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Methods for quantifying state change in phylogeny- consistency index

I have a cladogram, and I have mapped character states of different taxa onto it.

It seems that the most common indices used to measure homoplasy are still the consistency index and retention index. I am curious as to whether there are any other methods I should be looking at, and why consistency index is more common over Homoplasy Excess Ratio test.

sequence phylogenetics

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