The total variance explained and the unique contributions
of each subset and their joint effects were obtained by
the following: (1) RDA was run with all three subsets as
environmental variables and no covariables to obtain a
measure of the total variance, (2) partial RDA was run with
one of the three subsets as environmental variables and no
covariables, and (3) partial RDA was run with one of the
three subsets as environmental variables constrained by the
remaining two groups as covariables and reverse. The third
step was repeated three times and each subset was treated
as environmental variables constrained by the remaining
subsets as covariables. This procedure resulted in four runs
of RDA for each subset combination or a total of 13 runs of
RDA were done for the full set of analyses for each ecosystem
(Table 2). With three subsets of environmental
data, the total variation of water chemistry was then partitioned
into seven components including covariance terms
(Fig. 2, Table 3). The variation explained by these subsets
is subtracted from the total variation (1.0 in case of RDA)
to obtain the unexplained variation.