The Effects of Infectious Diseases on the Consequences of Interspecific Competition in Grassland Communities

Round 1

Reviewer 1 Report

The authors propose an eco-epedemic model by combining the very wellknown Tilman's competition model and an SI epidemic model under three different hypotheses: infected individuals cannot reproduce, infected individuals can reproduce but there is no vertical transmission, and infected individuals can reproduce and there is vertical transmission. To my knowledge, this is an original approach, since the usual base competition model is the Lotka-Volterra type equations (actually, Gause equations). The authors manage to derive the coresponding R_0 values (why not labeling them as R_0^i for system type i, i = 1,2,3?). Then, the authors analyze numerically the model ans derive interesting conclusions. I regret there is no complete mathematical analysis behind their study or, at least, it seems it is not. I would expected equivalent results to those in [16]: closed expressions for the corresponding equilibrium states and closed conditions for their stability, as in lines 124, 126-127 for the Tilman's model. 

In my opinion, the lack of mathematical support makes necessary to re-write most of the conclusions. These conclusions are not "absolute" as relie on particular parameter values, even if the authors have analized a wide rango of them. Thus, these findings a re "thigs that may happen" rather than "things that will happen". 

At the same time, the model may exhibit quite different features, and it can be tricky describe all together. Perhaps using subsections to gather the same type of results together (e.g., those not affecting coexistence, those promoting coexistence, those precluding coexistence, those enlarging total biomass) would yield a clearer picture. Also, in my experience, sometimes it is better to focus in few ideas and use not too much figures to be sure that the main ideas are clear.

In any case, I find the approach novel and interesting so that the manuscript deserves publication. The manuscript is well writen (but I found few paragraphs a bit confussing, see below), and the simulations enlight interesting results (but see below). Congratulations to the authors. 

MINOR COMMENTS:

* I would set in a single line each R0s and the equilibrium points, as they are key in the staudy of the model.

* Lines 242-244: Do species occupy the same patch? I would say no, but the sentence seems to me suggest the oposite...I reckon the sentence should be reformulated.

* Figure 1 shows three surfaces (one for the R_0 corresponding to each model) and the surfaces are "ordered" in a given way. Is this the only way to order them? I mean, can $R_0^1(\beta, d)$ upper bound $R_0^{12}(\beta, d)$ (or any other combination)? 

* I find a little bit confussing part of the manucript, since:

        lines 260-262:  the pathogen invasion does not alter the original coexistence for situations where the two species are otherwise stably coexisting

   but then, 

        line 291: which weakens the effect of disease on competition, is detrimental to species coexistence

   which seems to mean that it was coexitence and the disease precludes it. 

* Lines 402-403: what does "For the infected inferior species we introduced a weakly competitive non-host competitor" mean? I would say the model asumes that the superior competitor is the infected one and the inferior competitior is the non-host one.

* Lines 389-391. Note that other eco-epidemic competition models allow for disease-induced coexistence-removal, as in 

    Discrete Dynamics in Nature and Society Volume 2017, Article ID 5310837, 13 pages https://doi.org/10.1155/2017/5310837

* In line 425 it is stressed that the balance between intra and inter species competition plays a major role in species coexistence. Very recently (indeed, it seems after the manuscript under review was submited), it has been proved in https://doi.org/10.3390/math12040562 that individuals interference when competing (that is not exactly the same as competition) plays also a key role.

* Few of the findings of the effect of diseases on competition are not new in the literature (even if found using the Lotka-Volterra model). 

I advise to cite these results in the discusion. See for instance the above mentioned paper, Doi:10.3934/dcdsb.2019204 or (I think) the following

Bowers RD, Turner J (1997) Community structure and the interplay between interspecific infection and competition. Journal of Theoretical Biology 187:95–109.

Han L, Pugliese A (2009) Epidemics in two competing species. Nonlinear Analysis: Real World Applications 10:723–744

Han L, Ma Z, Shi T (2003) An SIRS epidemic model of two competitive species. Mathematical and Computer Modelling 37:87–108

Tompkins DM, White AR, Boots M (2003) Ecological replacement of native red squirrels by invasive greys driven by disease. Ecology Letters 6:189–196

TYPOS

line 46 re-production --> reproduction

line 200 transmission), Note --> transmission). Note 

line 256 Sucessfully --> sucessfully 

line 262 ; Whereas --> . Whereas

line 358. Why the authors talk about "longevity"? Is it in the equations? 

line 443 Is "infection by dominant species" correct? I cannot understand lines 443-445

Author Response

Thank you for reviewing the manuscript. Due to a problem with the word version, some of the formulas in the manuscript are automatically bolded, which interferes with the aesthetics and layout, so I am uploading the PDF version of the document along with it. The mathematical derivation of the existence and stability of partial equilibria I put at the end of the document.

