PCOMPBIOL-D-25-00481

Molecular surveillance of multiplicity of infection, haplotype frequencies, and prevalence in infectious diseases

PLOS Computational Biology

Dear Dr. Tsoungui Obama,

Thank you for submitting your manuscript to PLOS Computational Biology. I apologise for the extended time to get back to you, but we have now secured two reviews of your manuscript.

After careful consideration, we feel that it has merit but does not fully meet PLOS Computational Biology's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript within 60 days Sep 29 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at ploscompbiol@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcompbiol/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter

We look forward to receiving your revised manuscript.

Kind regards,

James M McCaw, PhD

Academic Editor

PLOS Computational Biology

Jennifer Flegg

Section Editor

PLOS Computational Biology

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Reviewers' comments:

Reviewer's Responses to Questions

Reviewer #1: Obama et al., present a novel statistical method for inferring the multiplicity of infection MOI and haplotype frequencies of pathogens within individuals from genetic data. The method addresses an important problem, as MOI can significantly complicate efforts to model the transmission, persistence and prevalence of infectious diseases.

Due to time constraints, I have not been able to go through all the derivations provided in full-detail. However, I have checked that the associated code implementing the methods runs as described. While I believe that this method provides a valuable addition to the literature, its limitations could be better described and I have outlined a number of issues that need to be addressed prior to publication.

Major issues:

- The authors focus primarily on data that considers only a very small number of loci (<100 markers). While this is certainly useful, many modern genomic studies of major human pathogens including Malaria typically consider many thousands of loci. For example, the MalariaGen project has whole genome sequencing from over 20,000 Plasmodium falciparum samples. It is important that the authors more clearly demonstrate the computational limitations of their approach. This could easily be done by generating a plot of the compute time versus dataset complexity in both the number of loci and number of samples. The authors should also describe some of the literature that attempts to make use of the large number of loci to more accurately estimate MOI and phase genotypes using WGS data. For example, methods such as DEploid (Zhu et al., 1017) and coiaf (Paschalidis et al., 2023) can consider many thousands of SNPs in a reasonable amount of time.

- The manuscript is currently quite hard to follow as many of the parameters are defined in the methods but not in the main text where they are first introduced (i.e lines 197-200). While I appreciate that including all derivations in the results would be tedious, the parameters should all be defined where they are first stated.

- The implementation of the model currently estimates unrealistically low haplotype frequencies. For example, line 29 of the ‘MOI-tutorial.R’ code outputs many (~50%) haplotypes with frequencies well below the limit of detection (0.01) given the example only contains 100 samples. The tendency of the approach to assign unrealistic frequencies to certain haplotypes needs to be discussed carefully in the text and perhaps a warning could be associated with results such as these that are unlikely to be accurate. Ideally, the method would include an approach to shrink these frequencies to zero perhaps using a regularisation penalty.

- Identifying SNPs and microsatellites is an error prone process. It is important that the authors consider what impact errors in the input data have on the results of the method. A plot indicating the impact of different levels of error in the input data would be very useful to wider readers.

Minor issues:

- The authors refer to the method being applicable to ‘arbitrary genetic architecture’ in a number of places. It is not clear what ‘arbitrary’ means in this context. For example, the method is not applicable to loci that are not consistently present in all genomes of a species. I think this statement should be replaced by a more specific one.

- The summary of alternative methods (lines 94-107) should be made slightly more detailed. Currently, it requires the reader to look up many of the references provided to understand what the authors are referring to (i.e I don’t automatically have a good intuition for what ‘ad-hoc methods’ are). It would be great if the ‘ad-hoc’ methods and the first statistical model (ref. 2) are explained with an additional sentence or two.

- Line 74: “Co-transmitted” would normally mean the transmission of multiple genotypes within a single transmission event. This does not match up with the definition of MOI which is correctly and nicely stated later on.

- Some of the figures have quite low resolution which should be addressed.

Reviewer #2: Tsoungui Obama and Schneider propose a method to estimate haplotype frequencies, haplotype prevalences and the multiplicity of infection based on unphased data from multiple multiallelic markers. The key advance relative to the authors’ previous work (references [10] and [12]) appears to be a generalisation to the case of multiple multiallelic markers. An expectation-maximisation algorithm is derived to compute maximum likelihood estimates for haplotype frequencies and the multiplicity of infection, which are then plugged into derived formulae for haplotype prevalences. Asymptotic variances and finite sample properties of these estimators are considered. The practical utility of this method in the context of malaria genomic epidemiology is illustrated through an analysis of markers associated with drug resistance in Plasmodium falciparum.

Major comments

• It would be useful if the authors could articulate more clearly the advance represented by the current manuscript, relative to the references [9], [10], [12], [22] and [25], particularly in the introduction and discussion. For instance, in the section “Deriving the EM-algorithm” of the Mathematical Appendix, the authors state that their “derivation generalizes the ones in [1] for n biallelic loci and [2] for two multiallelic loci to the case of n multiallelic loci. Namely, it turns out that the structure of the derivations is almost identical and only needs slight modifications”; this parallel, however, does not seem to be mentioned in the main text.

