Estimating fixed vs. random effects with lme (Hausman?)

#1
I have ran two lme mixed effects models in R, both using the same fixed effects variables but each with a different random effect variable. My reviewer has said I should use the Hausman test to estimate the effect of fixed vs. random effects. On looking in to this I can only find R code for the plm package for panel data analysis. This does not seem appropriate for lme models without a time element. Can anyone suggest a way of conducting this, or a more appropriate test for the significance of the random effects?

I calculated within and between group indices Rwg and ICC variables before modelling which suggested good within and between group variance, does this not adequately justify the random effects?