This paper describes a novel method to assess the integrity and amount of mixing between excavation layers. The method, termed the TSAR approach (Topological Study of Archaeological Refitting), uses network typologies and edge metrics to assess the level of cohesion and admixture between two layers. The nodes (artifacts) are connected based on object refitting and adjusts for sample size. The utility of this method compared to other approaches is tested using simulated data and excavation data. The author created a package in the R programming language to facilitate the method, which is freely available from R’s package archive and includes some of the data used in the article. Furthermore, the R package allows users to generate their own test scenarios. Assessing stratigraphic integrity is often a critical task for interpretation. Refitting alone is enough to determine whether some mixing occurred but a quantitative assessment of the mixing requires a more complex methodology. This is the problem addressed by the author. I found the overview of current methods and the comparison to the proposed TSAR method convincing and reasonable. The application of network methods is, to my knowledge, a novel approach that solves a challenging problem and reveals interpretable results. The use of both simulated data and field data to test the method strengthens the author’s argument. As stated in the article, testing this method in additional scenarios is necessary but not required to justify recommending this paper. I applaud the inclusion of a pdf containing the code used for analysis and explaining the steps. The development and publishing of an R package based on this method is a significant contribution. I would also appreciate the Rmd file as an additional supplemental document for easier reproducibility, but the code can be copied from the pdf. I recommend endorsing this paper and found no major concerns that should be addressed. There are a few minor corrections I have suggested included in the pdf of the article that I have submitted.

I think this is a valuable paper that should be published. The paper proposes a novel method to evaluate the stratigraphic integrity of archaeological deposits by combining refitting studies with graph theory. Usually, refitting work has been an ad hoc process providing some clues for excavators on how archaeological deposits might be related. This paper add significant methodological rigor to realise the full potential of refitting studies to assess the stratigraphy at complex sites. The most immediate relevance is probably for Palaeolithic cave sites and the like, but the method is potentially relevant to a wide range of situations.

I have to point out though I am not a statistician or particularly well versed in mathematics or graph theory. The calculations in the paper are therefore a bit beyond my abilities. I therefore hope that another reviewer was assigned to this paper that has this expertise and can comment on the mathematical aspects in more detail.

Three points I would like to raise are these: 1) On Page 3, the first Figure and the discussion related to it are somewhat abstract. I would suggest to add a real-world archaeological example to explain to the dumb folks like me what this actually means in a concrete archaeological example. Otherwise the abstraction might scare people off. 2) It would be nice, although not absolutely necessary, to see how this method could be deployed in conjunction with other methods of stratigraphic analysis, as well as Bayesian modelling of radiocarbon dates. I would think that this method would be extremely useful in fine-tuning the modelling of C14 dates. It would be useful if the author could maybe comment on that and give an idea how this method might be used in combination with others? 3) I guess this method is still under development, but I wonder if the author might be able to comment a little more on how we could make this method something more commonplace? At the moment, it seems fairly inaccessible, so what will be the pathway to making it more accessible to a wide range of archaeologists (especially those like me who are a bit challenged by the maths)?

In conclusion, I think this is a solid paper and I would recommend publishing it. It can be published as it is, but perhaps the author can take some of the comments I made above into consideration.

Review of “The strength of parthood ties. Evaluating archaeological layers using graph theory to model objects refitting” by Sébastien Plutniak

This paper presents a novel approach to assessing the mixing of archaeological layers using refitting analysis and the topology of refits. This is certainly different than most previous approaches which, as the author notes, rely largely on assessing counts of refits but not the structure connections among them. I think this approach is interesting and has the potential to be useful in helping researchers think thorough and simulate different scenarios involving fragmentation, deposition, and post-depositional processes to aid in the interpretation of real archaeological data. There are some changes I would suggest that I think could help to improve the clarity and usability of this manuscript and I outline those in detail here. I go through each section of the paper and then return to some overarching comments on the method and presentation at the end. The introductory section to the paper is clear and presents a good justification for why this approach could be useful and how it expands upon the existing literature. I am not particularly familiar with the body of literature cited on refits and disturbance processes, but the article cites several classic papers and a range of newer studies that capture much of the literature I have seen.

