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Redundancy analysis with ONLY factor variables

Tim Richter-Heitmann 
Dear list,

I wonder if RDA (and variance partitioning) is valid if the species 
table is regressed against three factor variables only. Factor1 has 
three levels, the other two Factors have two levels, resulting in a 
design with 12 different level combinations (nearly balanced).

The varpart would then look like varpart (species, Factor1, Factor2, 
Factor 3).

I am asking because if i repeat the RDA with a combined factor:

comb <- paste(Factor1, Factor2, Factor3)

rda(species~comb).

i get almost the exact same result as with

rda(species ~ Factor1+Factor2+Factor3).

In both cases, i get the same horseshoe-like ordination (showing a very 
strong separation on axis 1), but different sets of biplot arrows.

With varpart, no joint explained variability is found, and interestingly 
the ratio between the single explained fractions resembles the ratios 
between the F-statistics obtained with PERMANOVA 
(adonis2(species~Factor1+Factor2+Factor3)).

Ecologically, the results do make a lot of sense.

I was wondering if someone could explain if the approach is valid, if 
joint explained variability can be found with such a design, and if 
there are pitfalls one needs to take care of.

Thank you and best wishes, Tim