Research ArticleSOCIAL SCIENCES

Cultural selection shapes network structure

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Science Advances  14 Aug 2019:
Vol. 5, no. 8, eaaw0609
DOI: 10.1126/sciadv.aaw0609
  • Fig. 1 Increased connectivity leads to smaller trait diversity but higher trait proficiency.

    (A) Depending on the neighborhood size, ni, a focal individual (red), is connected to 2, 6, or 20 neighbors (blue). (B and C) Average repertoire size and average highest trait proficiency in populations with varying ni. Populations with larger ni (higher degree and shorter path length) have, on average, smaller repertoires and higher trait proficiency. (D to F) Example record of average proficiency of all traits in populations with varying ni. Highly connected populations (F) collectively have fewer traits but are more proficient at them than sparsely connected ones (D).

  • Fig. 2 Effect of network topology onto cultural complexity.

    (A and C) Sparsely connected populations (low pn and pr, low degree) have the largest individual repertoires, whereas well-connected populations (high pn and pr, high degree) show the highest trait proficiency (B and C). (D) As average degree increases, the total number of traits known to the population decreases. (E) Moreover, the trait distribution for highly connected populations is skewed such that a few traits are known to almost the entire population, whereas in sparsely connected populations, traits are more evenly distributed such that almost all available traits are known to different subsets of the population [compare bottom left and top right corner in (A) and (B)]. All values represent population averages.

  • Fig. 3 Specialist and generalist environments select for different network topologies.

    (A) Selecting for trait proficiency increases degree and decreases average path length, leading to dense networks (example in the top inset), whereas selecting for large repertoires decreases degree and increases path length, resulting in sparse networks (example in the bottom inset). (B) While generalist environments strongly select against random connections (pr), there is little selection against either linking parameter in specialist environments. (C) Selecting for generalists increases repertoire size while keeping proficiency at a minimum. Selecting for specialists reduces repertoire size only slightly but strongly increased individual proficiency. In addition, in simulations selecting for specialists, results are distributed in two clusters. Here, populations differ in the number of traits they converged on. Populations with higher proficiency converged on three traits, whereas populations with lower proficiency converged on four traits (note that average repertoire sizes are one trait larger due to trait innovation). Under specialist selection, trait distribution is highly skewed compared to generalist selection (inset).

  • Fig. 4 Trade-off between social inheritance and random connections depends on average connectivity.

    (A) Specialists benefit from convergence of traits in their neighborhood, which is achieved by increasing pn (at low connectivity) or increasing pr (at high connectivity). The opposite is the case for generalists who try to avoid trait convergence in their neighborhood. (B) This leads on average to shorter path lengths in specialists and longer paths in generalists (lines indicate possible combinations of pn and pr given degree k). (C) Populations are mainly made up of generalists at low connectivity and specialists at high connectivity. At intermediate connectivity, this is mediated by path length and clustering.

  • Fig. 5 Populations more easily transition from generalists to specialists than the other way around.

    (A to D) Trajectory of linking probabilities (pn and pr) and culture measures (repertoire size and proficiency) as selection regimes change from generalist (blue bars) to specialist (red bar) and back. Mean (black line) and SD (gray shading) for 100 repetitions are shown. Some simulations do not return to larger repertoires and lower proficiency after the specialist phase (red lines). Here, although pn decreases after increasing in the specialist phase, (A) pr keeps increasing even after selection is switched back to favoring generalists (B) (see main text for details). Note that the red lines remain on equilibria for repertoire size (C) and proficiency (D) that are identical to those shown in Fig. 3C and reflect the fact that for these parameters, populations may converge on three or four widely shared traits.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaaw0609/DC1

    Section S1. Social learning success probability

    Section S2. An alternative social learning model

    Section S3. Network metrics for fixed values of pn and pr

    Section S4. Coupling pr to pn to limit degree centrality

    Section S5. Time series for simulations with evolving pn and pr

    Section S6. Low mutation rate

    Section S7. Connection costs

    Section S8. Varying population size and trait number

    Section S9. Varying innovation and social learning success rate

    Fig. S1. The effect of increasing memory on trait repertoire and highest skill level.

    Fig. S2. If memory size is limited, then the two different social learning algorithms are qualitatively the same.

    Fig. S3. The effect of complex contagion on social learning dynamics, and of linking parameters on network characteristics.

    Fig. S4. Distribution of common traits depends on average connectivity.

    Fig. S5. Trait proficiency depends on the level of trait convergence and connectivity.

    Fig. S6. Trajectories for linking probabilities pn and pr averaged over all simulation runs for all three selection regimes (neutral, generalist, and specialist).

    Fig. S7. Results displayed as in Fig. 2 of the main text but with mutation rate μ = 0.01.

    Fig. S8. Adding a cost per connection reduces average degree in specialists, whereas generalists are less affected.

    Fig. S9. Added connection costs.

    Fig. S10. Varying the number of traits and individuals in a population.

    Fig. S11. Increasing population size also increases trait diversity in the population.

    Fig. S12. Varying innovation and social learning success rate.

    Reference (64)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Social learning success probability
    • Section S2. An alternative social learning model
    • Section S3. Network metrics for fixed values of pn and pr
    • Section S4. Coupling pr to pn to limit degree centrality
    • Section S5. Time series for simulations with evolving pn and pr
    • Section S6. Low mutation rate
    • Section S7. Connection costs
    • Section S8. Varying population size and trait number
    • Section S9. Varying innovation and social learning success rate
    • Fig. S1. The effect of increasing memory on trait repertoire and highest skill level.
    • Fig. S2. If memory size is limited, then the two different social learning algorithms are qualitatively the same.
    • Fig. S3. The effect of complex contagion on social learning dynamics, and of linking parameters on network characteristics.
    • Fig. S4. Distribution of common traits depends on average connectivity.
    • Fig. S5. Trait proficiency depends on the level of trait convergence and connectivity.
    • Fig. S6. Trajectories for linking probabilities pn and pr averaged over all simulation runs for all three selection regimes (neutral, generalist, and specialist).
    • Fig. S7. Results displayed as in <Fig. 2 of the main text but with mutation rate μ = 0.01.
    • Fig. S8. Adding a cost per connection reduces average degree in specialists, whereas generalists are less affected.
    • Fig. S9. Added connection costs.
    • Fig. S10. Varying the number of traits and individuals in a population.
    • Fig. S11. Increasing population size also increases trait diversity in the population.
    • Fig. S12. Varying innovation and social learning success rate.
    • Reference (64)

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