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I am working with ecological count data in order to analyze differences/any contrast in species composition between warm and cold year communities. The abundances of species were recorded from multiple sites, with two trips per site. For example in September of 1999, species were collected/recorded twice from Site 1. I have columns separated into years, site, trip (replicates), and group (warm or cold). I need to test if there is any significance in counts due to site effect or replicates within sites (the trips). Basic ANOVA was what was going to be used. This is essentially how I am attempting to setup the model:

aov(Count ~ Site * Trip + Years, data)

Like most count data it is not normal and has lot of zeros so its over-dispersed and negative binomial will be used as well (using the mvabund package). Some of my other parts of the analysis requires data to be fourth root transformed due to dominant species. But I am unsure if data should be transformed for ANOVA and GLM as well? When an ANOVA was performed with transformed data, there appeared to be significant $p$ values for the site and the interaction categories, but was neither was significant when applied on just raw counts. I'm just unsure if transformations are appropriate for this analysis.

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    $\begingroup$ It's hard to say without doing an exploratory data analysis/modelling of the data. However, if say your data could be modelled appropriately via a zero-inflated negative binomial model, then you would not have to further transform your data. That being said, counts in ecology are often incredibly dispersed so this may not be appropriate. Sometimes species richness is something that's easier to model, too $\endgroup$
    – Alex J
    Commented Feb 15 at 22:52

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In my honest opinion you should not use aov() for modeling repeated ecological count data. Further, transforming your outcome variables is usually not the best approach. Instead you should model your data using a distribution that best describes your data. Since it appears you are using R for your data analyses, I would suggest a mixed-model approach either using lme4::glmer(), or glmmTMB::glmmTMB(). There is a lot of information on this site and elsewhere on the WWW how to model ecological (zero-inflated / zero-altered) count data.

Maybe research a bit more about this and then perhaps come back to post another more specific question.

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    $\begingroup$ +1. The ANOVA to me is anyway redundant if you already have much more flexible tools like GLMMs that are specifically designed for this stuff. It doesn't really add anything to the analysis. $\endgroup$
    – Shawn Hemelstrand
    Commented Feb 18 at 4:05
  • $\begingroup$ @ShawnHemelstrand exactly! In McElreath's book "Statisitical Rethinking" 2nd Edition, page 15 he says "I want to convince the reader of something unreasonable: multilevel regression deserves to be the default form of regression. Papers that do not use multilevel models should have to justify not using a multilevel approach." $\endgroup$
    – Stefan
    Commented Feb 18 at 4:25

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