Hi everyone,

I'd like to use MCMCglmm to look at the importance of phylogenetic
relatedness to variation in a plant drought tolerance trait, while also
accounting for a random effect of study site and a fixed effect of climate.
The difficulty is that my drought tolerance trait data is significantly not
normally distributed (according to the *shapiro.test* function), even when
log or square-root transformed (all p < 0.001). This comes from the fact
that some arid species are very drought tolerant, producing a right-skewed
trait distribution. My data is best-fit by a gamma distribution, according
to the* fitdistrplus* package, but my data is better fit by a normal
distribution than any other family that MCMCglmm can model.

I know there are ways to fit mixed-effects models that allow for
permutation tests, to avoid assuming normal distributions, but these
packages (coin, lme4), don't allow for specifying a phylogenetic
relatedness matrix. This leads me to the problem that it seems incorrect to
use MCMCglmm to estimate a signal of relatedness for this non-normal data,
but it also seems incorrect to use packages that allow for permutation
tests without accounting for relatedness.

So, to try to figure out a way around this, my questions are:

1) How non-normal is "too" non-normal for MCMCglmm, if no other
distribution family is a better option? Is it ever acceptable to fit
non-normal data this way?

2) There seem to be permutation tests (like in the *coin* package) that can
handle significance testing for mixed-effects models, but not for models
with the phylogenetic relatedness matrix specified. Does something like
this exist that I'm not aware of?

3) Or, is there a way to apply a permutation test to the MCMCglmm output?

Thanks very much for your help!

Best,

Megan

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