The “preliminary definitions” section includes some useful information, but I also think this could be reduced not just to save space but also to add to the clarity of the argument. The distinction between “connection” and “similarity” is useful but I found the discussion of this distinction a bit confusing without a second glance. The reference to connections relying on “solid-state physics” and then the next sub-section with the discussion of Queen and Rook contiguity and the analogy to spatial analysis made a pretty clear distinction a bit more muddled in my reading. I section 2.1.3 could be basically eliminated and section 2.1.2 could be simplified to make the two basic points that are necessary for the rest of the paper 1) archaeologists identify potential refits by either identifying pieces that fit together across substantial surfaces in 3D space or alternatively by looking for similarities in the objects themselves and 2) you are only focused on the former in this paper. I think a very simple definition of connection and similarity refits and Figure 2 is plenty and felt that the Queen/Rook example did not add clarity and was not referred to again so could be removed.

Section 2.2 was straight forward and Table 1/Figure 4 are helpful. The method chosen for edge weighting makes sense and is clearly described with the equation as are the definitions for cohesion and admixture. The measures selected for assessing the topological properties of refits make intuitive sense as do the alternative methods and the criticisms of them (such as the issue of sample size and modularity).

The TSAR simulator is a sensible approach to evaluating the potential generative processes creating empirical patterns. There are several extensions that I could think of to this procedure (and some of those are mentioned in the conclusions) but this model is a good beginning. The parameter descriptions in table 2 and the flowcharts in Figure 6 make sense and help me understand what is happening under the hood with one exception. Reading this text, it wasn’t clear to me how the “merge graphs” step in the two initial layers works. I can think of several ways you might have chosen to implement this, but I do not think the choices you made are completely clear in this draft or the supplement. I think a short paragraph would be needed to address this.

One major question I have about this approach that is not discussed here or elsewhere is the degree to which missing connections would hamper our ability to connect empirical patterns to generative processes. Given the nature of fragmentation and post-depositional processes I expect that it would be common for archaeologists to miss refits due to damage to potential conjoining edges of pieces or all manner of other processes. How would this influence your results? I think this issue merits some discussion at least and perhaps some small analyses. I had one suggestion the author could consider here. Missing connections could potentially be evaluated with an additional global parameter such as a probability that a connection is removed once the graphs have been formed to essentially simulate “missed” or unidentifiable connections. Especially with the focus on “connections” rather than similarity, I think it’s likely that missed connections would be present in any empirical refit study and this simulation model provides a setup that could help evaluate the impacts. I’d be interested in how this influences the shape of distributions in Figure 9, for example.

Moving on to the examples, I think the theoretical graphs, the Liang Abu empirical example, and simulation based on the empirical example provide a good three-pronged approach to evaluating the technique. I have some questions about the results that I think could require some clarification in the text.

For the first analysis where archaeologists were asked to sort the theoretical graphs you got results that were extremely variable which is not surprising to me because it seems a pretty difficult task to evaluate these kinds of topological patterns on sight. In section 3.1.1 you compare the admixture model and others to the archaeological intuition. Given the variability in the archaeological intuitive coding, I don’t know that the methods used here fitting in the same cluster is a particularly convincing argument in favor of these new methods (and that’s okay). To me, the results you present suggest that people are generally not great at evaluating the relative order of topological patterns and that, in and of itself, argues for some sort of automated approach like you’ve developed here. The clustering diagram and the discussion in the text is a bit confusing, however, as it stands as not every bar in the cluster diagram is labeled and it’s unclear which “secondary clusters” you are referring to in the text. Beyond this, the Figure 8 caption says you are evaluating the four methods but it’s not entirely clear to me which is represented by which label in the existing cluster tree diagram. I think this figure will need to be modified.

