Ecological data is in complex and underlying model assumptions are till certain degrees always violated. For example, assume a plant species increases in abundance (y) with a decrease in temperature (x) in mountains which also means it increases with height (h) as proxy for SA.
We can fit a log-linear model with poisson error (e) as: log(E(y|x))=bx+f(h)+e, whereby f(h) corrects for the spatial construct according to Legandre:
Article Spatial Autocorrelation: Trouble or New Paradigm?
However, if x ≈ f(h), then b ≈ 0. Hence, if a function corrects for the spatial construct the estimate on b appoximates 0. However, also in rivers organic matter or otherwise conductivity increase downstreams and some species will naturally be more abundantly cluster along this spatial structure.On the other hand, if the residuals are strongly correlated with height as r ≉ y- log(E(y|x)), and h ≉ r. Then the assumption on iid is not strongly violated, given the realisations, modeled as e. But when h ≈ r we have SRA, this is what I understand as SRA. This is also discussed in https://doi.org/10.1111/j.1365-2699.2012.02707.x.
Question 1.) Thus, I believe SA is not an issue while SRA is. Is this correct?
Question 2.) Moreover, iid is ascribed to the realisations (not a property of it) based on the underlying knowledge of the data generating process (reasonable sample protocol and study setup/design) and till some extend visualisations (i.e., qq-plot). But, when h is unkown and h ≈ r are strongly correlated, our samples are still iid, simply because we have no knowledge of h ≈ r?
Thank you in advance!
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