Data from: A general and efficient algorithm for the likelihood of diversification and discrete-trait evolutionary models

As the size of phylogenetic trees and comparative data continue to grow
and more complex models are developed to investigate the processes that
gave rise to them, macroevolutionary analyses are becoming increasingly
limited by computational requirements. Here we introduce a novel
algorithm, based on the "flow" of the differential equations
that describe likelihoods along tree edges in backward time, to reduce
redundancy in calculations and efficiently compute the likelihood of
various macroevolutionary models. Our algorithm applies to several
diversification models, including birth-death models and models that
account for state- or time-dependent rates, as well as many commonly used
models of discrete-trait evolution, and provides an alternative way to
describe macroevolutionary model likelihoods. As a demonstration of our
algorithm's utility, we implemented it for a popular class of
state-dependent diversification models - BiSSE, MuSSE, and their
extensions to hidden-states. Our implementation is available through the R
package castor. We show that, for these models, our algorithm is one or
more orders of magnitude faster than existing implementations when applied
to large phylogenies. Our algorithm thus enables the fitting of
state-dependent diversification models to modern massive phylogenies with
millions of tips, and may lead to potentially similar computational
improvements for many other macroevolutionary models.