Hello,
I am working on an experiment analyzing rhizosphere and mycorrhizal fungal communities belonging to different tundra plant roots. Using two DNA extraction protocols on the same plant roots, I have generated both bacterial and ectomycorrhizal species matrices.
I want to compare the two matrices to see if the communities are correlated to each other but am running into problems executing. The bacterial matrix is obviously much larger than the ectomycorrhizal matrix which is causing problems when trying to do a mantel test in R.
I know in theory mantel tests do not require symmetrical matrices, however the packages I have tried using in R all do require symmetrical matrices (vegan, ape, ade4).
I was hoping somebody might have an idea how I can go about comparing these two matrices, either by modification so that the matrices are symmetrical, or perhaps another piece of code/ software package.
Thanks
In general, if the matrix A ( n by n) is non-symmetric real matrix, the matrix B( n by n) = (1/2) *( A + A'), where A' refers to the transpose of the matrix A, B is symmetric matrix constructed from A.
B is the projection of the matrix A in the subspace of all symmetric matrices of the space M( n by n, R), the subspace of all symmetric matrices V1, and the subspace of all skew-symmetric matrices V2, are completely disjoint subspaces and form a complete disjoint decomposition of the space M( n by n, R)
A( n by n) = (1/2) *( A + A') + (1/2) (A - A') = B + C
B is the projection of A in subspace V1, C is the projection of A in subspace V2, since these subspaces are mutually disjoint, the projection matrices B and C are unique for every such matrix A ( n by n).
Take a look at this search the download is the one that I thought was most useful to you. Best wishes David Booth
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