Hello,

I'm trying to analyse the effect of tree species richness within a plot on
the number of insect herbivores per tree.
Unfortunately, a huge proportion of the herbivore count data has zero
values. I have tried all the transformations I have come across in the
literature and have even tried ranking the data but to no avail.

Due to the nested nature of our experiment, I initially ran models using
lmer and the poisson family, specifying AREA and PLOT as random effects.
> m1 <- lmer(HERBIVORE ~ RICHNESS, (1|AREA/PLOT), family="poisson")

The residuals were not normally distributed so I tried to run the same
model using the AD model builder, accounting for zero inflation and trying
both the poisson family or the negative binomial family but still, there is
decreasing variance in the residuals for higher fitted values.
>m2 <- glmmadmb(HERBIVORE ~ RICHNESS, (1|AREA/PLOT), family="nbinom",
zeroInflation=TRUE)

My only other option, as far as I can see, would be to report analysis
based on the presence/absence of herbivores on each tree (using a binomial
error distribution in lmer) but I would be unable to discuss any effect of
tree species richness on herbivore densities.

Is there a further method of analysis I can try in R?
Could the MCMC method be used with this dataset? (From what I understand,
it is only to be used when you have 3 or more random effects but, as I am
new to this, I may be wrong.)

Thanks, in advance.

Eva

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