I am wondering if it is possible to conduct a Mantel test or any similar test in order to relate an asymmetric species x species matrix to a symmetric matrix (e.g. phylogenetic distance matrix)
The Mantel test is a statistical test usually of the correlation between two symmetric matrices of vectors. The matrices must be of the same rank (e.g. genetic versus geographical distance) – they are matrices of interrelations between the same vectors of objects. But the test can be modified for asymmetric matrices because the test itself does not appear to require any properties of the matrices themselves :)