Mathematical models of biological patterns: Lessons from Hamilton’s selfish herd
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.
KeywordsModels Idealization Gregarious behavior Voronoi diagrams
Earlier versions of this paper were presented at the Missouri Philosophy of Science Workshop (MOPS), March 2011 and the 14th Congress of Logic, Methodology and Philosophy of Science, Nancy, France, July 2011. I am grateful to both audiences and two journal referees for their comments and suggestions. I would also like to thank André Ariew for many insightful discussions about this paper and the philosophy of biology more generally.
- Early RL, Dugatkin LA (2010) Behavior in groups. In: Westneat DF, Fox CW (eds) Evolutionary behavioral ecology, Oxford University Press, Oxford, pp 285–307Google Scholar
- Forber P (2010) Confirmation and explaining how possible. Stud Hist Philos Biol Biomed Sci 41:32–40Google Scholar
- Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial tesselations: concepts and applications of Voronoi diagrams, 2nd edn. Wiley, HobokenGoogle Scholar
- Teller P (2009) Fictions, fictionalization, and truth in science. In: Suárez M (ed) Fictions in science: philosophical essays on modeling and idealization. Routledge, London, pp 235–247Google Scholar
- Viscido SV (2003) The case for the selfish herd hypothesis. Comments Theor Biol 8:665–684Google Scholar
- Weisberg M (2007a) Three kinds of idealization. J Phil 104:639–659Google Scholar