  Phylogenetic analyses which include fossils or molecular sequences that are
sampled through time require models that allow one sample to be a direct
ancestor of another sample. As previously available phylogenetic inference
tools assume that all samples are tips, they do not allow for this possibility.
We have developed and implemented a Bayesian Markov Chain Monte Carlo (MCMC)
algorithm to infer what we call sampled ancestor trees, that is, trees in which
sampled individuals can be direct ancestors of other sampled individuals. We
use a family of birth-death models where individuals may remain in the tree
process after the sampling, in particular we extend the birth-death skyline
model [Stadler et al, 2013] to sampled ancestor trees. This method allows the
detection of sampled ancestors as well as estimation of the probability that an
individual will be removed from the process when it is sampled. We show that
sampled ancestor birth-death models where all samples come from different time
points are non-identifiable and thus require one parameter to be known in order
to infer other parameters. We apply this method to epidemiological data, where
the possibility of sampled ancestors enables us to identify individuals that
infected other individuals after being sampled and to infer fundamental
epidemiological parameters. We also apply the method to infer divergence times
and diversification rates when fossils are included among the species samples,
so that fossilisation events are modelled as a part of the tree branching
process. Such modelling has many advantages as argued in literature. The
sampler is available as an open-source BEAST2 package
(https://github.com/gavryushkina/sampled-ancestors).
