  Understanding the processes that give rise to quantitative measurements
associated with molecular sequence data remains an important issue in
statistical phylogenetics. Examples of such measurements include geographic
coordinates in the context of phylogeography and phenotypic traits in the
context of comparative studies. A popular approach is to model the evolution of
continuously varying traits as a Brownian diffusion process. However, standard
Brownian diffusion is quite restrictive and may not accurately characterize
certain trait evolutionary processes. Here, we relax one of the major
restrictions of standard Brownian diffusion by incorporating a nontrivial
estimable drift into the process. We introduce a relaxed drift diffusion model
for the evolution of multivariate continuously varying traits along a
phylogenetic tree via Brownian diffusion with drift. Notably, the relaxed drift
model accommodates branch-specific variation of drift rates while preserving
model identifiability. We implement the relaxed drift model in a Bayesian
inference framework to simultaneously reconstruct the evolutionary histories of
molecular sequence data and associated multivariate continuous trait data, and
provide tools to visualize evolutionary reconstructions. We illustrate our
approach in three viral examples. In the first two, we examine the
spatiotemporal spread of HIV-1 in central Africa and West Nile virus in North
America and show that a relaxed drift approach uncovers a clearer, more
detailed picture of the dynamics of viral dispersal than standard Brownian
diffusion. Finally, we study antigenic evolution in the context of HIV-1
resistance to three broadly neutralizing antibodies. Our analysis reveals
evidence of a continuous drift at the HIV-1 population level towards enhanced
resistance to neutralization by the VRC01 monoclonal antibody over the course
of the epidemic.
