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3) I struggled a bit with the variance analysis which concludes the Results sections. In the second paragraph of the subsection 2Balance variance and microbiota assembly” it is argued that "When the variance of a balance between two clades approaches zero, the mean abundance of taxa in each of the two clades will be linearly related and thus exhibit shared dynamics across microbial habitats". While this is true (and must be true mathematically as when the variance approaches zero, the ratio of the two normalized abundances of the clades is constant, which means they will become perfectly linearly related with a positive slope), it's not clear to me that a high variance necessarily means "exclusionary dynamics across samples". I don't see how a high variance in this number indicated anything about how direct or indirect the interactions are within the tree. There are lots of reasons two clades could lack perfect linear correlation with a positive slope from direct competition to being completely unrelated biologically with abundances just shifting due to stochastic variation. Also, wouldn't variance have to be lower closer to the tips of the phylogenetic tree as the number of sequences is lower, so the pseudo-count has more of an effect depressing overall variance? Doesn't that explain Figure 4D-F ? And if I am reading these graphs correctly, below the species level there are not enough datapoints to support modeling via localized regression one way or another. Although not central to the arguments of the paper, I found Figure 4 to be less convincing than other sections of the paper.

Reviewer #2:

The manuscript introduces two new powerful ideas. They are: (a)construction of the sequential binary partition used to define

ILR coordinates on the base of phylogenetic trees; (b) use therecently published balances in weighted compositions to account forphylogenetic distances between OTU's or taxa. Both ideas aredeveloped and applied successfully to benchmark data sets.

For the originality of main ideas applied to microbiome analysis,the manuscript deserves publication.

Reviewer #3:

The manuscript is, in general, written in a clear and logical manner with a minimum of technical jargon. Figures 1 , 3 and 4 are outstanding examples of data visualization and demonstrate the utility of this approach over others extant in the field. Figure 5 seems an afterthought and could be combined with Figure 1 , or made supplementary. The binary portion could also be completely described in the Methods without a figure.

Figure 2 , and the associated descriptive text are somewhat underwhelming demonstrations of the utility of the approach, which, in theory, should clearly outperform all other methods if the compositional data approach is necessary. The use of box-plots probably does not aid the visual appeal.

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Translations of “represent”

替…行動, 作為…的代表(或代理人), 作為…的代言人…

~を代弁する, 代表する, ~を表す…

representar, equivaler a…

يَنوب عَن, يُمَثِّل…

mewakili, melambangkan, menunjukkan…

ทำหน้าที่แทน, เป็นสัญลักษณ์ของ, แสดงให้เห็น…

đại diện, tượng trưng, thể hiện…

stanowić, reprezentować, przedstawiać…

bercakap bagi pihak, melambangkan, sebagai contoh…

anlamına gelmek, ...ile eşit olmak, örneğini oluşturmak…

대표하다, (상징물로) 나타내다, -에 해당하다…

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