corncob DA for continuous covariates + spatial autocorrelation HELP

[AnnaAntonatouPap]

Hello,

So we are investigating the variations in gut microbiota of great tits across a gradient of urbanization. We would like to identify the differentially abundant microbial taxa between samples collected from urban and rural sites. Additionaly, we want to analyse abundance of which microbial taxa changes with changing amount of impervious surface area (ISA, a continuous covariate) We have 73 samples which are collected from different 9 Sites across an urban-rural gradient  Because of these 9 sites I want to control for statistical non- independence  So my question is if it's right and reasonable to control of the effect of Site in dispersion and by this I am kind off controlling for the non independence, lets say something as a random effect    The model that I have is this:

corncob_ISA<-differentialTest(formula = ~ ISA,
                              phi.formula = ~ISA+ Site,
                              formula_null = ~ 1,
                              phi.formula_null = ~ ISA+Site,
                              test = "Wald", boot = FALSE, 
                              data = data,
                              fdr_cutoff = 0.05)

Do you think this is the right way to go?  I will appreciate any help  and comment on this, Thanks in advance, Anna Antonatou - Papaioannou