Our results confirm that learning needs to be sufficiently protracted to generate traditions and cumulative cultural change. In Fig. 2 we can observe that task difficulty must be sufficiently high, (i.e. learning must be sufficiently protracted, before these cultural phenomena are generated, H>0.1). At H=0.1 learning is very easy and all foragers are effectively all knowing and all the groups are the same and there are no traditional differences. Once learning is sufficiently difficult (H>0.1) traditional differences can arise. However, the specific effects of different task difficulties varies between traditions and cumulative cultural increase, where the latter requires very high task difficulty before is detectable. Moreover, increasing task difficulty beyond H=1 does not necessarily lead to greater traditional differences, and after H=1 traditional differences actually level off or even decline. This occurs due to population-wide convergence on resource types that are easy to learn which becomes increasingly pronounced as task difficulty increases (see Section 2 in Additional file 1 for more details).