Cultural linkage: the influence of package transmission on cultural dynamics

Many cultural traits are not transmitted independently, but together as a package. This can happen because, for example, media may store information together making it more likely to be transmitted together, or through cognitive mechanisms such as causal reasoning. Evolutionary biology suggests that physical linkage of genes (being on the same chromosome) allows neutral and maladaptive genes to spread by hitchhiking on adaptive genes, while the pairwise difference between neutral genes is unaffected. Whether packaging may lead to similar dynamics in cultural evolution is unclear. To understand the effect of cultural packages on cultural evolutionary dynamics, we built an agent-based simulation that allows links to form and break between cultural traits. During transmission, one trait and others that are directly or indirectly connected to it are transmitted together in a package. We compare variation in cultural traits between different rates of link formation and breakage and find that an intermediate frequency of links can lower cultural diversity, which can be misinterpreted as a signature of payoff bias or conformity. Further, cultural hitchhiking can occur when links are common.

The overall design of this model is identical to the one described in the main text (see methods section for details) except links between cultural traits are not transmitted, as they are in the main text model. Specifically, after focal individuals chose their interaction partners and determined the packages for transmission, only the variants of the traits in the packages are transmitted and the links between traits in both the focal individual and the interaction partner remain unchanged. As a result, the parameter b no longer exists in the model and the parameter a (link formation) is set to zero so that no new links between traits are created during the simulation. For the initial condition, instead of starting with no links between traits, we randomly initialize the links, with each possible link existing with probability l ∈ {0, 0.1, 0.2, …, 1}. We run simulations that investigate both pairwise difference in a population as a result of links between traits and cultural hitchhiking. Where hitchhiking is examined, a burn in period is no longer needed since the links are static. Instead, the adjustment described in the main text (under Simulation set-up) that leads to the most challenging trait distribution for hitchhiking now become the starting condition. That is, one innovator has trait 1 variant 1 (the most beneficial) and trait 2 variant 4 (the rarest), while all other individuals have trait 1 variant 4 (the most detrimental).
With this model we observe some of the effects of links on pairwise difference, that we see in the model with transmissible links (Fig. A1.1). As before, when there are no links or when the links are rare we get π1>π WF and when links are common we see that π1=π WF (Fig. A1.2). As described in the main text, this result exists because links change the number of traits being transmitted per timestep. As the average package size increases, more transmission occurs, leading to lower pairwise difference.
However, unlike the model in which links between traits are transmitted, when the links are static at an intermediate frequency, π1 is not less than π WF (Fig. A1.2). Instead, the level of pairwise difference as a function of link frequency matches closely with the levels obtained in the original model with b=0.5. This occurs because where the configuration of large packages is not transmitted (or transmitted indeed at very low fidelity as is the case when b=0.5), the probability that a variant in a large package will remain in a large package after transmission is no higher than that probability for variants in small packages. In other words, the advantage of being in a large package is unlikely to persist over multiple timesteps.
We then compare the distributions of pairwise difference with (i) static links between traits and      Payoff bias: Conformist bias: Number of traits h 5 in neutral or payoff bias. 1 in conformist bias.

Number of variants per traits
k 4

S3. Robustness checks
To see whether our results are robust to changes in parameter values, we ran the simulation with the following changes in parameter values: a different copy rate, (c=0.8), a different innovation rate (μ=0.001), a different number of traits (h=8), a different number of variants (k=9), a different population size (N=200), varying N, h, and k simultaneously (N=200, h=8, k=2, or N=500, h=9, k=16. Only under neutral transmission).
In all parameter constellations that we investigated, the effect of links on pairwise difference follows the same qualitative pattern as described in the main text, with the exception of c, the copy rate. When there are no links between traits or when links are rare we find that π1>π WF , when links are common we see that π1=π WF , and when the links are at an intermediate frequency and b is small, we see that π1<π WF (Fig. A3.1). Lowering c leads to higher pairwise difference because less transmission occurs (Fig. A3.1C).
We also tested the robustness of our claims regarding the equifinality of neutral and linked models to changes in parameter values. The area of overlap between the distributions of pairwise difference under three different linkage assumptions: "linked" a=0.01 b=0.1, "Wright-Fisher", and "unlinked" a=0) can again be calculated. In general, the relative positions of the distributions remain similar ( Fig. A3.2). The calculated area of overlap are summarized in Table A1. 1. Parameters μ,N,h, appear to have minimal effect on the overlaps. Higher k leads to lower overlap between the linked and unlinked cases. Lower c increases the overlaps in general.  (Fig. A3.3) for all other values of the parameters. In most cases, as the link frequency approaches 1, the probability reaches 0.9-1. Where the copy rate is lower (c=0.8), the probability of hitchhiking driving the associative variant above 0.5 becomes very low even if link frequency is high.
Regarding     Only calculated if hitchhiking occurred in more than 10% of the simulation.

S4. Rate of adaptation
After we made the adjustments for hitchhiking at the 5000th timestep (see main text under Simulation setup), we also measure the average number of timesteps that occurs before the frequency of trait 1 variant 1 decreases for the first time, a sign that the selective sweep has ended. If this number is small, it suggests the rate of adaptation is high.
We find that with more links, the rate of adaptation become higher (Fig. A4.1). This is because under payoff-biased transmission, transmission increases the frequency of high-payoff variants in the population, and links increase the number of traits being transmitted in each timestep.