Procrustes analysis

适用：

（宿主的进化和菌体群落是否存在对应关系？）

数据要求：

词源

Procrustes，

原始古希腊神话里的一个强盗，大力士。他把人抓来之后放在一个铁床上，不符合床的大小就将将人拉伸或剁其头颅手脚，有点中国古语削足适履的意思。

图片来源（https://themossreports.files.wordpress.com/2010/12/procrustes1.jpg）

Procrustes analysis分析手段

R

library(vegan)>procrustes ()函数

Function procrustes rotates a configuration to maximum similarity with another configuration.

Function protest tests the non-randomness (‘significance’) between two configurations.

Procrustes analysis用于比较两个形状的相似性，将其中一个形状进行旋转以获得与另一个形状的最大相似度。

 

R输出结果解读

Function protest performs symmetric Procrustes analysis repeatedly to estimate the ‘significance’ of the Procrustes statistic.

Function protest uses a correlation-like statistic derived from the symmetric Procrustes sum of squares ss as r = sqrt(1-ss),# correlation 系数, t0, t

通过对对称Procrustes进行替换迭代，每次计算一个相关系数t，999次得出t的分布，再检验t0是否显著

and also prints the sum of squares of the symmetric analysis, sometimes called squared m12. Function protest has own print method, but otherwise uses procrustes methods. Thus plot with a protest object yields a “Procrustean superimposition plot.”

 

ss，sum of squares，Sum of squared differences between X and Yrot， //sometimes called squared m12，(m12还是m12的平方是ss)

Yrot	Rotated matrix Y.
X	Target matrix.
ss	Sum of squared differences between X and Yrot.
rotation	Orthogonal rotation matrix.
translation	Translation of the origin.
scale	Scaling factor.
xmean	The centroid of the target.
symmetric	Type of ss statistic.
call	Function call.
t0	This and the following items are only in class protest: Procrustes correlation from non-permuted solution.
t	Procrustes correlations from permutations. The distribution of these correlations can be inspected with permustats function.
signif	‘Significance’ of t
permutations	Number of permutations.
control	A list of control values for the permutations as returned by the function how.
control	the list passed to argument control describing the permutation design.

 

 

Mantel test

Reference：

http://mb3is.megx.net/gustame/other-methods/procrustes-analysis

Null hypothesis

The degree of concordance between two (or more) matrices is no greater than expected given random inter-matrix associations.

http://jackson.eeb.utoronto.ca/procrustes-analysis/

#########################################################e.g.

Tai, et al, 2015, AEM文章表中各项对应R输出结果

m12-->ss

correlation-->t0

significance-->signif