  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.
