Journal of lhearrtical Biology 399(2016) 103-116 1O4 aRt` SN ELSEVIER Contents lists available at ScienceDirect Journal of Theoretical Biology journal homepage: Conshlark Evolution of worker policing Jason W. Olejarz a, Benjamin Allen l'"', Carl yeller • Raghavendra Gadagkar -1. Martin A. Nowak a•d•g.s Program for twoltalonary Dynamks. Hanard University, Cambridge, MA 02(38. USA °Department of Mathematics. Emmanuel College, Bosron. MA 02115, USA `Center for Mathematical Sciences and Applicanons. Harvard Unhersky. Cambridge, MA 02138. USA Depaytmcnr of Organismic and Emlutionary Biology. Hamad University. Cambridge. MA 02178. USA • Centre for Ecological Sciences and Centre for Contemporary Studies. Indian Institute of Science. Bangalore 560 072. India 'Indian National Science Academy. New Delhi 110 002. India ▪ Deponent of Mathematics. Harvard University. Cambridge. MA OM& USA ARTICLE INFO Ankle history. Received 2 February 2015 Received in revised form 23 January 2016 Accepted 2 March 2016 Available online 11 March 2016 Keywords: Sociobiology Natural selection Evolutionary dynamics Modelsisimulations ABSTRACT Workers in insect societies are sometimes observed to kill male eggs of other workers, a phenomenon known as worker policing. We perform a mathematical analysis of the evolutionary dynamics of policing. We investigate the selective forces behind policing for both dominant and recessive mutations for dif- ferent numbers of matings of the queen. The traditional, relatedness-based argument suggests that policing evolves if the queen mates with more than two males, but does not evolve if the queen mates with a single male. We derive precise conditions for the invasion and stability of policing alleles. We And that the relatedness-based argument is not robust with respect to small changes in colony efficiency caused by policing. We also calculate evolutionarily singular strategies and determine when they are evolutionarily stable