to three actual spawning migrations. In Chapter 11, we discuss the application of bioenergetic models to this problem.