This video shows my research about the biological and socioeconomic consequences of climate change on fisheries. I wanted to tell a story explained the interesting system I study and that embraced, rather than shied away from, my usage of mathematics to study this complicated system. The girls at the New England Ballet Theatre (where I dance too!) did a fantastic job of telling the story of fish, a fisherman, climate change, and the math that I use to study how they are linked. Throughout, I tried to keep as much fidelity to my model as possible, while maintaining a narrative arc; for example, when the fish ventures outside the habitat and dies, that shows the Dirichlet or absorbing boundary conditions that my model uses. We had a great time dancing this, and hope you enjoy watching it!
More about my thesis: I use reaction-diffusion partial differential equations to model fisheries. There are two main parts of my models: fish and fishermen. For the fish, I use logistical growth model for their population—so it grows quickly at low densities and slowly at high densities. The fish live in a habitat which is represented by a region of a one dimensional line on which positive growth occurs. At the boundaries, where the habitat ends, fish die. To incorporate climate change into my model, I impose movement of the boundary conditions through time. This simulates how the region where climatically the fish can growth shifts poleward as climate change progresses. On top of this I add an economic component in the form of fishermen. The fishermen try to maximize profit by fishing a population that is following its moving habitat. Thus, profit is influenced by how many fish are in different locations, how quickly they grow, and where and when the fishermen harvest them. My thesis focuses on what actions are economically optimal for the fishermen, how these actions influence fish population levels and persistence, and how both the biological and economic components of the system changes as the habitat moves with climate change. I use both analytical and numerical methods for my work. Making these models requires much creativity and time working with different formulations or methods of solving, which I hoped to capture some of in my dance as well.
This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374