Evolutionary Dynamics Under Nonlinear Frequency-depenent Selection

Julian Kates-Harbeck, Harvard University

We study the evolutionary dynamics of a generic "infection" in a population whose reproductive fitness can depend nonlinearly on its frequency within the population. The nonlinearity can be thought of as capturing cooperative or generalized "social" effects in the infected population. The "infection" might in reality represent a biological, social, behavioral or economic pattern that spreads. We characterize analytically the behavior of infection epidemics for well-mixed populations. These predictions are found to be in quantitative agreement with Monte Carlo simulations of the infection dynamics. We then extend our model to structured populations on graphs, comparing and contrasting the results with the well-mixed case.

Abstract Author(s): Julian Kates-Harbeck, Michael Desai