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I am interested in investigating the relationship between species composition and several environmental factors. My question is whether it is appropriate to use PERMANOVA to select a 'best' combination of explanatory variables to use in subsequent CCA analyses.

I ask because a recent diet analysis paper Kemper 2017: Dietary variability in two common Alaskan skates used this approach.

PERMAVOVA was used to test individual explanatory variables. The significant explanatory variables were subsequently used in a CCA to visualize the results. Something like:

library(vegan)
data(varespec)
data(varechem)

perm.1 = adonis(varespec ~ N + P + Al + S + Mn, data = varechem, 
permutations = 1000 ); perm.1

# N, P, and Al are significant


# I now visualize the relationship of individual species along synthetic 
gradients composed of the three significant variables found in PERMANOVA

cca.1 = cca(varespec ~ N + P +Al, data = varechem); cca.1

anova(cca.1, by = 'term')
anova(cca.1, by = 'margin')

plot(cca.1, display = c('sp','cn'))

The paper claimed that "CCA results generally were consistent with those of PERMANOVA". This seems a bit circular, but I am wanting to know if this approach is an acceptable means of choosing several explanatory variables from a greater pool of possible variables.

Perhaps a related followup question: "Is CCA an appropriate means to visualize the relationships described by PERMANOVA?"

Kodiakflds
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    I don't see the point of the PERMANOVA step; CCA will work just fine with the original set of variables and you can do selection in CCA. Unless there was something special about the situation in the paper you cite, this seems like a superfluous step at best. – Gavin Simpson Jul 07 '17 at 17:45
  • Thank you @GavinSimpson. I also felt this was a bit redundant, but wanted some feedback. One reason they may have used PERMANOVA is that the R output gives an r^2 metric allowing the researcher to describe 'Variance explained" by different factors. Would you mind weighing in [on this question?](https://stats.stackexchange.com/questions/223389/interpreting-canonical-correspondence-analysis-cca-inertia-in-vegan?rq=1). The Kemper paper used Inertia to describe 'variance explained', but ask I layout in the other question, there seems to be some disagreement whether inertia can be used that way – Kodiakflds Jul 07 '17 at 19:18
  • **vegan** now has an adjusted R2 for CCA models. (I'm not sure if `varpart()` uses it but if not you can fit the models by hand to get it.) – Gavin Simpson Jul 07 '17 at 21:47

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