Despite an explosion of cross-disciplinary interest in researching the gut microbiome, there remains to be a gold-standard method for operationalizing gut microbiome alpha diversity. Controlling the false discovery rate: a practical and powerful approach to multiple testing. There’s logic in this view. Here, I introduce a novel microbial diversity association test, namely, adaptive microbiome α-diversity-based association analysis (aMiAD). Pan, W., Kim, J., Zhang, Y., Shen, X. and JavaScript.To relate microbial diversity with various host traits of interest (e.g., phenotypes, clinical interventions, environmental factors) is a critical step for generic assessments about the disparity in human microbiota among different populations. Then, I address details on the six candidate α-diversity metrics, Richness, ShannonHere, I notify that the α-diversity referred in this paper considers different types of operational taxonomic units (OTUs) in the bacterial kingdom per biological sample (e.g., human, mouse), indicating within-sample diversity of OTUs in the bacterial kingdom. Wu, C., Chen, J., Kim, J. Although I proposed aMiAD to relate microbial diversity with a continuous (e.g., BMI) or binary (e.g., disease/treatment status) trait of interest, it would be extendable to different types of trait (e.g., survival, multinomial trait)The utilized microbiome data are publicly available at the European Bioinformatics Institute (EBI) database (Hamady, M. & Knight, R. Microbial community profiling for human microbiome projects: Tools, techniques. Li, H. Microbiome, metagenomics, and high-dimensional compositional data analysis. We compared gut microbiomes of wild and captive black rhinos to test for differences in taxonomic diversity (alpha and beta) and in functional diversity of the microbiome… The methodological details for aMiAD can be found in the following Methods section. Diamond Project Group. $${{\rm{Y}}}_{{\rm{i}}}={\beta }_{0}+\sum _{{\rm{k}}=1}^{{\rm{q}}}\,{{\rm{X}}}_{{\rm{i}}{\rm{k}}}{\alpha }_{{\rm{k}}}+{\rm{h}}({{\rm{Z}}}_{{\rm{i}}})+{\epsilon }_{{\rm{i}}},$$$${\rm{l}}{\rm{o}}{\rm{g}}{\rm{i}}{\rm{t}}\,{\rm{P}}({{\rm{Y}}}_{{\rm{i}}}=1)={\beta }_{0}+\sum _{{\rm{k}}=1}^{{\rm{q}}}\,{{\rm{X}}}_{{\rm{i}}{\rm{k}}}{\alpha }_{{\rm{k}}}+{\rm{h}}({{\rm{Z}}}_{{\rm{i}}}),$$\(\sum _{{\rm{j}}=1}^{{\rm{p}}}\,{{\rm{\beta }}}_{{\rm{j}}}{{\rm{Z}}}_{{\rm{ij}}}\)$${\rm{h}}{({{\rm{Z}}}_{{\rm{i}}})}_{({\rm{\gamma }})}={{\rm{\beta }}}_{({\rm{\gamma }})}{{\rm{D}}}_{({\rm{\gamma }}){\rm{i}}},$$$${{\rm{D}}}_{{\rm{w}}}=\frac{1}{\sqrt[{\rm{w}}-1]{{\sum }_{{\rm{j}}=1}^{{\rm{p}}}{{\rm{r}}}_{{\rm{j}}}{{\rm{r}}}_{{\rm{j}}}^{{\rm{w}}-1}}}=({\sum }_{{\rm{j}}=1}^{{\rm{p}}}{{{\rm{r}}}_{{\rm{j}}}}^{{\rm{w}}}{)}^{1/(1-{\rm{w}})},$$$${{\rm{D}}}_{{\rm{Richness}}}={{\rm{D}}}_{0}={\rm{p}},$$\({{\rm{l}}{\rm{i}}{\rm{m}}}_{{\rm{w}}\to 1}{{\rm{D}}}_{{\rm{w}}}=\exp (-\sum _{{\rm{j}}=1}^{{\rm{p}}}{{\rm{r}}}_{{\rm{j}}}\,{\rm{l}}{\rm{n}}\,{{\rm{r}}}_{{\rm{j}}})\)\({{\rm{l}}{\rm{i}}{\rm{m}}}_{{\rm{w}}\to 1}{{\rm{D}}}_{{\rm{w}}}\)$${{\rm{D}}}_{{\rm{S}}{\rm{h}}{\rm{a}}{\rm{n}}{\rm{n}}{\rm{o}}{\rm{n}}}=\,{\rm{l}}{\rm{o}}{\rm{g}}({{\rm{l}}{\rm{i}}{\rm{m}}}_{{\rm{w}}\to 1}{{\rm{D}}}_{{\rm{w}}})=-{\sum }_{{\rm{j}}=1}^{{\rm{p}}}{{\rm{r}}}_{{\rm{j}}}\,{\rm{l}}{\rm{n}}\,{{\rm{r}}}_{{\rm{j}}},$$\({(\sum _{{\rm{j}}=1}^{{\rm{p}}}{{{\rm{r}}}_{{\rm{j}}}}^{2})}^{-1}\)$${{\rm{D}}}_{{\rm{Simpson}}}=-\,{{{\rm{D}}}_{2}}^{-1}=-\,\sum _{{\rm{j}}=1}^{{\rm{p}}}{{{\rm{r}}}_{{\rm{j}}}}^{2},$$$${{\rm{D}}}_{{\rm{PD}}}={\sum }_{{\rm{j}}=1}^{{\rm{p}}}{{\rm{l}}}_{{\rm{j}}},$$$${{\rm{D}}}_{{\rm{PE}}}=-\,\sum _{{\rm{j}}=1}^{{\rm{p}}}\,{{\rm{l}}}_{{\rm{j}}}{{\rm{r}}}_{{\rm{j}}}\,\mathrm{ln}\,{{\rm{r}}}_{{\rm{j}}},$$$${{\rm{D}}}_{{\rm{PQE}}}=-\,{\sum }_{{\rm{j}}=1}^{{\rm{p}}}{{\rm{l}}}_{{\rm{j}}}{{{\rm{r}}}_{{\rm{j}}}}^{2},$$$${{\rm{U}}}_{({\rm{\gamma }})}={\sum }_{{\rm{i}}=1}^{{\rm{n}}}({{\rm{Y}}}_{{\rm{i}}}-{\hat{{\rm{\mu }}}}_{{\rm{i}},0}){{\rm{D}}}_{({\rm{\gamma }}){\rm{i}}}$$\({\widehat{{\rm{\beta }}^{\prime} }}_{0}+{\sum }_{{\rm{k}}=1}^{{\rm{q}}}{{\rm{X}}}_{{\rm{i}}{\rm{k}}}{\widehat{{\rm{\alpha }}^{\prime} }}_{{\rm{k}}}\)\({{\rm{logit}}}^{-1}({\widehat{{\rm{\beta }}^{\prime} }}_{0}+{\sum }_{{\rm{k}}=1}^{{\rm{q}}}{{\rm{X}}}_{{\rm{ik}}}{\widehat{{\rm{\alpha }}^{\prime} }}_{{\rm{k}}})\)\({\widehat{{\rm{\alpha }}^{\prime} }}_{{\rm{k}}}\)$${{\rm{T}}}_{{\rm{a}}{\rm{M}}{\rm{i}}{\rm{A}}{\rm{D}}}={min}_{\gamma \epsilon {\rm{\Gamma }}}{{\rm{P}}}_{(\gamma )},$$\({{\rm{T}}}_{{\rm{a}}{\rm{M}}{\rm{i}}{\rm{A}}{\rm{D}}}={min}_{\gamma \epsilon {\rm{\Gamma }}}{{\rm{P}}}_{(\gamma )}\)\({{\rm{T}}}_{{\rm{a}}{\rm{M}}{\rm{i}}{\rm{A}}{\rm{D}}}={min}_{\gamma \epsilon {\rm{\Gamma }}}{{\rm{P}}}_{(\gamma )}\)\({{\rm{T}}}_{{\rm{a}}{\rm{M}}{\rm{i}}{\rm{A}}{\rm{D}}}={min}_{\gamma \epsilon {\rm{\Gamma }}}{{\rm{P}}}_{(\gamma )}\)$${\rm{aMiDivES}}=\frac{{{\rm{MiDivES}}}_{({{\rm{\gamma }}}_{{\rm{m}}})}-{\rm{E}}({{\rm{MiDivES}}}_{({{\rm{\gamma }}}_{{\rm{m}}}),0})}{{\rm{SE}}({{\rm{MiDivES}}}_{({{\rm{\gamma }}}_{{\rm{m}}}),0})},$$$${\rm{l}}{\rm{o}}{\rm{g}}{\rm{i}}{\rm{t}}\,{\rm{P}}({{\rm{y}}}_{{\rm{i}}}=1)={0.5}^{\ast }{\rm{s}}{\rm{c}}{\rm{a}}{\rm{l}}{\rm{e}}({{\rm{X}}}_{1{\rm{i}}}+{{\rm{X}}}_{2{\rm{i}}})+{\beta }^{\ast }{\sum }_{{\rm{j}}\in {\rm{\Lambda }}}{{\rm{w}}}_{{\rm{i}}}\ast {\rm{s}}{\rm{c}}{\rm{a}}{\rm{l}}{\rm{e}}({{\rm{Z}}}_{{\rm{i}}{\rm{j}}}),$$
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