Social network architecture and the tempo of cumulative cultural evolution

The ability to build upon previous knowledge—cumulative cultural evolution—is a hallmark of human societies. While cumulative cultural evolution depends on the interaction between social systems, cognition and the environment, there is increasing evidence that cumulative cultural evolution is facilitated by larger and more structured societies. However, such effects may be interlinked with patterns of social wiring, thus the relative importance of social network architecture as an additional factor shaping cumulative cultural evolution remains unclear. By simulating innovation and diffusion of cultural traits in populations with stereotyped social structures, we disentangle the relative contributions of network architecture from those of population size and connectivity. We demonstrate that while more structured networks, such as those found in multilevel societies, can promote the recombination of cultural traits into high-value products, they also hinder spread and make products more likely to go extinct. We find that transmission mechanisms are therefore critical in determining the outcomes of cumulative cultural evolution. Our results highlight the complex interaction between population size, structure and transmission mechanisms, with important implications for future research.


Do you have any concerns about statistical analyses in this paper? If so, please specify them explicitly in your report. No
It is a condition of publication that authors make their supporting data, code and materials available -either as supplementary material or hosted in an external repository. Please rate, if applicable, the supporting data on the following criteria.

Do you have any ethical concerns with this paper? No
Comments to the Author From the outset of cultural evolution research understanding the transmission of information within groups and populations has played a major role. In recent years, observational and theoretical work has shown the importance of different aspects of this complex process on cultural dynamics, from transmission modes to population size and connectivity. Only recently have actual social network aspects moved into the field's focus. The present manuscript provides a systematic study of different network types, network sizes, and network connectivity, and their combined and individual effects on the emergence of new traits and their spread in a population. . I enjoyed reading this manuscript. In my opinion, the topic is timely and relevant to the field. There is very little to criticise about the overall presentation of the work both in text and figures. The Background provides relevant information. The methods are (mostly) written clear and concise. The results are generally well presented and discussed.
Here is a list of specific comments: ll. 163-168 "For each population size, we used the Cumulative Incidence Function to estimate the proportion of simulations in which agents reached the recombination of each cultural lineage's products into a final high-payoff product. We used the nonparametric Kaplan-Meier product limit estimator to represent the time intervals based on observed recombination events from 5,000 simulations from model 1, calculating 95% confidence intervals with the Greenwood estimator." -Compared to the otherwise detailed description in the methods, there are three concepts mentioned here that should probably receive a little bit more attention. Why do the authors use them, how do they work, and/or what do they mean? l. 270 " Fig. S5" -There is neither a Figure 5 nor a Figure S5 in the files I could access ll. 322-324 "Our simulations demonstrate that the contribution of large differences in connectivity outweighs any effects pertaining to architecture, at least when information is broadcast (i.e. a one-to-many diffusion mechanism)." -Maybe rephrase. What do the authors mean by the contribution of large differences in connectivity? Figure 4 was confusing to me. What are the y-axes showing? In B-D there are too many lines colours and shades, the message is not clear, it is neither intuitive to grasp what the authors want to convey here, nor is it covered by the figure's caption. Figure S1, the different types of lines are hard to differentiate, maybe consider using different colours for the four possible traits (instead of using it for the different network types, which are already clearly delineated by the graph plots and the headings).
The deposited data, code, and results on GitHub are a great addition to the manuscript. (Note: I noticed that some files are missing, e.g. output for model 1 and model 2 in 3_R_agent_based_models, and the code for figures 1,2, and 4 in 4_create_figures). If possible, and to improve replicability, I would suggest adding even more comments, especially to the simulation code.

Review form: Reviewer 2
Recommendation Accept with minor revision (please list in comments)

Scientific importance: Is the manuscript an original and important contribution to its field? Good
General interest: Is the paper of sufficient general interest? Excellent Quality of the paper: Is the overall quality of the paper suitable? Good Is the length of the paper justified? Yes Should the paper be seen by a specialist statistical reviewer? Yes Do you have any concerns about statistical analyses in this paper? If so, please specify them explicitly in your report. No It is a condition of publication that authors make their supporting data, code and materials available -either as supplementary material or hosted in an external repository. Please rate, if applicable, the supporting data on the following criteria.

