Homeotic and non-homeotic patterns in the tetrapod vertebral formula

Vertebrae can be differentiated into five categories along the body axis in tetrapods, with its numerical distribution known as the vertebral formula. The vertebral formula is a principal tool for connecting development and phylogeny. This is largely due to its robust relationship with the conserved clusters of Hox genes, which exhibit expression boundaries coincident with vertebral divisions. One avenue for variations in the vertebral formula is thus through Hox-mediated homeotic transformations, which manifest as a relatively fixed sum of adjacent vertebral counts. This expectation is borne out in the mammalian thoracolumbar count, but to date, no similar vertebral patterns have been found. Here we conduct a systematic search by generating a large dataset of complete vertebral formulae in a diverse range of tetrapod species and probing the variance of linear combinations of vertebrae. We uncover additional mammalian homeotic patterns, but also unexpected balances between distal vertebrae not comprehensible with Hox-mediated regionalization. One distal pattern appears during the progression from theropods to birds, demonstrating its phylogenetic importance. We further show that several vertebral counts correlate with posterior intergenic distances in the HoxB gene cluster. By creating a vertebral formula database and mathematically defining patterns, our work establishes a quantitative approach for comparative genomics in morphology. ### Competing Interest Statement The authors have declared no competing interest.