Pollesch, Nathan L.2012-12-102012-12-102012-07https://hdl.handle.net/11299/140656University of Minnesota M.S. thesis. July 2012. Major: Applied and computational mathematics. Advisor:Harlan Stech. 1 computer file (PDF); vi, 130 pages, appendix p. 73-130.The purpose of this thesis is to explore the connections between agricultural runoff influx, oil influx, and oxygen levels in a near-coastal marine environment. The creation of oxygen deficient conditions is investigated through the use of a stoichiometric modeling approach that utilizes a system of ordinary differential equations. Agricultural runoff is modeled as a source of a limiting nutrient for algae. Oil influx is modeled as a carbon source for bacterial consumption. The investigation is motivated by the Gulf of Mexico-ecosystem in the wake of the Deepwater Horizon oil rig incident of 2010, which contributed large amounts of oil (carbon) to the Gulf system. The model consists of an algal class with flexible stoichiometry that utilizes the nutrient for growth and a bacterial class with fixed stoichiometry that assimilates the carbon. A consumer class with fixed stoichiometry that is dependent upon the oxygen present in the system is modeled and is used to indicate oxygen deficient conditions. Equilibrium, time series, and stability analysis of this five-dimensional system are presented. Through the analyses presented and simulations, it is found that this model reproduces the behavior of the biological processes associated with nutrient enrichment and the creation hypoxic areas, or ‘dead zones'.en-USApplied and computational mathematicsThesis or Dissertation