If r_i is the rate on the i’th branch then ucld.mean is simply the sum of r_i for all i divided by the number of branches (2n-2). It is the simple arithmetic mean of the branch rates. Since some branches represent much more time than others, this rate will not necessarily be the same as the total number of substitutions per site divided by the total amount of time that the tree represents. The meanRate parameter is in fact the total number of substitutions per site divided by the total amount of time that the tree represents. So the meanRate can be thought of as the mean of the r_i weighted by t_i (the length of time of the i’th branch). That is, it is the sum of r_i * t_i divided by the sum of t_i.

- If you have prior information on the overall rate it is best to reflect that with a prior distribution on the ucld.mean as that is the actual parameter of the model. This actually contradicts earlier advice to put it on the meanRate statistic.