For cumulative cultural change we focused on energy intake over time. We used a conservative approach to focus on whether cultural processes enable phenotypes that are beyond what foragers can achieve within a single lifetime. We therefore considered the difference between (1) year 20, which represents the maximum that individuals can achieve within their lifetime, and (2) year 120, the end of our simulation by which time the cumulative process had levelled off. The change was expressed as a proportion of the measure at year 20, where total energy intake is calculated as follows: (i) total energy intake \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$= \sum \limits _{r=1}^{r=R} d_{ir} e_{ir}$\end{document}=∑r=1r=Rdireir, where d ir is the total number of items of resource type r that were consumed by forager i, and e ir is the per item reward obtained. We repeated this analysis on other repertoire measures in order to analyze whether skill, repertoire quality and repertoire diversity also change cumulatively: (ii) repertoire quality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$= \sum \limits _{r=1}^{r=R} {z_{ir}} Q_{r}$\end{document}=∑r=1r=RzirQr; (iii) repertoire diversity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$= \sum \limits _{r=1}^{r=R} - {z_{ir}} \log {z_{ir}}$\end{document}=∑r=1r=R−zirlogzir; (iv) average skill \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$= \sum \limits _{r=1}^{r=R} {z_{ir}} s_{ir}$\end{document}=∑r=1r=Rzirsir, where z ir is the proportion of resource r in individual i’s diet, Q r is the quality of resource type r, and s ir is the skill forager i has for resource type r. Note that for repertoire diversity we only considered resource types that had been consumed (i.e. z ir>0). In contrast to measuring traditional differences, we used different random seeds for the environment in each simulation so as to not repeat the exact same pattern of environmental change.