How parasite virulence evolves is arguably the most important question in both the applied and fundamental study of host-parasite interactions. Typically, this research area has been progressing through the formalization of the problem via mathematical modelling. This is because the question is a complex one, as virulence is both affected and affects several aspects of the host-parasite interaction. Moreover, the evolution of virulence is a problem in which ecology (epidemiology) and evolution (changes in trait values through time) are tightly intertwined, generating what is now known as eco-evolutionary dynamics. Therefore, intuition is not sufficient to address how virulence may evolve.
In their classical model, Anderson and May  predict that the optimal virulence level results from a trade-off between increasing parasite load within hosts and promoting transmission between hosts. Although very useful and foundational, this model incurs into several simplifying assumptions. One of the most obvious is that it considers that hosts are infected by a single parasite strain/species. Some subsequent models have thus accounted for multiple infections, generally predicting that this will select for higher virulence, because it increases the strength of selection in the within-host compartment.
Usually, when attacked, hosts deploy defences to combat their parasites. In many systems, however, parasites can suppress the immune response of their hosts. This leads to prolonged infection, which is beneficial for the parasite. However, immunosuppressed hosts are also more prone to infection. Thus, multiple infections are more likely in a population of immunosuppressed hosts, leading to higher virulence, hence a shorter infection period. Thus, the consequences of immunosuppression for the evolution of virulence in a system allowing for multiple infections are not straightforward.
Kamiya et al. embrace this challenge. They create an epidemiological model in which the probability of co-infection trades off with the rate of recovery from infection, via immunosuppression. They then use adaptive dynamics to study how either immunosuppression or virulence evolve in response to one another, to then establish what happens when they both coevolve. They find that when virulence only evolves, its evolutionary equilibrium increases as immunosuppression levels increase. In the reverse case, that is, when virulence is set to a fixed value, the evolutionarily stable immunosuppression varies non-linearly with virulence, with first a decrease, but then an increase at high levels of virulence. The initial decrease of immunosuppression may be due to (a) a decrease in infection duration and/or (b) a decrease in the proportion of double infections, caused by increased levels of virulence. However, as virulence increases, the probability of double infections decreases even in non-immunosuppressed hosts, hence increased immunosuppression is selected for.
The combination of both Evolutionary Stable Strategies (ESSs) yields intermediate levels of virulence and immunosuppression. The authors then address how this co-ESS varies with host mortality and with the shape of the trade-off between the probability of co-infection and the rate of recovery. They find that immunosuppression always decreases with increased host mortality, as it becomes not profitable to invest on this trait. In contrast, virulence peaks at intermediate values of host mortality, unlike the monotonical decrease that is found in absence of immunosuppression. Also, this relationship is predicted to vary with the shape of the trade-off underlying the costs and benefits of immunosuppression.
In sum, Kamiya et al.  provide a comprehensive analysis of an important problem in the evolution of host-parasite interactions. The model provides clear predictions, and thus can now be tested using the many systems in which immunosuppression has been detected, provided that the traits that compose the model can be measured.
 Anderson RM and May RM. 1982. Coevolution of hosts and parasites. Parasitology, 1982. 85: 411–426. doi: 10.1017/S0031182000055360
 Kamiya T, Mideo N and Alizon S. 2017. Coevolution of virulence and immunosuppression in multiple infections. bioRxiv, ver. 7 peer-reviewed by PCI Evol Biol, 149211. doi: 10.1101/139147
I think that this new version of the manuscript has greatly improved in clarity and, because the science was already very good, we are at the verge on publishing a recommendation for this article. I do however have some minor points that you could address in this new version, if you agree. Here it goes:
- Title: wouldn’t it be ‘in’ rather than ‘through’?
- An article on the classical host-parasite interaction of rabbits and myxoma virus came out (Kerr PNAS 29 aug 2017) describing a novel strain that immunosuppresses the host, maybe worth mentioning?
- Abstract line 7: I would put “host-parasite interactions”.
