Phylogenetic Hidden Markov Models

Phylogenetic hidden Markov models, or phylo-HMMs, are probabilistic models that consider not only the way substitutions occur through evolutionary history at each site of a genome but also the way this process changes from one site to the next. By treating molecular evolution as a combination of two Markov processes—one that operates in the dimension of space (along a genome) and one that operates in the dimension of time (along the branches of a phylogenetic tree)—these models allow aspects of both sequence structure and sequence evolution to be captured. Moreover, as we will discuss, they permit key computations to be performed exactly and efficiently. Phylo-HMMs allow evolutionary information to be brought to bear on a wide variety of problems of sequence " segmentation, " such as gene prediction and the identification of conserved elements. Phylo-HMMs were first proposed as a way of improving phylogenetic models that allow for variation among sites in the rate of substitution [9, 52]. Soon afterward, they were adapted for the problem of secondary structure prediction [11, 47], and some time later for the detection of recombination events [20]. Recently there has been a revival of interest in these models [41, 42, 43, 44, 33], in connection with an explosion in the availability of comparative sequence data, and an accompanying surge of interest in comparative methods for the detection of functional elements [5, 3, 24, 46, 6]. There has been particular interest in applying phylo-HMMs to a multispecies version of the ab initio gene prediction problem [41, 43, 33]. In this chapter, phylo-HMMs are introduced, and examples are presented illustrating how they can be used both to identify regions of interest in multiply aligned sequences and to improve the goodness of fit of ordinary phylo-genetic models. In addition, we discuss how hidden Markov models (HMMs), phylogenetic models, and phylo-HMMs all can be considered special cases of general " graphical models " and how the algorithms that are used with these models can be considered special cases of more general algorithms. This chapter is written at a tutorial level, suitable for readers who are familiar with phylogenetic models but have had limited exposure to other kinds of graphi-cal models.