Topologies of the Conditional Ancestral Trees and Full-Likelihood-Based Inference in the General Coalescent Tree Framework

The general coalescent tree framework is a family of models for determining ancestries among random samples of DNA sequences at a nonrecombining locus. The ancestral models included in this framework can be derived under various evolutionary scenarios. Here, a computationally tractable full-likelihood-based inference method for neutral polymorphisms is presented, using the general coalescent tree framework and the infinite-sites model for mutations in DNA sequences. First, an exact sampling scheme is developed to determine the topologies of conditional ancestral trees. However, this scheme has some computational limitations and to overcome these limitations a second scheme based on importance sampling is provided. Next, these schemes are combined with Monte Carlo integrations to estimate the likelihood of full polymorphism data, the ages of mutations in the sample, and the time of the most recent common ancestor. In addition, this article shows how to apply this method for estimating the likelihood of neutral polymorphism data in a sample of DNA sequences completely linked to a mutant allele of interest. This method is illustrated using the data in a sample of DNA sequences at the APOE gene locus.