- Abstract line 17: “the shape of the trade-off determining the cost and benefit of immunosuppression” is not clear. What is being traded off with what? Maybe rephrase here.
- Line 36: help maintain -> helps maintaining.
- You state that immunosuppression translates into a longer infection period (eg line 43). Can’t we imagine that, instead, it leads to a higher parasite load for the same time period?
- Line 68: again, trade-off between what and what?
- Line 83: replace “the single species model” by “it”.
- Line 84: replace “than” with “which is not the case for”.
- Line 101: remove extra space before “doubly”.
- Legend of Table 1: put a comma after “evolve”.
- Line 168: replace “evolutionarily” by “evolutionary”.
- Line 188: replace “in which” by “therefore”.
- Line 201: again, trade-off between which variables?
- Line 242: I also found Koella and Boete 2003 Am Nat, I let you decide whether it is sufficiently relevant within this context.
- I still find figure 4 a bit cryptic but have no obvious suggestion for improvement…
The article presents a model analyzing the co-evolution of immunosuppression and virulence under multiple infections. This represents a very important contribution for the existing models on both the evolution of virulence under multiple infections and the evolution of virulence in immunosuppressing parasites (with the latter being clearly less explored than the former). The model is very well-designed and provides valuable insight into this important question. However, the reviewers and myself found that the presentation of several results was hard to follow. Also (I do not discard that this may be related to the previous sentence) some parameter choices seem rather arbitrary, or at least unjustified. I understand that the issue at stake is a complex one, with several factors operating simultaneously. However, it is important for the reader to take some message home… This is compromised at several instances, figure 3 being a paradigmatic example of this (cf. comments by rev1). On a more positive note, I think the discussion does a good job in summarizing the main findings. Overall, I’m convinced of the high quality of this manuscript, but would urge the authors to consider the reviewers comments to improve the clarity of their message. Below I also present my own comments.
Main comment: As mentioned in lines 187-190 and 211-216, and recapitulated in the Discussion (lines 282-284) double infections are protected from further infections. In my opinion, this may be the crucial factor of your model. That is, would you allow for triple infections (or more than that), wouldn’t high ESI at low virulence pattern vanish? Actually, the situation found here is much akin to models of niche construction (immunosuppression can be considered as a case of niche construction), in which the evolution of this trait is favored if niche constructers also evolve means to monopolize the resource (e.g., Krakaeur et al. 2009 Am Nat). Maybe establishing this parallel would be useful?
Line 15: The existence of different host types comes as a surprise… which types of hosts are there?
Line 27: any reason not to cite Van Baalen and Sabelis 1995 here?
Lines 31-34: I find the transition quite abrupt here. In the abstract you mention that most models do not consider the coevolution of traits in parasites. Maybe you could explore this a bit more here before turning to the particular traits you will tackle?
Lines 35-43: I know this is a bit biased, but if you would cite some examples from the plant-parasite literature, you would also attract more attention from that community, which unfortunately often neglects host-parasite theory. Eg Sarmento et al. Ecol Lett 2011, Burgyan and Havelda 2011 Trends Plant Sci. This can also be done in the Discussion section.
Lines 79-80: equations: why is the recovery rate of doubly infected to single infected the double of that from singly infected to susceptible (2 γ Drr vs γ Ir)?
Line 159: “convergently stable”, instead of “convergent stable” (cf also relevant comments of rev1 on this part).
Line 166: I would remove “game theoretically”.
Line 177: remove “assumption”.
Figure 1: Is there a specific reason for not exploiting the whole range of virulence? Especially, the slight increase observed for higher virulence values makes us wonder what will happen for even higher values. Figs 1d,e: I understand space is limited but maybe stating ‘relative frequency of (co)infected hosts’ in the Y axis would be much more intuitive… Also please consider a comment by rev1 on the trade-off values adopted here. Note also that the δ values stated here differ from those in table 1.
Lines 187-190: this section needs some streamlining, as the information on low virulence being correlated with more double infections is provided twice.