S1 Supporting Information -

<p><b>Fig A.</b> Relationship between score and (a) amount of REFINE as a proportion of all learning moves; (b) proportion of just REFINE and INNOVATE learning moves; (c) proportion of INNOVATE moves; (d) proportion of OBSERVE moves and (e) proportion of learning moves that are OBSERVE (and not INNOVATE or REFINE). <b>Fig B.</b> Distribution of final maximum refinement level in the tournament (a) in all simulations, and (b) in simulations that include only entries that use REFINE. Refinement levels above the value of 8 typically lead to payoffs that exceed the maximum basic payoff (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012436#pcbi.1012436.g001" target="_blank">Fig 1</a>). The maximum refinement level achieved across simulations varied substantially and showed a bimodal distribution. <b>Fig C.</b> Cultural diversity measures across extensions for Stage I. Cumulative culture leads to decreasing diversity in both the behaviors performed and behaviors known about, as populations converge on a small number of heavily refined, high-payoff behaviors. <b>Fig D.</b> Cultural diversity measures as a function of p<sub>c</sub> and p<sub>copyFail</sub> in Stage 2. Timelines of amount and evenness are presented as line charts, while the boxplots illustrate mean values for mean and maximum persistence. <b>Fig E.</b> Cultural diversity measures as a function of r<sub>max</sub> and n<sub>Observe</sub>, in Stage 2. <b>Fig F.</b> Cultural diversity measures for one run of the cumulative extension in Stage II. (top) Proportion of agents who use and know each act, acts ordered by rank frequency, at increasing timesteps. (bottom) Behaviour and Knowledge evenness over time, with red dots indicating the same timesteps as above. The population very quickly converges on a small set of acts–in the last quarter of the simulation the population knows and uses only one act. <b>Fig G.</b> Amount and evenness of both behavior and knowledge in simulations that only include top ten entries (teal) and simulations with the rest of the 41 entries (red), in Stage I (cumulative extension). <b>Fig H.</b> Mean and maximum persistence of both behavior and knowledge, in simulations that only include the top ten entries (teal) and simulations with the rest of the 41 entries (red), in Stage I (cumulative extension). <b>Fig I.</b> Distribution of mean proportion REFINE moves per simulation for each entry, ordered from the top left by score in Stage 1, in descending order. This plot only includes the 35 entries that used the REFINE move. Note the difference in scale on the x axis. The top four entries were also the top performers in Stage 3, which establishes that the best-performing entry used REFINE at low levels. <b>Table A.</b> Model averaged parameter estimates and summed Akaike weights (across an all-subsets model set of linear regression models with Gaussian error) for Stage 1 cumulative extension. Other extensions give similar findings (see Table B in S1 Supporting Information). The AIC<sub>c</sub> best model (adjusted R-squared = 0.86) contained <i>pLearnRefine</i> and <i>pObserve</i>, as well as <i>meanPayDiffObserve</i>, <i>meanBetweenLearn</i> and <i>doRefine</i>. The first two predictors were included in all of the 13 well-supported (ΔAIC<sub>c</sub><2) models; while the others were in 9, 6 and 7 respectively. <b>Table B.</b> Results from a linear mixed model predicting score as a function of the interaction between whether an environment was refined or not and whether an entry used refine or not, with a varying intercept for entry identity, using data for all 51 entries in the tournament. The model definition: score ~ environment type*entry type + 1|entry, assuming a non-refine entry in a non-refined environment as baseline. <b>Table C.</b> Results from a similar linear mixed model with a varying intercept for entry identity, using data for 20 entries, the top-scoring 10 entries that used REFINE and the top-scoring 10 entries that did not use REFINE. Model definition: score ~ environment type*entry type + 1|entry, assuming a non-refined entry in a non-refined environment as baseline. <b>Table D.</b> Definitions of new terms. <b>Table E.</b> Simulation parameters.</p> <p>(DOCX)</p>