The paper proves that any phylogenetic tree metric of height h can be displayed by an HGT network with h-1 reticulation arcs, so tree-likeness does not rule out many reticulate events.
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Tree-metrizable HGT networks
The paper proves that any phylogenetic tree metric of height h can be displayed by an HGT network with h-1 reticulation arcs, so tree-likeness does not rule out many reticulate events.