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Recently, there has been interest in extending long-known results about themultispecies coalescent tree to other models of gene trees. Results about thegene duplication and loss model have mathematical proofs, including speciestree identifiability, estimability, and sample complexity of popular algorithmslike ASTRAL. Here, this work is continued by characterizing the anomaly zonesof uniformly sampled gene trees. The anomaly zone for species trees is the setof parameters where some discordant gene tree occurs with the maximalprobability. The detection of anomalous gene trees is an important problem inphylogenomics, as their presence renders effective estimation methods to beingpositively misleading. Under the multispecies coalescent, anomaly zones areknown to exist for rooted species trees with as few as four species.  The gene duplication and loss process is a generalization of the generalizedlinear-birth death process to the rooted species tree, where each edge istreated as a single timeline with exponential-rate duplication and loss. Themethods and results come from a detailed probabilistic analysis of trajectoriesobserved from this stochastic process. It is shown that anomaly zones do notexist for rooted GDL balanced trees on four species, but they may exist forrooted caterpillar trees, as with MSC.

Anomaly zones for uniformly sampled gene trees under the gene duplication and loss model