Fig 1.
Assumed relationship between refinement level and payoff increment, illustrated by refinements in hammer technology.
The payoff to a behavior is given by its basic (unrefined) payoff plus an increment that is a function of refinement level. Refining resulted in payoff increments (illustrated by the black curve) surpassing the highest basic payoff (dashed blue line) after approximately 10 refine moves. The inset illustrates an example distribution for the basic payoffs–most payoffs are low, and few payoffs are high.
Fig 2.
Scores and learning in Stage 1.
Relationship between score and (A) the proportions of learning (INNOVATE+OBSERVE+REFINE) moves, (B) Score as a function of REFINE moves, averaged over each entry in Stage 1. (C) Distribution of the proportion of learning moves averaged by entry, for each extension over all entries and (D) for the top-ten best-performing entries.
Fig 3.
Cultural diversity measured across extensions for Stages 2 and 3.
(A-D) Cumulative culture led to plummeting diversity in both the behaviors performed and known about, as populations converged on heavily refined behaviors, that (E-H) persist for long periods of time. ‘Behavior’ refers to the acts that the population was using at each timepoint, and ‘Knowledge’ refers to the acts present in the repertoire of at least one individual, but not necessarily used. ‘Amount’ captures the proportion of behaviors or knowledge known about within the population (i.e., mean proportion of possible behaviors used or known by at least one agent in each round in the last quarter of the simulations), ‘evenness’ measures the flatness of the frequency distribution (using Pielou’s evenness index, see Materials and methods), and ‘persistence’ refers to the length of time the behavior or knowledge persisted in the population (i.e. mean or maximum number of rounds that a behavior within a population was exploited or that knowledge of it persisted within the population, without a break; see Materials and methods for more detail). Data for the ‘No extension’ case give a baseline comparison and are from 1,000 simulations using the top-ten tournament entries with randomly chosen parameter values.
Fig 4.
(A) and (B). Predicted scores from a linear mixed model accounting for between-entry variation, using Stage 1 data, for (A) all entries, and (B) top-ten entries, that did and did not play REFINE, in refined compared to non-refined environments (Tables B and C in S1 Supporting Information). Top-ten entries used refinement strategically, achieving higher scores, and constructing maximally refined environments beneficial to all. (Circles indicate entry means and diamonds show group means, as predicted by the model. Environments were defined as refined when a population reached the highest refinement level). (C) Relative fitness of ‘clever’ REFINE entries over a blind copier (OBSERVE-once-then-EXPLOIT-forever; see Materials and methods for details). ‘Clever’ entries had the advantage at low refinement levels, but were vulnerable to invasion at higher refinement levels.