Extended Data Fig. 8: Conditions for the evolution of a number of observations M under a fixed strictness threshold q.

a, The panel illustrates the criteria determining how a resident discriminator, which aggregates M_R observations, can resist invasion by a discriminator that aggregates a larger number of observations (M_I > M_R). The criterion for each resident type is shown by distinct curves. Below each curve are the conditions where the resident discriminator successfully resists invasion, while above the curves indicates vulnerability to invasion by discriminators aggregating a larger number of observation. The space between adjacent curves is a coexistence zone, where both resident and invading discriminators can stably exist together. Lower numbers of observations are favored by lower benefit-to-cost ratios. As error rates increase, the benefit-to-cost ratio required by a resident to resist invasion decreases exponentially. The dashed line shows b/c = 10 as an example, with different markers indicating specific values of the error rates. b, Panel shows the outcomes of the competition between multiple aggregating discriminators using M ∈ {2,4,6,8,10} in the presence of the unconditional strategies. Each bar correspond to each of the markers of panel a, showing the steady states reached by numerical integration from 100 different initial conditions. The steady states confirm the criteria of panel a and show that, as error rates increase with a fixed benefit-to-cost ratio, larger numbers of observations evolve. For all panels, we set q = 1/2 and fixed scoring as the social norm.