Dear Editor,

      It is really a bad news for us to receive a rejection letter of the revised manuscript, especially for our waiting for more than five months since its submission.

      We read and analyzed the decision letter and the comments of the referee 1 (lack that of the referee 2) more carefully. We found most of the comments are not objective or not in accord with the fact. For example:

1. “* The model is now formally defined. However, this formalization is dramatically too complex, making the understanding really hard (happily I had read the first version so I remembered the concepts helping me in understanding this actual version). Authors should find a good level between model explanation with hands and (simple but clear) formalisation.”

# We described the model as detailed as possible to accommodate the main blames of the original submission made by the referee 1, such as “the applied model is badly introduced”, “define formally the model. What is a different object given a context ?”. Now, he blames the complexity of the model, however the complexity of the model is absolutely necessary for the clear explanations of the many problems the referees raised, such as “What is the definition of "Object(i)" when several objects exist for context "i"? And how the I(i) definition handles such multiplicity?”.

 We spend the most of our efforts in building this model so that the spirit of the method could be delivered formally, though is complex however it makes the method more logical and scientific. The referee blames the complexity of the model, this is contradict with his original comments. 

 

2. “* The motivation of the model, now in the "discussion" section is not convincing...”

# This comment seems subjective and vague, and do not clearly point out the substantial problem.

 

3. “Some formula seem wrong. For instance, the proportion $q$ (p°6) should depend on the coverage, which is not the case. Moreover, there are still some undefined notations (see for instance formula F(X,Y) p°21)”
 #The referee seems not read our model carefully, may because it is “too complex”. The formula, indeed has considered the effect of coverage, which is controlled by the reads number n. We also carefully check the formula of F(X,Y), all notations used have been defined. The comment is ambiguous, which notations are undefined?

 

4. “The algorithm section contains much useless material. For instance the three algorithms fasta2co fastq2co and co2distance should not be so detailed as this description is somehow useless for the understanding and as some notations are not introduced (for instance what "read S(G'i) into H" means ?)”

# The three algorithms are described in detail to satisfy the comments by the second referee, such as, “cannot really understand the details of the method.  how large is the index table?  This is dependent on the values of C and O, yes?  what range of C and O were attempted?” and the detail of the algorithm is also necessary for illustrating the computation of the algorithm efficiencies which were demanded by both referees. Now referee 1 blames that the algorithm is too detailed, this is contradicted with himself and the other referees’ original comments.

We declared clearly in the end of the algorithm overview that “The notions used follow the convention established in the model definition section.” S(G'i) was indeed clearly defined in the model definition section and H was defined in the algorithm. Referee 1 seems didn’t review the paper carefully. It is unreasonable for Referee 1 blaming that some notations are not introduced.

 5. Many claims are not motivated or are based on unproven suppositions:
   - "The total number of different C-grams is approx. eq. to twice the size of all the N".

# The complete sentence was “The total number of different C-grams is approximately equivalent to twice the size of the genome (including the C-grams from reverse-complement counterparts), but it may be smaller. Suppose the largest genome size for all of the N organisms is M_max; then, the size of hash table H is O(M_max) (see page 10)”, the referee 1 misquoted the original sentence and express a different meaning by himself.
   - The comparison with other alignment free methods should come with formal and empirical comparisons by for instance curves showing for both co-phylog and alignment free methods the efficiency wrt the distance between genomes including computation and memory requirements.

      #The comparison with other alignment free methods indeed has been done at the ‘Results' - the ‘Performance on Escherichia/Shigella 26 genomes’ section usingformal and empirical comparisons and Figure 2 (c) shows the comparisons of the correlation coefficient vs. p-distance of distances computed by alignment-free and co-phylog. Referee 1 didn’t see that?

 6, *The comparison with alignment free methods should be done in the results section, not only discussed in conclusion.

 

The comparison with alignment free methods indeed have been done in the ‘Results’ section, see the ‘Performance on Escherichia/Shigella 26 genomes’ section, the referee probably haven’t read the full paper, this comment didn’t stand solidly.

7, * The bibliography is badly formatted (some years are missing, some first name appears and a title is missing).

# We should admit we are careless in the bibliography formatting and thank this comment made by referee 1, but it is perhaps a too serious punishment to reject our manuscript for this reason, we wish you could give us a chance to correct this mistake.

 

Based on the above analyzes, we found referee 1 just didn’t review our new manuscript carefully. If our manuscript indeed has the problems raised by referee 1, at least some of these problems would also be confirmed by the comments from another referee, however we didn’t see any comments from the second referee. We think it would be much fairer if the manuscript could be reviewed by a third referee. We wish you could take the above information into account and give us a chance.

 

Best wishes and sincerely yours

 

Huiguang Yi