The ancestral population size conditioned on the reconstructed phylogenetic tree with occurrence data

Abstract

We consider a homogeneous birth-death process with three different sampling schemes. First, individuals can be sampled through time and included in a reconstructed tree. Second, they can be sampled through time and only recorded as a point occurrence along a timeline. Third, extant individuals are sampled and included in the reconstructed tree with a fixed probability. We further consider that sampled individuals can be removed or not from the process, upon sampling, with fixed probability.\n\nGiven an outcome of the process, composed of the joint observation of a reconstructed phylogenetic tree and a record of occurrences not included in the tree, we derive the conditional probability distribution of the population size any time in the past. We additionally provide an algorithm to simulate ancestral population size trajectories given the observation of a reconstructed tree and occurrences.\n\nThis distribution can readily be used to perform inferences of the ancestral population size in the field of epidemiology and macroevolution. In epidemiology, these results will pave the way towards jointly considering data from case count studies and reconstructed transmission trees. In macroevolution, it will foster the joint examination of the fossil record and extant taxa to reconstruct past biodiversity.