Probabilistic Methods and Rate Heterogeneity

Evolutionary forces such as mutation, drift, and to a certain extent selection are stochastic in their nature. It is thus not surprising that probabilistic Models of sequence evolution quickly became the workhorse of molecular evolution research. The long, ongoing effort to accurately model sequence evolution stems from two different needs. The first is that of evolutionary biologists: Models of sequence evolution allow us to test evolutionary hypotheses to reconstruct phylogenetic trees and ancestral sequences [1–3]. The second is that of bioinformaticians and system biologists— probabilistic/evolutionary methods are critical components in numerous applications. For example, the construction of similarity networks is based upon all-against-all homology searches. Each pairwise evaluation is done using tools such as Blast and Blat [4, 5], which rely on evolutionary models. Additional examples include gene finding and genome annotation [6], alignment algorithms [7, 8], detecting genomic regions of high and low conservation [9, 10], prediction of transcription factor-binding sites [11], function prediction [12], and protein networks analysis [13, 14]. In this chapter, we describe how probabilistic models are used to study