Group selection models combine selection pressure at the individual level with selection pressure at the group level (Sober and Wilson, 1998; Traulsen and Nowak, 2006; Wilson and Wilson, 2007; Boyd and Richerson, 2009; Simon, 2010; Simon et al., 2013; Luo, 2014; van Veelen et al., 2014; Luo and Mattingly, 2017). Cooperation can be costly for individuals, but beneficial for the group, and therefore, if individuals are sufficiently much assorted, and cooperators find themselves in groups with disproportionately many other cooperators, cooperation can evolve. The existing literature on group selection generally assumes that competition between groups takes place in a well-mixed population of groups, where any group competes with any other group equally intensely. Competition between groups however might very well occur locally; groups may compete more intensely with nearby than with far-away groups. We show that if competition between groups is indeed local, then the evolution of cooperation can be hindered significantly by the fact that groups with many cooperators will mostly compete against neighbouring groups that are also highly cooperative, and therefore harder to outcompete. The existing empirical method for determining how conducive a group structured population is to the evolution of cooperation also implicitly assumes global between group competition, and therefore gives (possibly very) biased estimates.