Inferring the population history of an epidemic from a phylogenetic tree

Phylogenetic or family trees reconstructed from a sample of individuals belonging to a population or species can be used to infer population dynamic history. A method for making such inferences involves visual inspection of the graphs of the numbers of lineages in the phylogeny plotted against the times when they occur. One transformation of the lineages axis often produces a linear lineages-through-time plot if the population has been growing exponentially. However, that transformation is known to fail under certain circumstances. We report a series of simulation studies designed to determine the conditions under which the transformation fails. As long as the sample represents less than 0.5% of individuals in the total population, the Type 1 error rate is acceptable. This means that studies of virus populations are likely not to suffer from transformation failure, so long as a random sample from the population is represented. When the transformation does fail, the resultant lineages-through-time plot is very similar to a two-stage epidemic process.