This manuscript presents a study linking social structure to measures of individual health in captive primates. The authors show that individuals who were more connected when considering “multiplex” networks were healthier, while the opposite effect was found in “uniplex” networks. I found the results potentially interesting, but I have serious reservations regarding the network definitions and the analysis.

The most major issue is that multiplex networks are a type of multilayer networks, where there are several types of interactions between the same set of nodes/individuals. Here, both multiplex and uniplex interactions were analyzed as single-layer networks, with both types of networks using only one interaction type (lines 204-206). Basically, instead of analyzing one grooming network where some dyads also huddled, the authors split the same grooming interaction into two different networks. The authors did not offer any biological reasoning for defining the two networks, and I have never seen such analysis. This type of analysis makes the interpretation of the results very difficult. The networks were divided based on one interaction that was not included in the analysis (huddling). I suggest the authors rethink the analytical approach. The differences between the two networks can come from individual traits, such as sex, kinship, or rank. In that case these factors should be included in the analysis.

Other comments:

Line 73 and on: At some point I asked myself if this discussion relates only to non-human animals. It is worthy to clarify that, because the beginning of the introduction referenced both humans and other animals.

Line 100: Multiplex networks should be defined.

Line 129: Were there dyads that only huddled? How were these cases treated?

Line 133: Modularity and clustering are not the same. A network may be highly modular but not clustered, if in each module, or sub-group, clustering is low.

Lines 164-176: This paragraph should be part of the introduction. It provide general information on the species and why it was chosen.

Line 188: How were individuals identified?

Figure 1: Is there any text in each node? It’s impossible to read so either enlarge it or delete it.

Statistics: Was there any treatment of the fact that network measures are not independent? Usually, some sort of null model based on permutations of the data is being used to compare to the observed patterns.

Dominance: Perhaps I have missed it, but was there a correlation between dominance and measures of centrality in the multiplex network? I am wondering if the main result could be, at least to some extent, be explained by dominance. Readers would benefit from data addressing this question, for example by adding rank to the selected models and testing its effect.

Line 261: Multidimensional vs unidimensional network metrics?

Line 271: Why undirected?

Figure S1: What is the number of dyads without interactions?

Line 265 Table S2 or table S3?

I really like the idea of the paper and also the aim to explore social relationships in more complex way. The paper is very well written, the text is clear and comprehensive. The authors cite relevant literature sources. The specific aim of the study is clearly presented. The sample size in terms of groups and individual females is impressive. The paper is overall very informative in terms of discrepancies in previous studies and methods used.

My major concern stems if the presented results of the comparison of uni vs multiplex networks is really representative of the two types of networks or if it is more related to the way how data were filtered for each network. In the methods section Affiliative network analysis the authors stated that “…and a network containing edges for dyads that groomed but were never seen huddling (uniplex affiliative relationships).“ However if one would do an independent study using grooming for uniplex network one will not filter out edges based on the huddling behavior thus the resulting uniplex network based on grooming will be different of that presented by the authors. So it might not be completely fair to say that the uniplex network is “grooming only” because is grooming only and never huddling”, thus grooming ties between individuals who also huddled were not included in this grooming network. This approach in my opinion leads to bigger differences in the two networks which is not necessarily connected to multiplex vs uniplex networks but to the way how the edges were filtered.

In other words if the uniplex network would be based on all grooming edges (without filtering out the dyads that huddle as well) would there be same differences between the two networks? I understand that using the approach the authors made the two networks rather independent in terms the data used but then I think you are comparing rather two different types of relationships one based on grooming and huddling and one based on grooming only and never huddling but not necessarily uniplex and multiplex networks. 

This also has consequences when comparing results of previous studies which in many cases would use “full” grooming uniplex networks which is not completely comparable with the uniplex grooming network in this study.

Additional comments:

Although authors stated in conclusion that is not clear if using different behaviors like proximity would provide similar results, still I would like to know why huddling was selected for this study? Why not the more traditional proximity or body contact? It makes me think that the authors in fact did expect different results with huddling behavior.

Is it possible from this study to say if huddling might be also beneficial just as a thermoregulatory behavior? In other words, it is not beneficial for one’s health because of the social relationship it represents but because one is not cold?

Just a nitpicky question which is not specific to this paper but Is the word “multiplex” warranted if there are two types of interactions only? 

The paper proposed very interesting approach in order to assess how the quality of affiliative relationships affects the health status of Rhesus macaques. Overall, I found the study well-designed and nicely presented. Although the results seem robust and convincing, you will find several questions and comments below requesting additional input from the authors to justify and clarify some analytical approaches and expressions in the manuscript.

Comments and questions:

Would you please explain why you did not examine the opposite version of the network, i.e. creating huddling network and using grooming to filter it? The authors used huddling degree in the model to exclude the possibility that huddling behavior itself has an effect on the inflammation, but to be more precise, I thought it is better that you also compare only huddling and, huddling and grooming network.

Line 80: I suggest you to change “assess the quality of affiliative social relationships” to something like “assess the overall amount/frequency of multiple behaviors”. To my understanding, DSI is just a method of averaging all the correlated dyadic interactions, thus it is indicating the overall frequency of affiliative behavior and not actually measuring the quality (and I guess it is the point of your discussion).

Line 109: It is better to specify what is “huddling” behavior here, as it is not a very common term (especially for non-primatologist). 

Line 113-115: “Therefore to understand the impact of social relationships on individual health and fitness, we must examine the cumulative impact of an individual’s diversity and breadth of social relationships to really understand their potential influence on health.”

I felt this part is duplicating the meaning. Please revise.

Line 187: Did you also observe other types of direct affiliative behavior? As you mentioned “Affiliation in primates takes many forms, including grooming, huddling, proximity, embracing, and less commonly coalitionary support” in Introduction, I presume that huddling and grooming are the main forms of direct affiliations, but I wondered if there is a possibility that other affiliative behavior potentially affects the inflammation.

Line 213: To my understanding, information centrality is based on concept of efficient propagation of information in a group. I rarely see it is used in the context similar to this study. Please justify the reason of using it here. In addition, the authors explain that information centrality indicates the social cohesion, but you should put the citation or more detailed explanations.

Table 2: As I mentioned above, I thought it is better to put citation for each interpretation of the network metrics.

Figure 1. I cannot read the labels of each node. Also, the image resolution seems not good enough. Please make it clearer.