Adonis又称置换多因素方差分析（permutational MANOVA）或非参数多因素方差分析（nonparametric MANOVA）。它利用距离矩阵对总方差进行分解，分析不同分组因素对样品差异的解释度，并使用置换检验对划分的统计学意义进行显著性分析。

输入：

样本距离矩阵

示例：distance matrix

         Bio1 Bio2 Bio3 Bio4 Bio5

Bio1 0.0    0.483232790448      0.728662546493      0.652673920891      0.88918523617      

Bio2 0.483232790448      0.0    0.644148006987      0.541510920158      0.868933369893

Bio3 0.728662546493      0.644148006987      0.0    0.655220559361      0.871789401126

Bio4 0.652673920891      0.541510920158      0.655220559361      0.0    0.887469388959

Bio5 0.88918523617        0.868933369893      0.871789401126      0.887469388959      0.0

样品分组信息表：

Bio1 G1

Bio2 G1

Bio3 G1

Bio4 G1

Bio5 G2

Bio6 G2

Bio7 G2

Bio8 G3

Bio9 G3

Bio10        G3

输出：

Adonis 分析结果文件：

Call:

adonis(formula = dm ~ Group, permutations = 999)

         Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)

Group      2   0.38455 0.19227   1.677 0.32393  0.016 *

Residuals  7   0.80257 0.11465         0.67607        

Total      9   1.18712                 1.00000        

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

注：

Df --- 表示自由度；

SumsOfSqs --- 总方差，又称离差平方和；

MeanSqs --- 均方（差），即SumsOfSqs/Df；

F.Model ---- F检验值；

R2 --- 表示不同分组对样品差异的解释度，即分组方差与总方差的比值，R2越大表示分组对差异的解释度越高；

Pr --- 表示P值，小于0.05说明本次检验的可性度高。

分析模块引用了R语言（v2.12.1）vegan包（v2.0-1）中的Adonis分析。

相关文献如下所示：

Anderson, M.J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26: 32–46.

Crawley, M.J. 2002. Statistical Computing: An Introduction to Data Analysis Using S-PLUS

Excoffier, L., P.E. Smouse, and J.M. Quattro. 1992. Analysis of molecular variance inferred from metric distances among DNA haplotypes: Application to human mitochondrial DNA restriction data. Genetics, 131:479–491.

Legendre, P. and M.J. Anderson. 1999. Distance-based redundancy analysis: Testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69:1–24.

McArdle, B.H. and M.J. Anderson. 2001. Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology, 82: 290–297.

Zapala, M.A. and N.J. Schork. 2006. Multivariate regression analysis of distance matrices for testing associations between gene expression patterns and related variables. Proceedings of the National Academy of Sciences, USA, 103:19430–19435.