“…On the contrary, in this work we have demonstrated that, even if the motility of cooperators and defectors is the same and the spatial domain is homogeneous -so that there are no physical barriers -the natural tendency of cooperators to aggregate into clusters is su cient to preserve cooperation. These findings confirm the results presented in previous theoretical studies by Allison (2005), Durrett and Levin (1994), Fletcher and Doebeli (2009), Hauert and Doebeli (2004), Korolev and Nelson (2011), Nowak and May (1992), Ohtsuki et al (2006), Perc and Szolnoki (2008), Santos and Pacheco (2005), Szabó and Fath (2007) and Taylor et al (2007), and experimental works by Gri n et al (2004), Julou et al (2013), Kümmerli et al (2009) and Momeni et al (2013), and provide further evidence that spatial clustering enhances the benefits of mutual cooperation and plays a crucial role in preserving cooperative behaviours. The spiral structures created by defectors share some striking similarities with spiral waves arising in models of host-parasitoid dynamics, such as those reported by Comins et al (1992), May (1995) and Solé et al (1992).…”