In this chapter I describe how Felsenstein’s pruning algorithm can be used to calculate the likelihoods of Mk and extended-Mk models on phylogenetic trees. I have also described both ML and Bayesian frameworks that can be used to test hypotheses about character evolution. This chapter also includes a description of the “total garbage” test, which will tell you if your data has information about evolutionary rates of a given character.
Analyzing our example of lizard limbs shows the power of this approach; we can estimate transition rates for this character over macroevolutionary time, and we can say with some certainty that transitions between limbed and limbless have been asymmetric. In the next chapter, we will build on the Mk model and further develop our comparative toolkit for understanding the evolution of discrete characters.
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