  Recently, there has been interest in extending long-known results about the
multispecies coalescent tree to other models of gene trees. Results about the
gene duplication and loss (GDL) tree have mathematical proofs, including
species tree identifiability, estimability, and sample complexity of popular
algorithms like ASTRAL. Here, this work is continued by characterizing the
anomaly zones of uniformly sampled gene trees. The anomaly zone for species
trees is the set of parameters where some discordant gene tree occurs with the
maximal probability. The detection of anomalous gene trees is an important
problem in phylogenomics, as their presence renders effective estimation
methods to being positively misleading. Under the multispecies coalescent,
anomaly zones are known to exist for rooted species trees with as few as four
species.
  The gene duplication and loss process is a generalization of the generalized
linear-birth death process to the rooted species tree, where each edge is
treated as a single timeline with exponential-rate duplication and loss. The
methods and results come from a detailed probabilistic analysis of trajectories
observed from this stochastic process. It is shown that anomaly zones do not
exist for rooted GDL balanced trees on four species, but do exist for rooted
caterpillar trees, as with the multispecies coalescent.
