Unifying Phylogenetic Birth–Death Models in Epidemiology and Macroevolution

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. 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. This unification includes both models where the process is the same for all lineages and those in which it varies across types. We also outline a straightforward procedure for deriving likelihood functions for arbitrarily complex birth-death(-sampling) models that will hopefully allow researchers to explore a wider array of scenarios than was previously possible. By re-deriving existing single-type birth-death sampling models we clarify and synthesize the range of explicit and implicit assumptions made by these models.

Robust phylodynamic analysis of genetic sequencing data from structured populations

“…We focused on an epidemiological application of bdmm , where we co-infer the phylogenetic trees to take into account the phylogenetic uncertainty. However, the bdmm modelling assumptions are equally applicable to the analysis of macroevolutionary data, in which context bdmm allows for the joint inference of trees with fossil samples under structured models [23]. When using a multi-type birth-death model in the macroevolutionary framework, ρ -sampling can be used to model fossil samples originating from the same rock layer.…”

Deep learning from phylogenies to uncover the epidemiological dynamics of outbreaks

“…This is especially true for CBLV representation, which does not require the design of new summary statistics, when applied to trees generated by new mathematical models. A direction for further research would be to explore such models, for example based on structured coalescent [38, 39] , or to extend the approach to macroevolution and species diversification models [40] , which are closely related to epidemiological models. Other fields related to phylodynamics, such as population genetics, have been developing likelihood-free methods [41] , for which our approach might serve as a source of inspiration.…”

The scaling of diversification rates with age is likely explained by sampling bias

“…For example, stem4 conditions the likelihood on the sampling of at least 4 tips at present day, assuming that the cladogenic process started at the stem age. This conditioning is achieved by dividing the raw tree likelihood with the probability that the process yields at least 4 tips at present day (MacPherson et al., 2022) (see Appendix for mathematical details). Similarly, crown4 conditions the likelihood on the observed MRCA age and the sampling of at least 4 tips.…”