Daniel A. Vasco and Keith A. Crandall

Intra-host HIV evolution within patients is a dynamic process dependent upon the interaction of the virus and the host. Viral population parameters such as generation time, growth rate and genetic diversity are determined by this interaction. This interaction can cause the effective population size and genetic diversity of the viral population to change rapidly over time. Therefore, it is important to have efficient and fast estimators of these parameters which can take into account more realistic features of the varying host environment of the virus. In my talk I discuss several coalescent statistical methods based upon summary statistics estimated from HIV genealogies in varying host environments. Such summary statistics include the number of segregating sites in the sample, the pairwise differences between sequences, the estimated number of segregating sites along a branch of a genealogy and some other more recently developed measures. By combining phylogeny reconstruction and coalescent theory powerful methods of analysis can be developed which include: parameter estimation, statistical tests of neutrality and hypothesis testing. However, coalescent and phylogenetic theory that includes varying host environments is essentially a nonlinear estimation problem which makes computation of statistical inferences challenging. Some problems include: inferring estimation bias, determining consistency of the estimators, Monte Carlo estimation of the sampling variance of estimated parameters determined from a single genealogical history, as well as demonstrating existence of minimum variances for such histories. A case study illustrating these problems is presented using set of 1200 HIV sequences serially sampled from three patients over a three week time interval.