How do the actions of an individual impact the collective? Does it matter if you pick up a piece of litter as you're walking along the beach? Can your vote influence the outcome of an election? Is it worth your effort to “do the right thing”? In this research project, I am analyzing and quantifying the influence that actions of a single individual have upon properties of a community. Likewise, I want to understand how the actions of individuals are constrained and influenced by collective properties.
My research strategy consists of two prongs: a mathematical analysis of community interactions and an empirical simulation of such interactions. So far, the former has focused on a simple model of voting behavior while the latter has explored interactions between predators and prey. In simulations of predator/prey interactions between wolves and sheep, the introduction of a unique sheep individual has a statistically significant improvement on the survival rate of the flock.