I am attempting to partition variance of a site by species matrix between
two explanatory matrices (let's call them [E] and [S]). [E] is composed of
environmental variables and [S] is a distance matrix of phylogenetic
distances.


Below is a subset of the phylogenetic distance matrix.
[S] :
       1     2     3     4     5     6     7     8     9    10
1    0.0  69.0  69.0 156.0 156.0 156.0 156.0  63.4  63.4 156.0
2   69.0   0.0  13.8 156.0 156.0 156.0 156.0  69.0  69.0 156.0
3   69.0  13.8   0.0 156.0 156.0 156.0 156.0  69.0  69.0 156.0
4  156.0 156.0 156.0   0.0  15.0  52.2  52.2 156.0 156.0  52.2
5  156.0 156.0 156.0  15.0   0.0  52.2  52.2 156.0 156.0  52.2
6  156.0 156.0 156.0  52.2  52.2   0.0  19.6 156.0 156.0  40.0
7  156.0 156.0 156.0  52.2  52.2  19.6   0.0 156.0 156.0  40.0
8   63.4  69.0  69.0 156.0 156.0 156.0 156.0   0.0  31.4 156.0
9   63.4  69.0  69.0 156.0 156.0 156.0 156.0  31.4   0.0 156.0
10 156.0 156.0 156.0  52.2  52.2  40.0  40.0 156.0 156.0   0.0


I am using R package 'vegan' and function 'varpart' to examine the relative
contribution of both matrices, but the output is confusing.



No. of explanatory tables: 2
Total variation (SS): 9.7659
            Variance: 0.69756
No. of observations: 15

Partition table:
                            Df          R.squared      Adj.R.squared
 Testable
[a+b] = X1            14          1.00000
    TRUE
[b+c] = X2             6            0.4895            0.10662
TRUE
[a+b+c] = X1+X2   14         1.00000
 TRUE

Individual fractions
[a] = X1|X2             8                           TRUE
[b]                           0                            FALSE
[c] = X2|X1              0                            FALSE
[d] = Residuals                                      FALSE



What does it mean to have an R squared of 1 in this situation? Is there a
better way to test for the contribution of phylogenetic distance? Any
advice would be appreciated.

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