Confidence interval for Repeatability from a lme mixed model I have a (lme) mixed model of this type:                  
model=lme(trait1~tl_s+year+month_s+I(month_s^2)+I(month_s^3),random=~1|ID,correlation=corAR1(form=~tim),data=depm3,method="REML") 

I'm interested in estimating the repeatability of the trait I'm modelling (trait1 in this case). I get a point estimate with this code:
R=as.numeric(VarCorr(mod))[1]/(as.numeric(VarCorr(mod))[1]+as.numeric(VarCorr(mod))[2])

But what would be the code to extract confidence interval for R estimate? I read that parametric bootstrapping would be an option here, but I don't really know how to implement it.
I have check some recent posts on the topic like this one...
How to calculate estimated proportions and their confidence intervals from a mixed model?
...but I haven't really found the answer to my question.
Any advise would be appreciated
Thanks
 A: There is no package to deal with lme repeatability when it includes autocorrelation and/or variance functions. I tried to code the function myself using the boot function for bootstrapping in order to get the confidence intervals.
library(boot)
rsq <- function(formula,cor.b,weights.b,random.b, data,indices) {
d <- data[indices,] # allows boot to select sample
fit <- lme(formula, data=d,correlation=cor.b,weights=weights.b,random=random.b)
VarComps=VarCorr(fit)
var_G <-as.numeric(as.character(VarComps[1,1]))
var_R <- as.numeric(as.character(VarComps[2,1]))
var_P <- sum(as.numeric(VarComps [,1]))
R=var_G / var_P
return(R)
}
results <- boot(data=depm3, statistic=rsq, R=2, formula=trait1~tl_s+year+month_s+I(month_s^2)+I(month_s^3), random.b=~1|ID, cor.b=corAR1(form=~tim))
boot.ci(results, type="bca") #to get confidence intervals
Usually, R should be around 1000 but it will take too long to be done.
However, the question here is: does the autocorrelation and variance function remain valid for the new dataset after bootstrapping?
