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  1. Author Response

    Reviewer #1 (Public Review):

    This manuscript discusses evolutionary patterns of manipulation of others' allocation of investment in individual reproduction relative to group productivity. Three traits are considered: this investment, manipulation of others' investment, and resistance to this investment. The main result of the manuscript is that the joint evolution of these traits can lead to the maintenance of diversity through, as documented here, cyclic (or noisier) dynamics. Although there are some analytical results, this main conclusion is instead supported by individual-based simulations, which seem correctly performed (but for clonal populations, as emphasized below).

    There could be material for a good paper here but the organization of the manuscript makes it difficult to fully evaluate. The narrative is highly condensed, with the drawbacks that this often entails in terms of accurately conveying the results of a study, as illustrated here by the following issue.

    The population is apparently assumed to be clonal (more than just "haploid"), meaning that there is no recombination between the loci controlling the three traits. In the one case where this assumption is relaxed (quite artificially), the cyclic dynamics disappear (section 4.4 of the appendix). This is crucial information that cannot be appreciated in the main text.

    The paragraph at line 368 offers a simple explanation for the joint dynamics of traits. However, this explanation would hold identically for a sexual population and a clonal population, whereas these two cases seem to have completely different dynamics. Thus, there is something essential to explain these differences, that is missing from the given explanation.

    Yes, our model was asexual with no recombination. To address this comment, we carried additional simulations where recombination was allowed (Appendix 1— 4.8). We found that recombination does not change our results (predictions), and describe this on line 469-475. By assuming additive effects of traits and each traits having the same dispersal property, our haploid asexual model is also equivalent to a diploid sexual model (Taylor 1996; Day & Taylor 1998).

    This is especially important because the finding that the joint evolution of several traits can lead to some form of diversity maintenance is not surprising. As the discussion acknowledges (but the introduction seems to downplay), it is also well understood that manipulation and counter-adaptations to it can occur in many contexts and lead to the maintenance of diversity. For this reason, similar results in the present case are not surprising, and the main outcome of the study should be to provide a deeper understanding of the forces leading to the different outcomes in the current models.

    I do not see clearly what distinguishes "manipulative cheating" from other forms of manipulations that have been previously discussed in the literature (e.g, as cited lines 461). Couldn't this be clarified by some kind of mathematical criterion?

    Thanks for pointing out that there is room to improve the distinction between our model and previous models! We have added more description to explain the conceptual difference on line 187-193, and a new subsection in appendix to show these differences through mathematically examine the fitness formulations in previous models (Appendix 1—1.3).

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  2. Evaluation Summary:

    The authors use theoretical models to examine the joint evolution of different cheating strategies: selfish cheating (not contributing to a common good), and manipulative cheating (inducing a competitor to preferentially provide benefits to the cheat). The models seem well formulated and the results robust. That said, improvements could be made to the presentation to clarify the assumptions and wider applicability of the model. An improved article would provide a better understanding of the mechanisms behind cheating, which would be of interest to readers working on the evolution of cooperation, potentially opening up new directions for theoretical and empirical work.

    (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. The reviewers remained anonymous to the authors.)

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  3. Reviewer #1 (Public Review):

    This manuscript discusses evolutionary patterns of manipulation of others' allocation of investment in individual reproduction relative to group productivity. Three traits are considered: this investment, manipulation of others' investment, and resistance to this investment. The main result of the manuscript is that the joint evolution of these traits can lead to the maintenance of diversity through, as documented here, cyclic (or noisier) dynamics. Although there are some analytical results, this main conclusion is instead supported by individual-based simulations, which seem correctly performed (but for clonal populations, as emphasized below).

    There could be material for a good paper here but the organization of the manuscript makes it difficult to fully evaluate. The narrative is highly condensed, with the drawbacks that this often entails in terms of accurately conveying the results of a study, as illustrated here by the following issue.

    The population is apparently assumed to be clonal (more than just "haploid"), meaning that there is no recombination between the loci controlling the three traits. In the one case where this assumption is relaxed (quite artificially), the cyclic dynamics disappear (section 4.4 of the appendix). This is crucial information that cannot be appreciated in the main text.

    The paragraph at line 368 offers a simple explanation for the joint dynamics of traits. However, this explanation would hold identically for a sexual population and a clonal population, whereas these two cases seem to have completely different dynamics. Thus, there is something essential to explain these differences, that is missing from the given explanation.

    This is especially important because the finding that the joint evolution of several traits can lead to some form of diversity maintenance is not surprising. As the discussion acknowledges (but the introduction seems to downplay), it is also well understood that manipulation and counter-adaptations to it can occur in many contexts and lead to the maintenance of diversity. For this reason, similar results in the present case are not surprising, and the main outcome of the study should be to provide a deeper understanding of the forces leading to the different outcomes in the current models.

    I do not see clearly what distinguishes "manipulative cheating" from other forms of manipulations that have been previously discussed in the literature (e.g, as cited lines 461). Couldn't this be clarified by some kind of mathematical criterion?

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  4. Reviewer #2 (Public Review):

    This is a nice theory paper that examines the conditions under which manipulative cheating can evolve. Manipulation is a form of coercion, where individuals can achieve a benefit by actively manipulating others to help them at a cost to their own fitness. This is in contrast to the more standard form of cheating, which is simply refraining to contribute to a collective good that one benefits from. This paper has a number of strengths, including a seamless integration of both a multilevel selective framework and inclusive fitness, as well as a rigorous analysis of the joint dynamics of selfishness, manipulation, and suppression of manipulation. The results are novel and important and will help us better understand the spectrum of social cheating.

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  5. Reviewer #3 (Public Review):

    The paper uses a mixture of game-theoretical models and individual-based simulations to study the coevolution of manipulation and resistance to manipulation in social interactions. This is a very impressive piece of theoretical research that will likely open new directions for both theoretical and empirical work.

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