A Multi-Type Birth-Death model for Bayesian inference of lineage-specific birth and death rates

Heterogeneous populations can lead to important differences in birth and
death rates across a phylogeny. Taking this heterogeneity into account is
necessary to obtain accurate estimates of the underlying population
dynamics. We present a new multi-type birth-death model (MTBD) that can
estimate lineage-specific birth and death rates. This corresponds to
estimating lineage-dependent speciation and extinction rates for species
phylogenies, and lineage-dependent transmission and recovery rates for
pathogen transmission trees. In contrast with previous models, we do not
presume to know the trait driving the rate differences, nor do we prohibit
the same rates from appearing in different parts of the phylogeny. Using
simulated datasets, we show that the MTBD model can reliably infer the
presence of multiple evolutionary regimes, their positions in the tree,
and the birth and death rates associated with each. We also present a
re-analysis of two empirical datasets and compare the results obtained by
MTBD and by the existing software BAMM. We compare two implementations of
the model, one exact and one approximate (assuming that no rate changes
occur in the extinct parts of the tree), and show that the approximation
only slightly affects results. The MTBD model is implemented as a package
in the Bayesian inference software BEAST~2, and allows joint inference of
the phylogeny and the model parameters.