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Relationship between instantaneous rate of change and global clock model?

What is the relationship between the instantaneous rate of change in the rate matrix of continuous time Markov chain and the branch rate/clock rate in a global/strick clock model? For instance, in an F81 or GTR model of nucleotide substitution, should the individual instantaneous rates of change (e.g., A -> C, T -> C, etc.) sum up to the global clock rate?

clock model markov chain rate of change

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