[R-sig-eco] Doing repeated measures on a randomized block design

[Dixon, Philip M [STAT]]

Rick,

There are (at least) two ways to set up a model for your experiment.  The difference is a detail of your sampling.  The two most likely schemes are:
1)	Each time you sampled, you went to the same branch (or perhaps same leaf).  Here, the repeated measurements are on the branch, not the tree.  Exposure (N/S) is characteristic of the branch.  In terms of the model variables, a branch is identified by combination of tree and exposure.  This leads to the traditional between/within repeated measures design.  If you assume compound symmetry (nested random effects), the lmer model  would be FvFm ~ Tree + Exposure + Date + Date:Exposure + (1|Tree:Exposure)
2)	Each time you sampled, you went to different branches.  Now the only level of repeatedness is the tree.  Now there is one observation per branch; each is characterized by exposure and date.  The model is simply a 2 way factorial inside blocks.  If you wanted to set up something like a compound symmetry model, you would have tree and observation as the random effects.  Since there are only 4 trees, I would treat trees as fixed. The lmer model is FvFm ~ Tree + Exposure + Date + Date:Exposure 

With 18 dates, I would stongly advice against a compound symmetry (split plot in time) model.  There is probably some structure to the correlations.  This means using lme() with something like a corAR1() correlation structure.  You can add that to either model, (to get CS+AR(1) for the first option or AR(1) in blocks for the second).  Or you could a "just an AR(1)" model for the first option by replace (1|Tree:Exposure) with the corAR1().
Best,
Philip Dixon