The results discussed and shown in Figure 9 are helpful for thinking about how different values for these variables change with variation in balance and disturbance. I think this figure could be improved with a bit more guiding text. The x-axis is labeled Cohesion but Admixture is shown on this same axis with the same 0-1 scale so I would suggest changing that. It would also help to label the rows and columns with balance and disturbance respectively. Also, I think this is an excellent place for you to return to your Table 1 insights and discuss how you might interpret various of these plots in light of that table. Finally, I would suggest just increasing the border for the Admixture color as it isn’t really visible in the plots further to the left.

Figure 10 works and makes the point discussed in the text well. It would be interesting if these were also associated with a non-parametric correlation test like Spearman’s rho just to get a sense of how they differ in terms of rank order correlations. Consider splitting Figure 11 into two figures so that the labels in the boxplot are clearer. The differences in the stabilization of disturbance values for edge count and admixture (edge betweenness) are interesting.

The empirical example from Liang Abu is informative for thinking about how this all would actually work in practice. Notably, the values for cohesion differ in a pretty obvious way but the other three measures (excluding Modularity) show pretty minor differences (and all show 0 for the 0&1 comparison which makes sense). How might you think about these results in relation to your schema in table 1? Is the difference in Cohesion substantial? What would you interpret as a meaningful difference here? Discussing this a bit in section 3.3.1 would be helpful in walking a reader through what you’ve done and provide a justification for the hypothesis testing and simulation you do in the next section.

The hypothesis testing is an important part of the overall argument and I have some questions and need a bit of clarification in a couple of places here. I followed along with your results and also replicated them in R using the code in the supplement. I found the presentation of these results to be fairly brief given that some major interpretations hinge on them. The set up makes sense as your question is basically whether you could consider this context as having one or two layers initially. You use Wilcox test to assess rank order differences in several variables, which seems like a sensible approach and find evidence for differences in the simulated distributions and not others. Given that you have a low but non-null admixture you are really conducting these simulations to assess differences in cohesion in terms of the schema you laid out in table 1. Since scenario 3 and scenario 4 have the same interpretation (and admixture doesn’t differ for either scenario) how do the results you present in this section and Figures 12 and 13 related to the setup you initially provided in table 1? I feel like this needs more discussion. The results for specific variables differ in terms of which hypothesis is more or less supported. The results seem equivocal for several variables and looking at the supplement the although there are statistically significant rank order shifts the distributions are quite similar for some variables suggesting the actual effect is small. You land on an interpretation of two independent layers but I think this needs to be better justified. Given the low admixture value and the setup in table 1, is there a scenario that would have generated different results? I would also be interested in seeing an exploration of the relationship between structural admixture and the absolute difference in cohesion for a range of scenarios.

In general, the results outlined here make sense for this particular example, but I think this empirical example is only able to capture a small range of the possible scenarios that might be encountered in real settings. In general, I would like to see what kind of numbers would generate higher admixture values and how those might compare to what is shown here. In general, the set up in the beginning of the paper outlines the relationship between admixture and cohesion in table 1 but this doesn’t come in to play in the interpretation of the empirical example and I think this makes the final interpretation of the hypothesis test less impactful. I would suggest returning to the table 1 set up in the hypothesis testing section and perhaps even discussing in more detail other realistic simulated datasets that would land you somewhere else on table 1.

Overall, I think this method is potentially useful and most of the implementation was described in an understandable way. I think the major thing that could be improved is the connection between the initial discussion of the method (section 2.2 in particular) and the hypothesis testing and simulation in the end.

In addition to the text and supplement, I also installed and reviewed the R package. I was able to install this but I had to roll back to and earlier (3.6) version of R as one dependency was not available for the most recent version (4.0) of R. If that is an easy fix (looking at the BiocManager packages) it would be helpful to potential future users. As for the supplement, I was not able to fully replicate those results because there are a couple of files that were called in the code that weren’t provided on the OSF link as the markdown document in pdf was the only document posted. I think it would be useful to post the supplement as an Rmd file along with all of the required files to completely replicate the results. Once I was able to get the package installed in R 3.6, I was able to run all of the functions without any problems.