Tree-like Reticulation Networks - When Do Tree-like Distances Also Support Reticulate Evolution?

Hybrid evolution and horizontal gene transfer (HGT) are processes where evolutionary relationships may more accurately be described by a reticulated network than by a tree. In such a network, there will often be several paths between any two extant species, reflecting the possible pathways that genetic material may have been passed down from a common ancestor to these species. These paths will typically have different lengths but an `average distance' can still be calculated between any two taxa. In this article, we ask whether this average distance is able to distinguish reticulate evolution from pure tree-like evolution. We consider two types of reticulation networks: hybridization networks and HGT networks. For the former, we establish a general result which shows that average distances between extant taxa can appear tree-like, but only under a single hybridization event near the root; in all other cases, the two forms of evolution can be distinguished by average distances. For HGT networks, we demonstrate some analogous but more intricate results.