# How to deal with spatio-temporal autocorrelation?

Hi!
I have a field study in which the abundance of insects is measured in 4 nests (`NestID`) at 32 Sites (`Site`) 5 times (`Round`). Each round was one month apart, but I am missing data from Round #4, so virtually I have only 4 rounds with uneven spacing between them. The average abundance across rounds is hump-shaped:

My interest is the environmental factors (`x`) that might affect abundance.
I am unsure how to proceed. I want to account for the autocorrelation at the `Site` level with`(1|Site)`, and also for the temporal aspect. On forums proposed solution is usually: `y ~ Round + (1 + Round|NestID)`, and since my `NestID` is nested in `Site` I thought of doing :

``````m1 <- bf(y ~ x + Round + (Round|Site/NestID))
``````

or

``````m2 <- bf(y ~ x + Round + (Round|NestID) + (1|Site) + (1|NestID:Site))
``````

or

``````m3 <- bf(y ~ x + s(Round, k = 4) +  (1|Site/NestID))
``````

but I am not sure if this is what I want exactly and if including both `NestID` and `Round` is not redundant.

I actually wondered if, given I am not interested in temporal effects, `y ~ x + (1|Site/NestID)` would be the appropriate model, since it averages over different nests, so no need to add the `Round` to the model?
Alternatively `y ~ x + Round + (Round|Site)` (or equivalent with a spline) if I am interested in the temporal effect on the abundance.

I am also not sure if I should treat `Round` as numerical or categorical predictor.

Do the factors `x` vary only across sites, or also across nests and/or rounds within sites?
@jsocolar, would you suggest using the `NestID` in models with nest-level predictors and `Site` in models with site level-predictors?