Do you have any ethical concerns with this paper? No
Comments to the Author This paper presents two agent-based models that explore how network architecture affects cumulative culture evolution. Six different network architectures (random, small-world, lattice, modular, modular lattice, and multilevel) capturing different levels and combinations of clustering and modularity have been implemented in populations with different sizes and densities of connections. The simulations confirm recent results that combinatorial innovation is optimized at intermediate densities of connections but also reveals that the optimal level of connectivity varies with population size. Although not entirely surprising, this result is important to the current debate regarding whether humans' unique multilevel social structure accelerates cumulative cultural evolution. The comparison between the two models implementing either one-to-many or one-to-one diffusion processes also reveals interesting results and highlight the complex interaction between population size, structure and transmission mechanisms. My opinion is that, although the paper does not yield any major finding, it provides a lot of food for thought to the large community of scholars interested in the relationship between demography and cumulative culture. The goal of the paper of disentangling the relative contribution of network architecture from those of connectivity and population size is clearly an important one. My only concern is that the authors limited their investigations to a situation where innovations of cultural products can only take place along two cultural lineages. I don't think this threatens the validity of their main result (that is optimal level of connectivity varies with population size) but this clearly increases the chance that cultural products all emerge from the same lineage. I would expect the results of their simulations to be less influenced by stochastic events were the fitness landscapes to include more cultural lineages. I would recommend the authors to either run additional simulations to verify this relationship or explicitly mention this limitation when they discuss the role of stochastic events on cumulative culture.

25-Jan-2021
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Best wishes, Dr Robert Barton mailto: proceedingsb@royalsociety.org Associate Editor Board Member: 1 Comments to Author: This paper uses agent-based models to examine how the structure of social networks influences cumulative cultural evolution. This is a critical issue in the field of cultural evolution, with relevance across a range of fields and the two reviewers agree, as do I, that the paper is interesting and timely. However, as Reviewer 1 points out, there are a number of places where revisions are needed to provide further detail and clarity on aspects of the methodology and presentation of results (some figures also seem to be missing). Reviewer 2 has a deeper concern that, by allowing innovations to occur along only two cultural lineages the models artificially increase the probability that all cultural products emerge from the same lineage. If possible, additional simulations would be very useful to address this concern.
Reviewer(s)' Comments to Author: Referee: 1 Comments to the Author(s) From the outset of cultural evolution research understanding the transmission of information within groups and populations has played a major role. In recent years, observational and theoretical work has shown the importance of different aspects of this complex process on cultural dynamics, from transmission modes to population size and connectivity. Only recently have actual social network aspects moved into the field's focus. The present manuscript provides a systematic study of different network types, network sizes, and network connectivity, and their combined and individual effects on the emergence of new traits and their spread in a population. I enjoyed reading this manuscript. In my opinion, the topic is timely and relevant to the field. There is very little to criticise about the overall presentation of the work both in text and figures. The Background provides relevant information. The methods are (mostly) written clear and concise. The results are generally well presented and discussed.
Here is a list of specific comments: ll. 163-168 "For each population size, we used the Cumulative Incidence Function to estimate the proportion of simulations in which agents reached the recombination of each cultural lineage's products into a final high-payoff product. We used the nonparametric Kaplan-Meier product limit estimator to represent the time intervals based on observed recombination events from 5,000 simulations from model 1, calculating 95% confidence intervals with the Greenwood estimator." -Compared to the otherwise detailed description in the methods, there are three concepts mentioned here that should probably receive a little bit more attention. Why do the authors use them, how do they work, and/or what do they mean? l. 270 " Fig. S5" -There is neither a Figure 5 nor a Figure S5 in the files I could access ll. 322-324 "Our simulations demonstrate that the contribution of large differences in connectivity outweighs any effects pertaining to architecture, at least when information is broadcast (i.e. a one-to-many diffusion mechanism)." -Maybe rephrase. What do the authors mean by the contribution of large differences in connectivity? Figure 4 was confusing to me. What are the y-axes showing? In B-D there are too many lines colours and shades, the message is not clear, it is neither intuitive to grasp what the authors want to convey here, nor is it covered by the figure's caption. Figure S1, the different types of lines are hard to differentiate, maybe consider using different colours for the four possible traits (instead of using it for the different network types, which are already clearly delineated by the graph plots and the headings).
The deposited data, code, and results on GitHub are a great addition to the manuscript. (Note: I noticed that some files are missing, e.g. output for model 1 and model 2 in 3_R_agent_based_models, and the code for figures 1,2, and 4 in 4_create_figures). If possible, and to improve replicability, I would suggest adding even more comments, especially to the simulation code.

