A Bayesian approach to Nested Clade Analysis

The purpose of this study is to identify genetically distinct clusters of individuals based on related characteristic traits (namely phenotypic data) or geographical locations (namely phylogeographic data). There are 2 main steps to this process: inferring the genetic history of the sequences under study, and subsequently identifying significant clusters according to the phenotypic/phylogeographic measurements. Based on an evolutionary model and an appropriate model for the distribution of the phenotype, such inference is possible in a number of different ways. However, due to the multiple level uncertainty and the complexity of the models, it is essential that the methods avoid stepwise optimization in order to give statistically reliable conclusions. The main methods currently used for analysis of this type are called Nested Clade Analysis (NCA) and Nested Clade Phylogeographic Analysis (NCPA) for phenotypic and phylogeographic data respectively. In short, they rely on finding the optimal genetic history based on a simplified evolutionary model, and identifying significantly different clusters for the phenotype/geography (assuming the inferred genetic history as fixed) by using Nested Analysis of Variance and permutation tests. Such methods do not allow for the uncertainty of each step to fully propagate through the model and have been shown by simulations often to lead to false conclusions. Here we describe a coherent statistical framework for NCA/NCPA by taking a (Reversible Jump) Markov chain Monte Carlo approach to the genetic clustering problem. By considering a general evolutionary model and clustering constructions using haplotype trees for the phenotypic and phylogeographic analysis respectively, we construct a holistic method in order to obtain the global optimum of the parameters of interest. Several challenges arise in this process. The presence of homoplasy (representing convergent evolution, usually through back mutations) can obscure the analysis, increasing the number of possible histories that underly the data. This leads to intractable likelihoods and normalisation constants. Here we use Approximate Bayesian Computation to address these issues. In addition, the parameter space of clusterings is vast, so we employ adaptive methods and efficient proposals to ensure mixing and convergence. Lastly, we address inherent issues of similar clustering and phylogenetic inference problems such as label-switching (for the cluster parameters) and representation of trees (essential for convergence assessment). We implement our method for 3 datasets and discuss the results in relation to NCA and NCPA.