• To improve the readability of the main text, perhaps the authors could consider introducing a table of notation? The equations stated in the main text results, with forward-reference to equations in the methods, are difficult to interpret. For instance, the PGF G first appears in Equation (1b) but is defined later on in the text.

• The authors frame the statistical model with respect to the notion of superinfection vs co-transmission. However, my understanding is that the statistical model is more simply predicated on the assumption of a Poisson-distributed number of unrelated/independent clones within a sample. I wonder if it might be clearer to introduce the model with respect to the latter notion, and then link this back to a more ‘mechanistic’ notion of superinfection? To aid readability, perhaps the authors could include a self-contained summary or list of model assumptions?

Minor comments

• Perhaps the authors could provide several examples of pathogens or organisms, beyond falciparum malaria, to which this method could be applied? Perhaps the authors could also comment on the interpretation of superinfection if this method was applied to vivax malaria, especially given the inoculation of multiple hypnozoites per mosquito bite and related relapses?

• Some of the terminology used by the authors is ambiguous. For instance, the term “general genetic architecture” is defined to refer to “multiple multiallelic markers” on lines 590 and 647, but is used earlier in the introduction without definition. Rather than referring to “more complicated underlying genetic architectures” or “simple genetic architectures” (line 118), it would be useful to explicitly specify the case in consideration.

• In Table 2, why are there MOI estimates < 1if the method is tailored to disease-positive specimens?

• Line 783: should “beta distribution” be replaced with “gamma distribution”?

• In the Introduction (line 102), the authors mention that references [13] and [14] also handle multiple multiallelic markers; given the generalisation of the authors’ previous work to the case of multiple multiallelic markers appears to be a key advance, a brief explanation of the key difference between references [13] and [14], and the present model, would be useful.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: No

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PCOMPBIOL-D-25-00481R1

Molecular surveillance of multiplicity of infection, haplotype frequencies, and prevalence in infectious diseases

PLOS Computational Biology

Dear Dr. Tsoungui Obama,

Thank you for submitting your manuscript to PLOS Computational Biology.

I apologise for the time that your revision was out for review, but it coincided with the extended summer holiday period in the southern hemisphere and both reviewers and I (as editor) were away for some time.

Both (original) reviewers and I agree that you have substantially improved the manuscript, and have just a few additional queries and minor requirements for you to address.

Please note one of the reviewer's comments were provided to me from outside of the formal PCB system so I have pasted them in to this email by hand. Please address them as usual.

Below is the remainder of the standard PCB form-letter and reviewer's comments.

James

After careful consideration, we feel that it has merit but does not fully meet PLOS Computational Biology's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Apr 24 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at ploscompbiol@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcompbiol/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

* A letter that responds to each point raised by the editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to formatting updates and technical items listed in the 'Journal Requirements' section below.

* A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

* An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

James M McCaw, PhD

Academic Editor

PLOS Computational Biology

Jennifer Flegg

Section Editor

PLOS Computational Biology

Journal Requirements:

If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors have addressed most of my concerns, and I appreciate the addition of the new benchmarking section. While CPU time is now reported, several references are made to the algorithm running out of memory. The memory usage of the algorithm should also be stated, or at the very least the maximum amount of memory available during benchmarking should be clearly specified so that readers can properly interpret what “memory overflow” refers to.

Reviewer #2: The authors have largely addressed my previous comments. The readability of the revised manuscript is much improved with respect to notation, and the method is better contextualised in the literature.

I appreciate the authors’ point that the manuscript is largely targeted to a biological audience. However, I would still argue that a concise, self-contained list of key model assumptions and rationales/limitations could be practically useful for practitioners to decide whether the present model is suited to their particular context (e.g. the number of markers, the expected degree of genotyping error and the associated error structure, genotype missingness, whether markers are relatively fast or slow-evolving, etc), and to be aware of potential biases or artefacts when interpreting the model outputs (e.g. due to outliers, imputation or limited sample sizes). Given the model assumptions are largely motivated in the context of falciparum malaria, this could be particularly useful for broader applications to other diseases.

Perhaps the authors could also comment on any biases that might arise if this method (predicated on the assumption of independent pathogen variants) is applied to data with significant relatedness between pathogen variants (e.g. due to significant co transmission as characterised by Wong et al [doi: 10.1186/s13073-017-0398-0] or related relapses of vivax malaria)? Perhaps the authors could also expand on lines 595-596 to discuss possible biases in MOI estimates due to selection?

Minor comment: it might be worth including SH in Table 1.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

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Reviewer #1: No

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Dear Dr. Tsoungui Obama,

We are pleased to inform you that your manuscript 'Molecular surveillance of multiplicity of infection, haplotype frequencies, and prevalence in infectious diseases' has been provisionally accepted for publication in PLOS Computational Biology.

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Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology.

Best regards,

James M McCaw, PhD

Academic Editor

PLOS Computational Biology

Jennifer Flegg

Section Editor

PLOS Computational Biology

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