[R-sig-eco] mantel within mantel? multidimensional variance

[Mgr. Martin Weiser]

Dear friends,

I need to quantify variance within variance, and what is worse, say if
it is non-random.
This is the setup: in the experiment, there were 2 (partly correlated)
treatments, each of six levels (but theoretically of infinite levels,
so I treated them as continuous).
Different species responded to them, and we measured various traits
("endotraits").

We used R2 from the per-species redundancy analyses (RDA) as a
reaction norm: higher R2, more the species responds to the treatment
(so traits were used as "species" in the community ecology jargon). We
have twice as much RDAs as there were species (because of 2
treatments).

Next, we correlated these R2 (reaction norms) with some other traits
per species ("exotraits"). As there were 2 correlated treatments (lets
say irrigation and fertilisation), and we used the same reaction norms
for correlation with different exotraits, the correlations were
obviously non independent. To overcome this, we run Mantel test
(matrix1= species x reaction norms to treatment, matrix2=species x
exotraits).

Next, we are interested in "endotraits" x "exotraits" correlation. For
this, we used endotrait scores from the per-species RDAs on the
treatment axis (constraining variable). Correlations are
non-independent again, so we wanted an overall test. And here comes
the problem: results of Mantel tests (matrix1=species x endotrait
scores, matrix2=species x exotraits) are suprisingly weak. Some single
correlations of endotrait scores x exotraits seem to be pretty afar
from random, but the overall mantel...

I think this is because single endotrait can not show better
correlation than the overall reaction norm, which is based on them, so
something like (pval of this mantel)*(1-pval of the correlation of
reaction norm with exotraits) may be desirable for the overall test,
but I simply do not know.

Any advice?

Best,
Martin Weiser

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