From genealogies to sequences

Abstract

Abstract In the previous chapter we discussed how genes or sequences are related in a population through their common ancestry. However, to model real data a model of how mutations cause changes in the DNA is necessary. To meet this several mutation models have been developed. Historically, the infinite alleles model appeared first (Kimura and Crow 1964), followed by the infinite sites model (Kimura 1969), and the finite sites model (Jukes and Cantor 1969). This development illustrates an increased focus towards analysis of nucleotide sequence data sets, but also a development towards increasing complexity of analysis. In this chapter we first introduce the three different types of mutation models, then a mathematical framework for working with probabilities of a sample configuration is discussed. We will mainly focus on the infinite alleles and infinite sites models and relate these models to the underlying genealogy of a sample. Mutations are assumed to be selectively neutral. This has the desirable effect that the mutation process can be separated from the genealogical process, because, in the absence of selection, the mutational process and the transmission of genes from one generation to the next are independent processes (genes have the same probability of transmission whatever their type). Thus, a sample configuration for n genes can be simulated using a two step procedure: (1) simulate the genealogy of n genes; (2) add mutations to the genealogy according to the chosen mutation model.