Understanding the evolution of multiple drug resistance in structured populations
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Reviewer #2 (Public Review):
In this manuscript, McLeod and Gandon present a thorough mathematical modeling framework to describe the evolution of multidrug resistance (MDR) in microbial populations. By expressing the model in terms of linkage disequilibrium, the equations take on a form that make it easier to identify the key drivers of MDR evolution and propagation. This work helps to unify and generalize previous studies and constitutes an important advance in our understanding of microbial population dynamics.
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Reviewer #1 (Public Review):
In this manuscript, McLeod and Gandon propose a framework for understanding multidrug resistance (MDR) evolution in a structured population in terms of linkage disequilibrium (LD) dynamics, and apply this framework to three concrete examples of MDR evolution. I was asked to evaluate this manuscript, as well as the authors' response to comments from previous reviewers. My expertise is in epidemiological modelling of antibiotic resistance; I am not hugely familiar with population genetics.
Overall, I think the authors address an important and interesting question, and I think the approach has the potential to generate valuable insights. I also think the authors addressed the previous reviewers' comments well. However, I have substantial concerns about the modelling framework and the interpretation of the …
Reviewer #1 (Public Review):
In this manuscript, McLeod and Gandon propose a framework for understanding multidrug resistance (MDR) evolution in a structured population in terms of linkage disequilibrium (LD) dynamics, and apply this framework to three concrete examples of MDR evolution. I was asked to evaluate this manuscript, as well as the authors' response to comments from previous reviewers. My expertise is in epidemiological modelling of antibiotic resistance; I am not hugely familiar with population genetics.
Overall, I think the authors address an important and interesting question, and I think the approach has the potential to generate valuable insights. I also think the authors addressed the previous reviewers' comments well. However, I have substantial concerns about the modelling framework and the interpretation of the results. In particular: i) there are some problems with the interpretation that LD arises from variation in susceptible density; ii) presenting these results as a reinterpretation and generalisation of Lehtinen et al. 2019 is incorrect; and iii) the modelling of additive transmission costs needs further thought/explanation.
Interpretation of results and reinterpretation of Lehtinen et al. 2019.
The authors present their results as a generalisation of the effect observed in Lehtinen et al. 2019. Both models show that variation in the strength of selection for resistance between populations can give rise to LD in a model of multiple resistances. In Lehtinen et al., this variation in selection is attributed to variation in clearance rate. The authors reinterpreting the effect as arising from variation in susceptible density instead. This reinterpretation is incorrect: the change in how costs of resistance are modelled (additive here, multiplicative in Lehtinen et al.) changes the evolutionary dynamics, so the two models capture different evolutionary effects. (See points 2 and 3 for further discussion of additive vs multiplicative costs).
One way to see this is to consider a simple model of single resistance as presented in Lehtinen et al. eqn 1, in which resistance is selected for when: B_r/a_r > B_s/(a_s + tau), where "B" is the transmission rate, "a" the clearance rate and tau the treatment rate. Rearranging for tau shows how the threshold of selection for resistance depends on the strain's properties (B and a) under different assumptions about cost. With an additive cost in transmission (i.e. B_r = B_s  c), this threshold depends on both transmission rate and clearance rate, predicting LD if populations vary in either transmissibility or duration of carriage. With an additive cost in clearance, this threshold is independent of the strain's properties, predicting no LD. These are precisely the results the authors describe lines 268277 and Figure 3.
However, if the costs are multiplicative, this threshold depends on clearance rate only, whether costs are modelled as part of clearance or transmission rate. This is why the model in Lehtinen et al. 2019 predicts LD when populations vary in duration of carriage, even when there is no transmission cost. The author's reinterpretation of the effect in Lehtinen et al. as arising from variation in the density of susceptibles, contingent on an explicit transmission cost, is therefore not correct. More generally, representing one model as a generalisation of the other is misleading.
I am also not sure about the authors' interpretation that the effects in the model with additive costs arise from variation in susceptible density. Variation in the density of susceptibles can also be generated by variation in the overall population density, so if I understand correctly, this interpretation would predict that LD would arise if the population density was different between populations? And that the selective pressure on single resistance would also depend on overall population density (argument stating line 261)? I am not able to reproduce this dependence of population density in a simple model. I would instead interpret the effect the authors observe as arising because the same additive transmission cost is much more significant if the baseline transmission rate is low (e.g. with c = 1, a strain with B_s 1 would never evolve resistance because B_r would be 0, which would not be the case for a strain with baseline transmission rate B_s = 3).
The problem with the interpretation in terms of susceptible density is clear in the section on serotype dynamics. The main text refers to serotypespecific susceptibles (S^x) (line 303) and explains observed effects in terms of variation in S^x. In the supporting information however, the authors present a model of serotype dynamics which does not have serotypespecific susceptible classes and the pool of susceptibles is the same for all serotypes (eqn 43). While I absolutely agree this is a better model to study transient effects than introducing a serotypespecific susceptible class, I don't understand what the authors mean by serotypespecific susceptible density in the main text.
The use of an additive transmission cost
The use of an additive transmission cost requires further consideration/discussion. An additive transmission cost is difficult to interpret epidemiologically and can lead to implausible consequences. For example, if costs are high enough compared to baseline transmission rate, additive costs with no epistasis would lead to a negative transmission rate for the dually resistant strains, which does not make sense (say B_ab = 2 and B_Ab = B_aB = 0.5, then B_AB = 1).
Why is epistasis defined in terms of an additive rather than multiplicative expectation?
I also have quite a basic question about the overall framework (eqn. 2). In the modelling framework, epistasis is the difference between the actual per capita growth rate of the duallyresistant infections and the expected growth rate, defined as the sum of the difference between the growth rates of the singlyresistant infections and the baseline rate. It was not obvious to me whether the expectation needs to be additive, or whether this is a question of definition (could the expectation be defined, for example, as a multiplicative rather than additive effect?). In particular, I was wondering about this in the context of the authors' suggestion that multiplicative costs are problematic because they give rise to epistasis  this seemed a little tautological to me because epistasis has been specifically defined as deviation from an additive expectation. I think a discussion about why epistasis is defined in terms of additive effects, and the implications for the derivation of the dynamics of D, would be very interesting and also helpful in making the paper more accessible.
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Evaluation Summary:
This paper addresses the important question of multidrug resistance evolution, which is of both theoretical and applied interest. The authors efforts to carefully distinguish population and metapopulation linkage disequilibrium and to develop a framework to rigorously analyze the relationship between the two has promise, although we have noted concerns about the modeling framework used and results interpretation. If these concerns can be sufficiently addressed, then this paper has the potential to represent a clear advance in our understanding of microbial population dynamics.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #2 agreed to share their names with …
Evaluation Summary:
This paper addresses the important question of multidrug resistance evolution, which is of both theoretical and applied interest. The authors efforts to carefully distinguish population and metapopulation linkage disequilibrium and to develop a framework to rigorously analyze the relationship between the two has promise, although we have noted concerns about the modeling framework used and results interpretation. If these concerns can be sufficiently addressed, then this paper has the potential to represent a clear advance in our understanding of microbial population dynamics.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #2 agreed to share their names with the authors.)
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