Abstract
Birth-death stochastic processes are the foundation of many phylogenetic models and are widely used to make inferences about epidemiological and macroevolutionary dynamics. There are a large number of birth-death model variants that have been developed; these impose different assumptions about the temporal dynamics of the parameters and about the sampling process. As each of these variants was individually derived, it has been difficult to understand the relationships between them as well as their precise biological and mathematical assumptions. And without a common mathematical foundation, deriving new models is non-trivial. Here we unify these models into a single framework, prove that many previously developed epidemiological and macroevolutionary models are all special cases of a more general model, and illustrate the connections between these variants. To do so, we develop a novel technique for deriving likelihood functions for arbitrarily complex birth-death(-sampling) models that will allow researchers to explore a wider array of scenarios than was previously possible. As an illustration of the utility of our mathematical approach, we use our approach to derive a yet unstudied variant of the birth-death process in which the key rates emerge deterministically from a classic susceptible infected recovered (SIR) epidemiological model.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
Removed orhid ID