A phylogenetic tree of Peytoiidae (= “Hurdiidae”) based on Moysiuk & Caron (2022). The silhouettes of Peytoia and Hurdia are by Junnn11 (Wikimedia Commons, CC BY-SA 4.0).
The family “Hurdiidae” was first named by Vinther et al. (2014; suppl. info) for a clade of radiodont stem-arthropods (also known as anomalocarids) including Hurdia, Peytoia, and related genera. However, they did not give a character-based diagnosis for the family as required by Articles 13.1 and 13.2 of the International Code of Zoological Nomenclature (ICZN, 1999). Since that made it an unavailable name, Lerosey-Aubril & Pates (2018; suppl. info) attempted to rename “Hurdiidae” following the Code. While they did have a proper diagnosis, their paper was not registered in the ZooBank database. It was published in Nature Communications, an online-only journal, for which Article 8.5.3 of the Code requires a ZooBank registration. This means that both “Hurdiidae” Vinther et al., 2014 and “Hurdiidae” Lerosey-Aubril & Pates, 2018 are unavailable names.
What all of these authors also overlooked is that naming “Hurdiidae” was unnecessary, as there is already an available name for the same clade. The family Peytoiidae was named by Conway Morris and Robison (1982) and it meets the requirements of the Code. It is both the oldest and only available family name for the clade containing Peytoia, Hurdia, and their close relatives, and is thus the correct one to use.
References
- Conway Morris, S., & Robison, R.A. (1982). The enigmatic medusoid Peytoia and a comparison of some Cambrian biotas. Journal of Paleontology, 56(1), 116-122.
- ICZN. (1999). International code of zoological nomenclature (4th ed.). The International Trust for Zoological Nomenclature; The Natural History Museum, London.
- Lerosey-Aubril, R., & Pates, S. (2018). New suspension-feeding radiodont suggests evolution of microplanktivory in Cambrian macronekton. Nature Communications, 9, Article 3774. https://doi.org/10.1038/s41467-018-06229-7
- Moysiuk, J., & Caron, J.-B. (2022). A three-eyed radiodont with fossilized neuroanatomy informs the origin of the arthropod head and segmentation. Current Biology, 32(15), 3302-3316. https://doi.org/10.1016/j.cub.2022.06.027
- Vinther, J., Stein, M., Longrich, N.R., & Harper, D.A.T. (2014). A suspension-feeding anomalocarid from the Early Cambrian. Nature, 507(7493), 496-499. https://doi.org/10.1038/nature13010
Incertae Sedis 
