To do so we calculated the difference between within-group similarity over time and between-group similarity at one specific point in time . We calculated within-group similarity over time as the overlap in repertoires at year 120 and 100. This 20 year period ensured there is no overlap in foragers at the two time points. For between-group similarity we calculated overlap between a group and other groups in an independent simulation with the exact same environment. In this way we controlled for relatedness between groups, and competition between groups, which increase and decrease between-group similarity respectively. We calculated average repertoire similarity between groups k and l as: 10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \bar{O}_{k,l} = \frac{1}{G_{k} G_{l}}\sum_{i=1}^{i=G_{k}} \sum_{j=1; j!=i}^{j=G_{l}} \frac{\vec{d_{i}}\bullet\vec{d_{j}}}{|\vec{d_{i}}|.|\vec{d_{j}}|} $$ \end{document}Ōk,l=1GkGl∑i=1i=Gk∑j=1;j!=ij=Gldi→∙dj→|di→|.|dj→|