Referee: 2
Comments to the Author(s) This paper presents two agent-based models that explore how network architecture affects cumulative culture evolution. Six different network architectures (random, small-world, lattice, modular, modular lattice, and multilevel) capturing different levels and combinations of clustering and modularity have been implemented in populations with different sizes and densities of connections. The simulations confirm recent results that combinatorial innovation is optimized at intermediate densities of connections but also reveals that the optimal level of connectivity varies with population size. Although not entirely surprising, this result is important to the current debate regarding whether humans' unique multilevel social structure accelerates cumulative cultural evolution. The comparison between the two models implementing either one-to-many or one-to-one diffusion processes also reveals interesting results and highlight the complex interaction between population size, structure and transmission mechanisms. My opinion is that, although the paper does not yield any major finding, it provides a lot of food for thought to the large community of scholars interested in the relationship between demography and cumulative culture. The goal of the paper of disentangling the relative contribution of network architecture from those of connectivity and population size is clearly an important one. My only concern is that the authors limited their investigations to a situation where innovations of cultural products can only take place along two cultural lineages. I don't think this threatens the validity of their main result (that is optimal level of connectivity varies with population size) but this clearly increases the chance that cultural products all emerge from the same lineage. I would expect the results of their simulations to be less influenced by stochastic events were the fitness landscapes to include more cultural lineages. I would recommend the authors to either run additional simulations to verify this relationship or explicitly mention this limitation when they discuss the role of stochastic events on cumulative culture.

