Extended Data Fig. 5: Fixed costs on a dense cluster of stars.

Consider a population consisting of m stars, each of size n, connected by a complete graph at their hubs. Provided m > 1, this structure results in extremely low critical ratios under both PC and DB updating when n is large. Illustrated here is the case in which m = 5. This structure has the interesting property that ff-goods result in lower critical thresholds than pf-goods (both of which are lower than that of pp-goods, which is not depicted here). Qualitatively, the results are similar for both PC and DB updating, with the exception that producers can never be favored by selection on the star (m = 1) under DB updating but can be favored under PC updating. We derive explicit formulas for \({\left(b/c\right)}^{* }\) for any m and n in the SI.