Methods of macroevolutionary systematics as recently modified are explained and applied to the genus Anoectangium Schwägr. (Pottiaceae) in hyperoceanic areas of coastal northwestern North America. It was revealed that this area harbored species like those reported for the Himalayan region of northern India. Keys are provided for North American and Himalayan species of the genus. A macroevolutionary analysis, detailed in the Methods section, distinguishes and gives relationships between the species. There is strong Bayesian support for progenitor-descendant pairs and lineages. Anoectangium thomsonii Mitt. is considered a synonym of A. aestivum (Hedw.) Mitt. Anoectangium crassinervium Mitt. is transferred to Molendoa Lindb., under a nomen novum with A. handelii Schiffn. as a synonym. Anoectangium incrassatum Broth., related to the Asian A. clarum Mitt., is reported as a well-characterized species from the West Indies. Anoectangium stracheyanum Mitt. is re-lectotypified. Distinctions between A. aestivum and A. euchloron (Schwägr.) Spruce in the New World are clarified. Causal explanations in systematics are equated with entropy maximization in Shannon information analysis in the context of serial descent. A Pleistocene species pump hypothesis is advanced to explain the stenomorphic populations of species of the genus in eastern North America.