Male genitalia, hierarchical homology, and the anatomy of the bullet ant (Paraponera clavata; Hymenoptera, Formicidae).

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The male genitalia of insects are among the most variable, complex, and informative character systems for evolutionary analysis and taxonomic purposes. Because of these general properties, many generations of systematists have struggled to develop a theory of homology and alignment of parts. This struggle continues to the present day, where fundamentally different models and nomenclatures for the male genitalia of Hymenoptera, for example, are applied. Here, we take a multimodal approach to digitalize and comprehensively document the genital skeletomuscular anatomy of the bullet ant (Paraponera clavata; Hymenoptera: Formicidae), including hand dissection, synchrotron radiation microcomputed tomography, microphotography, scanning electron microscopy,confocal laser scanning microscopy,and 3D-printing. Through this work, we generate several new concepts for the structure and form of the male genitalia of Hymenoptera, such as for the endophallic sclerite (=fibula ducti), which we were able to evaluate in detail for the first time for any species. Based on this phenomic anatomical study and comparison with other Holometabola and Hexapoda, we reconsider the homologies of insect genitalia more broadly, and propose a series of clarifications in support of the penis-gonopod theory of male genital identity. Specifically, we use the male genitalia of Paraponera and insects more broadly as an empirical case for hierarchical homology by applying and refining the 5-category classification of serial homologs from DiFriscoet al.(2023) (DLW23) to all of our formalized concepts. Through this, we find that: (1) geometry is a critical attribute to account for in ontology, especially as all individually identifiable attributes are positionally indexed hence can be recognized as homomorphic; (2) the definition of "structure" proposed by DLW23 is difficult to apply, and likely heterogeneous; and (3) formative elements, or spatially defined foldings or in- or evaginations of the epidermis and cuticle, are an important yet overlooked class of homomorphs. We propose a morphogenetic model for male and female insect genitalia, and a model analogous to gene-tree species-tree mappings for the hierarchical homology of male genitalia specifically. For all of the structures evaluated in the present study, we provide 3D-printable models - with and without musculature, and in various states of digital dissection - to facilitate the development of a tactile understanding. Our treatment of the male genitalia of P. clavata serves as a basic template for future phenomic studies of male insect genitalia, which will be substantially improved with the development of automation and collections-based data processing pipelines, that is,collectomics. The Hymenoptera Anatomy Ontology will be a critical resource to include in this effort, and in best practice concepts should be linked.