Fig 1.
Evoked and Transmitted Culture (ETC) model.
ETC can be represented as a probabilistic directed graph [38], where nodes Etr and Atr are observed, while nodes Ttr are unobserved. Cultural traits Ttr evolve through time in a set of interconnected regions (here 4, depicted by different colours). Horizontal arrows represent how cultural trait is inherited from previous time step in same region, while diagonal arrows represent diffusion from interconnected regions (cultural communication). Vertical arrows pointing to cultural traits node represent the influence of ecological factors on cultural trait, while vertical arrows pointing from cultural trait represent the observation process, i.e. how cultural artifacts observed at a specific time t in region r depends on the cultural trait at the same time and location. Left inset: connectivity between different regions, where each edge represent the existence of cultural communication between two regions (G can also take continuous values, i.e. scale inversely to the distance between regions). The information is summarized in the connectivity matrix G below.
Fig 2.
Fitting a binary ETC model on synthetic data.
A. True vs. inferred cultural traits across time in all regions (bottom to top, from region 1 to region 6). Full lines represent the true binary cultural trait Tt,r, while dotted line represent the posterior probability of the cultural trait given by estimated parameters , where parameters are estimated using the EM procedure from observed data (E, A). B. Value of parameters estimated with the EM procedure (gray bars) against true value of the parameters (red ticks). C Model comparison between full and reduced models. Value of ΔBIC = BIC(reduced) − BIC(full), for two different reduced models: evoked-only model and diffusion-only model.
Fig 3.
Trait variables estimated from continuous ETC model, using moment, Laplace or Expectation-Propagation method in the E-step.
The true trait value is represented by thick gray lines, the inferred trait posterior is represented by its posterior mean (dotted coloured lines) and standard deviation (shaded areas). Each colour represent values in a different region. Note that in this example region 2 was created from region 3 at time step 31, region 1 was created de novo at time step 51, while region 3 was suppressed at time step 300.
Fig 4.
A-G Estimated ETC parameters for each type of approximate method in E-step (Laplace approximation, EP or moment method). Dotted line represent the true value. H: mean squared error on cultural trait. Bars: average value over datasets; error bars: standard deviation across datasets.
Fig 5.
Model selection for simulated datasets using different metrics (AIC, BIC, CVLL or boostrapping p-values) and approximate inference methods for E-step (moment: Blue bars; Expectation-Propagation: Red bars; Laplace method: Green bars).
Each bar represents the proportion of simulated datasets where the corresponding model (full, no evoked model, no diffusion model or control model) was selected. CVLL was computed using 5-fold cross-validation.
Fig 6.
Comparison of the one-stage and two-stage estimation procedures.
A. Left: Estimates of cultural trait using the standard ETC model. Legend as in Fig 3. Vertical lines marks the transition from low to high cultural production period. Right: Direct estimates of cultural trait by averaging cultural artifacts in same region and within a certain window of time. B. Parameter estimates using one-stage (blue bars) vs two-stage (red-bars) method. Vertical dashed line indicate true value of the parameters. Error bars: standard deviation of estimates across datasets. C. Average mean-squared-error on cultural traits using one-stage vs. two-stage method (log-scale).
Fig 7.
Fitting ETC model on synchronous dataset.
A. Value of binary ecological factor along phylogenetic tree of regions. The tree represents 50 regions, where parenthood indicates that the new region takes the value of the cultural trait from its parent. Ecological factor is color coded, with blue indicating that the factor is inactive, and red indicating that the factor is active. B. Value of cultural trait along the phylogenetic tree, simulated from ETC model. Value is color coded, with blue indicating negative values, and red positive values. C. Posterior mean over cultural trait inferred from full ETC model fitted to synchronous data. Same colour code as B. D. Same as C, for ETC model that does not include cultural diffusion. E. Estimated parameters using full ETC model (blue bars) vs. ETC model without spatial diffusion (red bars). Same legend as Fig 2. F. Reconstructing error on cultural trait, for the two variants of the model.