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12.1 Background

A phylo-HMM can be thought of as a machine that probabilistically generates a multiple alignment, column by column, such that each column is defined by a phylogenetic model. As with the single-sequence HMMs ordinarily used in biological sequence analysis [7], this machine probabilistically proceeds from one state to another1, and at each time step it “emits” an observable object, which is drawn from the distribution associated with the current state (Figure 12.1). With phylo-HMMs, however, the distributions associated with states are no longer multinomial distributions over a set of characters (eg,{A, C, G, T}) but are more complex distributions defined by phylogenetic models.

Phylogenetic models, as considered here, define a stochastic process of substitution that operates independently at each site in a genome.(The question of independence will be revisited below.) In the assumed process, a …