Mathematical models of biological patterns: Lessons from Hamilton’s selfish herd

Abstract

Mathematical models of biological patterns are central to contemporary biology. This paper aims to consider what these models contribute to biology through the detailed consideration of an important case: Hamilton’s selfish herd. While highly abstract and idealized, Hamilton’s models have generated an extensive amount of research and have arguably led to an accurate understanding of an important factor in the evolution of gregarious behaviors like herding and flocking. I propose an account of what these models are able to achieve and how they can support a successful scientific research program. I argue that the way these models are interpreted is central to the success of such programs.