[R-sig-ME] spatial auto-correlation or more complicated pseudo-replication?

[Thomas Merkling]

Hi all,

I'm wondering how to best model data from an experimental design 
involving a spatial component. This is a study on seabirds nesting on 
artificial cliffs: each nest has been attributed an experimental 
treatment (supplemented or not), while making sure that there was a 
variable proportion of surrounding nests of the opposite treatment. Our 
main goal was to investigate if laying date of a focal pair was 
influenced by its treatment and/or by the proportion of surrounding 
nests of the opposite treatment (hereafter, "Prop"), which we calculated 
at 3 different spatial scale (local, panel and global, see 
https://drive.google.com/open?id=1OrJQCkNfBO6KOBHSlkOoQyAdTrqtIdY8 for a 
visual representation).

Hence, the treatment information of a focal pair is used in the 
"Treatment" predictor variable, but also in the calculation of "Prop" 
for the surrounding pairs (the number of pairs affected depending on the 
spatial scale considered), thereby leading to some pseudo-replication.  
Since this is dependent on the distance (i.e. "Prop" of pairs closer to 
a focal one are more influenced than pairs further away), we thought 
that accounting for spatial auto-correlation for be sufficient. We used 
the spaMM package to do so, and our models look something like:

Laying ~ Treatment * Prop + Year + (1|PairID) + Matern(Y2011|x + y) + 
Matern(Y2012|x + y)

with two Matérn correlation random effects (one for each year of the 
study) being included (x and y being the spatial coordinates of the nests).

My question is: Is this random effect structure taking into account the 
fact that "Prop" of a focal pair depends on the "Treatment" of the 
surrounding pairs or not ? If not, how can we account for that?

Thanks in advance for your help!
Thomas


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