The “Growth Curve”: An Autocorrelation Effect

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the present paper, the authors study an interesting problem relating to fitting a population in terms of time. It is an interesting problem for several areas related to biology and is also interesting for chemistry and mathematics, specifically for the mathematical modeling of epidemics. In a broad sense, the paper is well written: the problem is well formulated, the methodology is appropriate, and there are some didactic illustrations. However, there is a space that can help to improve the quality of the presentation: some numerical simulations or numerical examples applying the model of section 5. Hence, my suggestion is to include a new section 6 with at least two numerical examples of the application of the model to experimental data available in the literature.

 

On the other hand, minor points related  to English grammar are the following:

 

-Line 39: At the end of the paragraph, “.” is missing “[5, 8 - 11]” should be “[5, 8 - 11].”

 

-The punctuation marks at the end of "almost all" equations are missing. For instance, on line 108 at the end of equation (1) should be inserted “.”;  on line 119 at the end of the definition of equation (2) “,” should be inserted, Etc

 

-Remove indentation after equations, for instance, below equation (2) the word “where” should be without indentation, similar observation to equation (3).

Comments on the Quality of English Language

No comments

Author Response

In the present paper, the authors study an interesting problem relating to fitting a population in terms of time. It is an interesting problem for several areas related to biology and is also interesting for chemistry and mathematics, specifically for the mathematical modeling of epidemics. In a broad sense, the paper is well written: the problem is well formulated, the methodology is appropriate, and there are some didactic illustrations.

However, there is a space that can help to improve the quality of the presentation: some numerical simulations or numerical examples applying the model of section 5. Hence, my suggestion is to include a new section 6 with at least two numerical examples of the application of the model to experimental data available in the literature.

 

On the other hand, minor points related  to English grammar are the following:

 

-Line 39: At the end of the paragraph, “.” is missing “[5, 8 - 11]” should be “[5, 8 - 11].”

 

-The punctuation marks at the end of "almost all" equations are missing. For instance, on line 108 at the end of equation (1) should be inserted “.”;  on line 119 at the end of the definition of equation (2) “,” should be inserted, Etc

 

-Remove indentation after equations, for instance, below equation (2) the word “where” should be without indentation, similar observation to equation (3).

 

Reviewer 2 Report

Comments and Suggestions for Authors

Comments:

Prof. Schiraldi performed a naive and semi-empirical model to describe the phenomenological behavior of any real microbial culture by adjusting the values of three parameters (a, b and q₀.). The work is sound. I only have a few comments to improve the understanding of this work to more general audiences who do not have a strong math background.

 

1.     In Figure 3, you have 4 different y-axis labels, which is hard to understand. It would be better to split the plot into 4 panels. Was the “102” a typo of “10²”? To keep consistent with the other figures, you can use “N10^-2” to replace the “N/10²”

 

2.     In Figure 4, the labels of the y-axis were not included.

 

3.     In Figure 5, the y-axis is log₁₀(N). Is it a typo of log₂(N)? Because only log₂(N) was used in Equation 8 and Figure 6. The y-axis value of q^* can be added to the figure (for example, log₂(N₀2^b)) for better understanding.

 

4.     In Figure 6, a lot of arrows were added. What these arrows mean is not clear. In addition, the q_end can be linked with the ideal straight line.

 

5.     In Figure 7, the cut-off value between the growth curve and the decay curve should be presented. The function of the decay curve only works when q is higher than the cut-off value.

 

 

 

 

Comments for author File: Comments.pdf

Author Response

Prof. Schiraldi performed a naive and semi-empirical model to describe the phenomenological behavior of any real microbial culture by adjusting the values of three parameters (a, b and q₀.). The work is sound. I only have a few comments to improve the understanding of this work to more general audiences who do not have a strong math background.

 

1. In Figure 3, you have 4 different y-axis labels, which is hard to understand. It would be better to split the plot into 4 panels. Was the “102” a typo of “10²”? To keep consistent with the other figures, you can use “N10^-2” to replace the “N/10²”

 

2. In Figure 4, the labels of the y-axis were not included.

 

3. In Figure 5, the y-axis is log₁₀(N). Is it a typo of log₂(N)? Because only log₂(N) was used in Equation 8 and Figure 6. The y-axis value of q^*can be added to the figure (for example, log₂(N₀2^b)) for better understanding.

 

4. In Figure 6, a lot of arrows were added. What these arrows mean is not clear. In addition, the q_end can be linked with the ideal straight line.

 

5. In Figure 7, the cut-off value between the growth curve and the decay curve should be presented. The function of the decay curve only works when q is higher than the cut-off value.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This reviewer suggests the publication of the work since the authors have included the requirements of this reviewer.