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

[Bob O'Hara]

Do you need to run Mantel tests at all? I don't see that you have 
measured any distances, as such, so I think you can do at leat as well 
by using standard [genrealized] linear [mixed] models.

I'm not sure I understand everything, but it sounds like you run an 
experiment with 2 treatments, and N species, and you measure T traits. 
So, for each trait you could have a model

y_t ~ (Treat1 + Treat2)*Species
(you could run this separately for each species, if that makes things 
easier)

and size of the Treat1:Species effect tells you how the species responds 
to the treatment (if you want a measure over all traits, a PCA on the 
coefficients should suffice).

It sounds like you are then asking how these reactions, i.e. the 
Treat1:Species effects are related to traits which are constant within a 
species, i.e. a Treat1:Trait effect.

So, for each y_t you could run a model

y_t ~ (Treat1 + Treat2)*(Trait+Species)
(or even make Species a random effect)

So, now I think you just want the Treat1:Trait effects. if the Trait's 
are discrete classes, then you can (again) run a PCA on the effects, to 
visualise the effects.

If you want to analyse all of the y_t's together, it gets a bit more 
complicated, but in principle it's the same, except you have a 
MANOVA-like structure. I think you could use a Seemingly Unrelated 
Regression approach.

Bob

On 06/08/2014 05:56 PM, Mgr. Martin Weiser wrote:
> 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 sed 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
>


-- 
Bob O'Hara

Biodiversity and Climate Research Centre
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