Wicked Forest

In probabilistic models of gene trees conditional on species trees, it is possible that both of the following hold at once: (1) given a species tree \(S_1\) with topology \(T_1\), gene tree topology \(T_2\) has a greater probability than gene tree topology \(T_1\); (2) given a species tree \(S_2\) with topology \(T_2\), gene tree topology \(T_1\) has a greater probability than gene tree topology \(T_2\). Because this counterintuitive scenario generates particularly challenging scenarios for species tree inference, the species trees \(S_1\) and \(S_2\) are said to belong to a "wicked forest." Degnan & Rhodes (2015) have shown that trees with a caterpillar shape cannot be in a wicked forest—giving rise to their article title “There are no caterpillars in a wicked forest.” The occurrence of a wicked forest in tree space is a relatively unusual phenomenon—like the wildfire-induced orange sky that gives this Stanford forest a "wicked" look.