article published yes Andreas Pavlogiannis author 49704004-F248-11E8-B48F-1D18A9856A870000-0002-8943-0722 Krishnendu Chatterjee author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X Ben Adlam author Martin Nowak author KrCh department Modern Graph Algorithmic Techniques in Formal Verification project Rigorous Systems Engineering project Quantitative Graph Games: Theory and Applications project Microsoft Research Faculty Fellowship project Population structure can facilitate evolution of cooperation. In a structured population, cooperators can form clusters which resist exploitation by defectors. Recently, it was observed that a shift update rule is an extremely strong amplifier of cooperation in a one dimensional spatial model. For the shift update rule, an individual is chosen for reproduction proportional to fecundity; the offspring is placed next to the parent; a random individual dies. Subsequently, the population is rearranged (shifted) until all individual cells are again evenly spaced out. For large population size and a one dimensional population structure, the shift update rule favors cooperation for any benefit-to-cost ratio greater than one. But every attempt to generalize shift updating to higher dimensions while maintaining its strong effect has failed. The reason is that in two dimensions the clusters are fragmented by the movements caused by rearranging the cells. Here we introduce the natural phenomenon of a repulsive force between cells of different types. After a birth and death event, the cells are being rearranged minimizing the overall energy expenditure. If the repulsive force is sufficiently high, shift becomes a strong promoter of cooperation in two dimensions. https://research-explorer.ista.ac.at/download/1624/4947/IST-2016-466-v1+1_srep17147.pdf application/pdfno Nature Publishing Group2015 eng 00036529950000110.1038/srep17147 5 Pavlogiannis, A., Chatterjee, K., Adlam, B., &#38; Nowak, M. (2015). Cellular cooperation with shift updating and repulsion. <i>Scientific Reports</i>. Nature Publishing Group. <a href="https://doi.org/10.1038/srep17147">https://doi.org/10.1038/srep17147</a> A. Pavlogiannis, K. Chatterjee, B. Adlam, M. Nowak, Scientific Reports 5 (2015). Pavlogiannis A, Chatterjee K, Adlam B, Nowak M. Cellular cooperation with shift updating and repulsion. <i>Scientific Reports</i>. 2015;5. doi:<a href="https://doi.org/10.1038/srep17147">10.1038/srep17147</a> Pavlogiannis A, Chatterjee K, Adlam B, Nowak M. 2015. Cellular cooperation with shift updating and repulsion. Scientific Reports. 5, 17147. A. Pavlogiannis, K. Chatterjee, B. Adlam, and M. Nowak, “Cellular cooperation with shift updating and repulsion,” <i>Scientific Reports</i>, vol. 5. Nature Publishing Group, 2015. Pavlogiannis, Andreas, et al. “Cellular Cooperation with Shift Updating and Repulsion.” <i>Scientific Reports</i>, vol. 5, 17147, Nature Publishing Group, 2015, doi:<a href="https://doi.org/10.1038/srep17147">10.1038/srep17147</a>. Pavlogiannis, Andreas, Krishnendu Chatterjee, Ben Adlam, and Martin Nowak. “Cellular Cooperation with Shift Updating and Repulsion.” <i>Scientific Reports</i>. Nature Publishing Group, 2015. <a href="https://doi.org/10.1038/srep17147">https://doi.org/10.1038/srep17147</a>. 16242018-12-11T11:53:06Z2025-09-23T08:13:52Z