Test groups of spatially dependent data? I have a set of ~100 forested natural reserves surrounded by multiple non-overlapping buffers of 100, 500, 1000 and 2000m. 
I would like to understand if there is a higher rates of disturbances in the natural reserves, or in surrounding buffers. The null hypothesis assumes that the disturbance rates are the same in natural reserves and in surrounding buffers. My disturbance data comes from Global Forest Watch dataset and represent sum of yearly disturbances. I have standardized the area of disturbances to "disturbance rates", i.e. recalculated disturbed area to the area of original forest in 2000.

However, I am not sure how to analyze this type of data? can I simply run ANOVA on sum of disturbances by reserves and buffers, but what is its spatial equivalent? I assume my data are not spatially independent, as my buffers surround my natural reserves.
Boxplots look like:
 
What are your thoughts about how can I test my hypothesis?
 A: I think ANOVA might be misleading - the spatial structure might be important. How much is anyone's guess. You may check out Conditional Auto-Regressive (CAR) models, there is a nice case study using Stan. Also you may be interested in spatial (2D/multivariate) Gaussian processess - can be used from the brms package (letting you stick to R's formula syntax). There is also a more advanced case study in Stan. Neither of those will exactly "test a hypothesis", but you will be able to say things like "probability that the rate of disturbances differs by more than Y is X%" which is IMHO better.
Note however that this stuff is not exactly straightforward and it may be better to lose some information with a simpler model than use a tool you do not understand well. 
A simpler approach that might be OK would be to add a specific (a.k.a. random/group) effect/intercept for each area (reserve + its buffers). Really depends on your data if this is reasonable. In any ways, always do a lot of visualisations and sanity checks (e.g. if your effect estimates are surprisingly large, they are likely wrong).
