Horizontal transfers can reveal ghost birth events and complete species trees
Extinct and unsampled species vastly outnumber the species typically included in phylogenetic studies. Most of these so-called ``ghost lineages'' are unknown and, among them, those that are extinct may have left no trace in the fossil record. Horizontal gene transfers (HGTs), however, provide a potential source of information about these missing lineages, because transfers can connect sampled ancestral species to lineages outside the sampled species tree. Such transfers may leave observable signatures in gene trees. Here, we formalize this signal under idealized models of duplication, transfer, and loss, and characterize the information that can be retrieved about the complete species tree (containing ghost and non-ghost lineages) thanks to sampled gene trees and sampled species trees (containing only the non-ghost lineages). We establish four identifiability results, assuming an infinite number of gene families and errorless dated gene trees. First, transfers identify the lineage through time (LTT) curve of the complete tree, averaged over each time interval induced by the nodes of the sampled species tree. Second, in the presence of transfers, the distribution of node heights in sampled gene trees uniquely determines the internal speciation times of the complete species tree, including ghost speciations. Third, these hidden speciation times suffice to restore identifiability of birth-death-sampling parameters, through a reduction to a recent theorem of Dieselhorst and Stadler. Finally, when duplication, transfer, and loss rates are known constants and the transfer rate is non-zero, the distribution of sampled gene trees almost surely uniquely determines the topology and branch lengths of the complete species tree, including all ghost branches. These results provide a theoretical basis for using signatures left by HGTs in gene trees to recover information about extinct and unsampled lineages, and suggest ways in which this signal could be exploited in practice.