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The ecology and evolution of sub-exponential replicators

PLOS Computational Biology

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Academic Editor

PLOS Computational Biology

Zhaolei Zhang

Section Editor

PLOS Computational Biology

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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 manuscript by B. Kovacs et al investigates an ecology of exponential

and sub-exponential replicators. Overall, the paper is interesting and

provide some new insights in the behavior such a system:

(a) the rules of coexistence of a (single) exponential replicator and

a set of parabolic replicators, and

(b) the effect of changing the resource concentration which, somewhat

counterintuitively, decreases diversity.

It also recovers behavior of such dynamics systems described previously in

simpler approximations of the dynamics.

Overall the manuscript is well written and the derivations in the appendix

are correct. Personally, I would have liked the main technical results to

be stated as formal Propositions to facilitate the exact comparison of the

results with the existing literature.

Regarding the behavior of the purely parabolic model, many of the results,

have been described previously in the setting of Michaelis-Menten kinetics,

i.e., assuming a fast equilibration of single-stranded and double stranded

forms. From my reading of the present manuscript, the observed behavior is

very similar. "Evolution in Systems of Ligation-Based Replicators"

(Z.Phys. 10.1524/zpch.2002.216.1.021) derives explicit survival conditions

in equilibrium, observes the monotonic increase in diversity with

increasing replicator concentration. Prop.2 in the same publication covers

the case of invasion based on an earlier result by Hofbauer at al: It implies

that the omega-limit of any trajectory starting within a subsimplex that

contains an interior fixed point is that fixed point. In other words,

Prop.2 immediately implies that invasion is successful if and only if a new

parabolic replicator is a survivor in the new equilibrium. (I suspect that

an analogous result could be proved for the author's model.)

The same publication also describes simulation results for invasion

scenarios.

As a minor note, the correspondence of a regulated flow that keeps

concentrations constant and fixed flow systems was studied "Autocatalytic

replication in a CSTR and constant organization" (Bull.Math.Biol

10.1007/s002850050155) showing that for small flow rates the dynamics

become equivalent.

In summary, I suggest to compare in more detail to the conclusions drawn in

particular from the simpler Michealis-Menten type model and to focus on on

effects provided by the present model, if any, and effects that have not be

observed already on the basis on the Michaelis-Menten approximation.

Reviewer #2: the review is uploaded as an attachment.

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: Yes: Onofrio Mazzarisi

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Attachments

Attachment

Submitted filename: recommendation.pdf

Dear Professor Szathmáry,

We are pleased to inform you that your manuscript 'The ecology and evolution of sub-exponential replicators' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

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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,

Jacopo Grilli

Academic Editor

PLOS Computational Biology

Zhaolei Zhang

Section Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: I have no further concerns.

Reviewer #2: The author addressed all my concerns.

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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: None

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: Yes: Onofrio Mazzarisi