[R-sig-eco] mixed effects in ordination (?)

[Martin Weiser]

Dear friends,

Could you please help me with analysis? I am afraid that it involves
crossed random effects in the mixed-effect constrained ordination
setting, so to say.

Goal:
Show an effect of the species trait (single one) and treatment (four
levels, quantitative scale) on parameters. Trait x treatment
interaction is possible. If possible, show changes through time. 

Data:
Individuals of 7 species, subjected to 4 treatment levels (fully
factorial) - from 6 to 12 individuals in each combination. Each
individual scored 4 times (same times: 1st wk, 2nd wk, 3rd wk, 4th wk).
Several (10) parameters scored every time on each individual.

What I did:
In order to avoid multiple testing (the parameters are likely to be
correlated to each other), I decided to use multivariate analysis
(RDA). I am by far much more accustomed to vegan than ade4, so excuse
me if I use some "veganisms". Predictors: time, trait, treatment
(possibly with interactions), conditioned on individual identity to
avoid treating records from the same plant as independent. Variance
partitioning.

Here comes the problem: how to set permutations in order to be able to
report p_vals (some people just are not happy without them)? Since
individuals of the same species share the same trait value, maybe the
right way is to: shift observations within individual (if time is among
predictors for the particular model) and permute trait value among
species. Is it so? Is this treatment of the pseudoreplication at the
species level (i.e. only in the significance testing, not in the
ordination per se) ok?

I also tried to use different approach: I averaged all params
individual-wise (getting rid of temporal pseudoreplication, but also
time effects), and subsequently I averaged the result within treatment
x species levels. I assume that I can go for simple free permutations
this way? Pity is that this way, I cannot see development in time.

And another way: I averaged params for species x treatment x time
groups, ignoring interdependence of records from the same individual,
hoping that the effect of an individual "dissolves" in the average. Is
that meaningful? If yes, what is the appropriate permutation structure
in this case?

But maybe I miss something and there are better ways how to deal with
this problem?

Any suggestions (ok: not any, just those made in an attempt to help :-)
) are appreciated.

With the best regards,
Martin Weiser