ABOUT THIS IMAGE. This image provides an illustration of an inductive proof that all species tree topologies with five or more taxa, and asymmetric four-taxon species tree topologies, have anomalous gene trees.

Anomalous gene trees (AGTs) are gene tree topologies that are more likely to be produced under the multispecies coalescent than the topology that matches the species tree. The subtree in color in the lower left corner illustrates how an AGT can arise for a particular six-taxon topology. The existence of AGTs in the general case can be demonstrated by selecting branch lengths for large trees such that embedded small subtrees produce AGTs. The figure is inspired by the work of Degnan & Rosenberg (Discordance of species trees with their most likely gene trees; PLoS Genetics 2: 762-768, 2006).

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