Author Response File: Author Response.pdf

Reviewer 2 Report

Investigating the effects of infectious diseases on plant colonization (invasion and survival) is gaining a lot of interest. This research aimed to find effects of infectious diseases on the competitive coexistence of species in grassland communities, which is important for revealing the diversity of species. The research topic is very interesting and matching the scope of this journal. The models are presented to simulate disease infection, and reveal the importance of disease in species coexistence and grassland biodiversity maintenance. However, the manuscript requires significant corrections before it is suitable for publication.

The specific items:

Introduction:

(1)  In general, the introduction is not logically contextualized enough, and needed to be streamlined and organized.

(2) Some testable hypotheses should be presented or some scientific questions should be addressed in the last paragraph.

Materials and Methods:

(1) For the model in which the infected individuals cannot be vertically transmitted (Line 168), there seems to be some problems here. The assumption that infected offspring can encroach on patches already occupied by inferior competitors is captured in the first equation, however, accordingly, this component should be captured in the rate of change of the inferior population, which is not in the third equation, please check it.

(2) Line 148 used " random contact between individuals leads to the spread of disease ", how do plants spread by contact? Please explain or standardize terms. The same problem also occurs in Line 206 and Line 226.

Results and discussion:

(1) The part of the equilibrium point E in the Figure 5 (Line 319) is weakly relevant to the main body of the article and can be considered for deletion. Here, however, the discussion of the effect of the parameter " c " on the system is omitted and should be added.

(2) How are the values of the parameters determined during numerical simulation? Is it supported by literature or experiments?

(3) This should be Figure 6 (Line 368), Please check the whole article for such minor errors.

(4) Please distinguish between the results and the discussion. Figure 7 and related sections are also at the conclusion rather than the discussion. The discussion should be compared with the research results of others.

(5) The section on outlook (Line446-449) is not strongly linked to the above, and it is suggested that this section be reworked.

Finally, manuscript requires significant editing for English grammar.

Manuscript requires significant editing for English grammar

Author Response

Thank you for reviewing the manuscript. Due to a problem with the word version, some of the formulas in the manuscript are automatically bolded, which interferes with the aesthetics and layout, so I am uploading the PDF version of the document along with it. The mathematical derivation of the existence and stability of partial equilibria I put at the end of the document.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I am glad the authors found the suggestions useful. The manuscript has been improved accordingly to the comments made. I do appreciate the effort of including the mathematical analysis, and it is a great idea set it as Supplementary Materials.

I don't want to bother the authors with more suggestions. However, I think that the new text needs of being reviewed. Please, find below a (non exhaustive) list of suggestions.

I am not native English speaker but the I find expressions that sound extrange to me in the new text (the one in red). Also, there are quite a lot long sentences. I am not saying that they are necesarily wrong, but I suggest a careful second reading. For instance:

Line 69: "therefore it is more suitable to be discussed in the framework of SI (Susceptible-Infected) epidemics". --> "therefore it is more suitable to consider SI (Susceptible-Infected) epidemics".

Line 71:  I would replace "except" by "along with" or equivalent.

Line 72: diseases, and we --> diseases. We

Line 74: cases in which the infection kills the host --> infections that kill the host

Line 157: infected person is weaker --> person?

Line 316: coexistence. under --> coexistence. Under

Line 321: What the sentence "Vertical transmission,...,essentially equates to increased transmission rates" mean? Does "equates" mean "is equivalent to"

Line 335: Does "offspring" mean "susceptible individuals"?

Line 337: Perhaps I am missing somethig but I find contradictory the sentence "increased colonization of healthy offspring (𝛿)" and the content of lines 169-170.

Line 357: I regret say that I do not understand this sentence.

396: While this  --> This

413: also help  --> also helps ??

Author Response

I have revised all the reviews and had them professionally edited in English.

Author Response File: Author Response.pdf