Figure 1.
Simulations under the state-dependent multivariate Brownian motion process. The
process is either in discrete state 0 (blue) or discrete state 1 (orange), where the
rate of change between discrete states is equal (), and the rate of
continuous-character evolution is higher when the process is in the orange state
(
,
). A) A single sample path
from
to
. The process begins and ends in the
blue state, but spends some time in the orange state. Note that there is more
evolution in the orange state than in the blue state. B) The distribution of end
states for 10 million simulated realizations. Solid lines represent the simulated
joint probability densities of the discrete and continuous states. Dashed lines
represent the normal densities with parameters estimated from the simulated end
states. Note that the simulated densities depart from the normal densities (both
Kolmogorov–Smirnov