Date of Award
5-2011
Major
Mathematics
Faculty Advisor
Pericak-Spector, Kathy
Abstract
The main operating concern of all species in any ecosystem or natural environment is rooted in the battle for survival. This constant battle for survival is most highlighted in the two main modes of species interaction; categorized as predation or competition. This research focused on applying biological mathematics to analyzing predation relationships, especially the relationship between the Canadian Lynx and the Snowshoe Hare. This predation relationship is quite special, because these species interact in a relatively isolated manner compared to others, meaning their populations fluctuated in a regular cycle. These population fluctuations can be defined and analyzed mathematically using systems of linear ordinary differential equations, built of course upon several minimizing assumptions in order to exclude incalculable variables. One of these models is the Lotka-Volterra Model, which was reformulated and analyzed in this research. By Applying the Lotka-Volterra Model to the predator-prey relationship between Canadian Lynx and the Snowshoe Hare, it is discovered that their populations fluctuate on average ten-year phases. Predator-Prey population cycle charts as well as direction fields of the system were analyzed. This model was then compared to other real life models, like the Kermack-McKendrick Model and the relationship between fish and sharks in the Mediterranean. Future research could expand on the Lotka-Volterra model by accounting for variables like hunting, natural disaster, epidemic, or other predators. This research is important in biological fields studying predation, especially when predation leads to species endangerment or yields intense coevolution.