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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
that affect the intensity of policing, Our paper is based on an analysis of evolutionary dynamics and population genetics of haplodiploid species (Nowak et al., 2010; Olejarz et al., 2015). It does not use inclusive fitness theory. Spe- cifically, we adapt the mathematical approach that was developed
ry and eusociality. Nature 471. E1-F9. Alkay. E. Van Cleve. J.. 2016. There is no fitness but fitness. and the lineage is its bearer. Philos Trans. R. Soc. 13371. 20150085. Allen. Et, Nowak. MA.. Wilson, E,0.. 2013. Limitations of inclusive fitness. Proc. Nail, Mad. 50. U.SA 110.20135-20139. Allen. B
tkin. I. B. Formal properties of the probability of fixation: identities, inequalities and approximations. Them. Poput Blot 99, 98-113 (2015). 5. Nowak, M. A. Evolutionary Dynamics (Harvard University Press, Cambridge, MA. 2006). 6. Moran, P. A. P. The Statistical Processes of Evolutionary Theory
s. Nature 359. 826429 (1992). 9. Durrett. It & Levi,.. S. A. Stochastic spatial models: a user's guide to ecological applications. Philos. Trans. R. Soc. Lond. Ser. B Blot Set 343.329-350 (1994). 10. Whitlock, M. Fixation probability and time in subdivided populations. Genetics 779,767-779 (2003).
eractions (Anderson & May 1991, Nowak & May 1994), the evolution of metabolic pathways (Pfeiffer et al 2001), theoretical approaches to immunology (Nowak et al 1991, 1995), and the study of animal and human behavior (Parker 1974, Enquist & Leimar 1983, McNamara & Houston 1986, Milinski 1987, Fudenber
rock-paper-scissors. Nature, 418, 171-174. [69] Killingback T, Doebeli M, 1996. Spatial evolutionary game theory: Hawks and Doves revisited. Proc. R. Soc. B, 263, 1135-1144. [70] Kingman, J.F.C., 1976. Coherent random-walks arising in some genetic models. Proc. R. Soc. Lond. Ser. A, 351, 19-31. [71]
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