We show that the topology of separate elements in avian compound rhamphothecae are strongly similar among different clades, not only in external appearance but in how these elements conform to underlying structures. We conducted a morphological survey of 81 extant bird species and tested superficial similarities in external beak morphology for substantive similarity in associated skeletal structures and nerve courses. A revised set of morphological characters for compound rhamphothecae was optimized onto three recent phylogenetic trees to assess the relationships of homology and homoplasy in rhamphothecal morphology. Osteological correlates of rhamphothecae from the extinct basal ornithurine birds Hesperornis and Ichthyornis show that compound rhamphothecae are the primitive state for the clade including extant birds (Neornithes). Simple rhamphothecae are the result of the loss of softer keratinous grooves between rhamphothecal components, and there are many examples of transitional forms between compound and simple rhamphothecae in which the grooves remain as shallow depressions without a pronounced edge. Ancestral-character-state reconstructions of rhamphothecal morphology within Neornithes also show a considerable amount of homoplasy. We suggest that frequent homoplasy in rhamphothecal morphology is the result of underlying similarity in facial development.
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