08-Feb-2021
Dear Dr Cantor I am pleased to inform you that your manuscript entitled "Social network architecture and the tempo of cumulative cultural evolution" has been accepted for publication in Proceedings B.
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Thank you for your fine contribution. On behalf of the Editors of the Proceedings B, we look forward to your continued contributions to the Journal. We appreciate the time invested by the two Referees and the Associate Editor in this thorough review. We were particularly encouraged by the positive remarks by the Reviewer#2 highlighting that the "goal of the paper of disentangling the relative contribution of network architecture from those of connectivity and population size is clearly an important one" as well as by the Reviewer#1 who emphasize that our work "is timely and relevant".
In addition to such very positive feedback, both Reviewers provided additional critical comments. We found these comments extremely helpful for improving the readability of our text and figures. We addressed every comment, giving special consideration to the suggestion by Reviewer #2 on the number of cultural lineages considered in our simulations. Reviewer #2 suggested that the influence of stochasticity might be lower when including more than two cultural lineages. We decided to address this in the discussion, since running simulations with more than two lineages would require multiple decisions about how to implement these (e.g. should the final high pay-off product include products of all lineages or only two?), which in turn could influence the outcomes to beyond the scope of our current manuscript. In our revised Discussion, we now discuss how future work can address these open questions appropriately.
By addressing these suggestions, we now feel that our work has gained both in value and clarity. Please find our point-by-point responses below, as well as the revised manuscript with all changes tracked. We therefore resubmit the revised version of our manuscript for your consideration for publication in Proceedings of the Royal Society.
Thank you for the insightful reviews and excellent editorial services provided. Comment#1 by Associate Editor: This paper uses agent-based models to examine how the structure of social networks influences cumulative cultural evolution. This is a critical issue in the field of cultural evolution, with relevance across a range of fields and the two reviewers agree, as do I, that the paper is interesting and timely. However, as Reviewer 1 points out, there are a number of places where revisions are needed to provide further detail and clarity on aspects of the methodology and presentation of results (some figures also seem to be missing). Reviewer 2 has a deeper concern that, by allowing innovations to occur along only two cultural lineages the models artificially increase the probability that all cultural products emerge from the same lineage. If possible, additional simulations would be very useful to address this concern.
Authors' reply: We are grateful for such a welcoming perspective on the relevance and timeliness of our questions and approach. We appreciated the reviewers' comments as they helped us to significantly improve the clarity and presentation of our findings. We were particularly grateful for the critical point raised by Reviewer 2 on the set up of our models.
We understand that, relative to a case where several cultural lineages are considered, our models accounting for two cultural lineages may increase the chance that all cultural products all emerge from the same lineage. The reviewer suggested two ways around this-to either develop further models to allowing innovations to occur along multiple cultural lineages, or acknowledge the potential limitations of our approach. After carefully consideration, we opted to rephrase our discussion section to give full consideration to the influence of stochastic events in the context of the number of cultural lineages. Our decision was based on (i) the technical implementation of multiple lineages in our current models, and (i) the original scope of our study.
In revisiting the structure of our agent-based models, it became clear that adjusting the code to include multiple cultural lineages implies a series of new design decisions that are not trivial. For instance, one needs to decide the rules for the agents to integrate inventory items of multiple lineages, and how to design the payoff structure for the resultant high-value products. Such decisions will have an impact on the model outcomes, therefore will require an entirely new model to accommodate them. Our concern is that such changes in design can cause their outcomes to be incomparable with our previous models, which were themselves built upon empirical and theoretical research that considered only 2 cultural lineages. With an entirely new model, and new sets of results and figures, we would require more room for discussion, which is beyond the scope of the current manuscript, and obscure our main message on the effects of optimal levels of connectivity varying with population size and social architecture.
We believe that the point raised by the reviewer can only be appropriately tackled in a follow-up study. Therefore, we opted to follow their second suggestion. We have carefully revised our Discussion section to add a full paragraph (L343-359) that (i) acknowledges the limitation of our approach with few cultural lineages when discussing the role of stochasticity on cumulative culture evolution, but also (ii) provides avenues for future work aiming to develop specific models that verify the relationship between stochasticity and diversity of cultural lineages.

COMMENTS BY REVIEWER 1
Comment#1 by Reviewer 1: From the outset of cultural evolution research understanding the transmission of information within groups and populations has played a major role. In recent years, observational and theoretical work has shown the importance of different aspects of this complex process on cultural dynamics, from transmission modes to population size and connectivity. Only recently have actual social network aspects moved into the field's focus. The present manuscript provides a systematic study of different network types, network sizes, and network connectivity, and their combined and individual effects on the emergence of new traits and their spread in a population.
I enjoyed reading this manuscript. In my opinion, the topic is timely and relevant to the field. There is very little to criticise about the overall presentation of the work both in text and figures. The Background provides relevant information. The methods are (mostly) written clear and concise. The results are generally well presented and discussed.
Authors' reply: Thank you for the very positive feedback highlighting the strong points of our work. We appreciate the attentive review and useful suggestions, each of which we addressed as follows. Note that line numbers refer to the version with in-line tracked changes.
Comment#2 by Reviewer 1: ll. 163-168 "For each population size, we used the Cumulative Incidence Function to estimate the proportion of simulations in which agents reached the recombination of each cultural lineage's products into a final high-payoff product. We used the nonparametric Kaplan-Meier product limit estimator to represent the time intervals based on observed recombination events from 5,000 simulations from model 1, calculating 95% confidence intervals with the Greenwood estimator." -Compared to the otherwise detailed description in the methods, there are three concepts mentioned here that should probably receive a little bit more attention. Why do the authors use them, how do they work, and/or what do they mean?