Teeth act as tools for acquiring and processing food and so hold a prominent role in 14 vertebrate evolution 1,2 . In mammals, dental-dietary adaptations rely on tooth shape and 15 complexity variations controlled by cusp number and pattern -the main features of the 16 tooth surface 3,4 . Complexity increase through cusp addition has dominated the 17 diversification of many mammal groups 3,5-9 . However, studies of Mammalia alone don't 18 allow identification of patterns of tooth complexity conserved throughout vertebrate 19 evolution. Here, we use morphometric and phylogenetic comparative methods across 20 fossil and extant squamates ("lizards" and snakes) to show they also repeatedly evolved 21 increasingly complex teeth, but with more flexibility than mammals. Since the Late 22Jurassic, six major squamate groups independently evolved multiple-cusped teeth from a 23 single-cusped common ancestor. Unlike mammals 10,11 , reversals to lower cusp numbers 24 were frequent in squamates, with varied multiple-cusped morphologies in several groups 25 resulting in heterogenous evolutionary rates. Squamate tooth complexity evolved in 26 correlation with dietary change -increased plant consumption typically followed tooth 27 complexity increases, and the major increases in speciation rate in squamate evolutionary 28 history are associated with such changes. The evolution of complex teeth played a critical 29 role in vertebrate evolution outside Mammalia, with squamates exemplifying a more 30 labile system of dental-dietary evolution. 31As organs directly interacting with the environment, teeth are central to the acquisition and 32 processing of food, determine the achievable dietary range of vertebrates 1 , and their shapes are 33 subject to intense natural selective pressures 8,12 . Simple conical to bladed teeth generally 34 identify faunivorous vertebrates, while higher dental complexity -typically a result of more 35 numerous cusps -enables the reduction of fibrous plant tissue and is crucial to the feeding 36 apparatus in many herbivores 4,8,13 . Evidence of such dental-dietary adaptations dates back to the 37 first herbivorous tetrapods in the Palaeozoic, about 300 million years ago (Ma) 13 . Plant tooth morphogenesis 23 . Epithelial signalling centres -the enamel knots -control tooth crown 56 morphogenesis 24 , including cusp number and position and ultimately tooth complexity, by 57 expressing genes of widely conserved signalling pathways 18,25 . Experimental data show most 58 changes in these pathways result in tooth complexity reduction, or complete loss of teeth 25 , yet 59 increasing tooth complexity largely dominates the evolutionary history of mammals [6][7][8][9]16 . To 60 determine whether similar patterns of tooth complexity underlie all tetrapod evolution or are 61 the specific results of mammalian dental development and history, we used morphometric and 62 phylogenetic comparative methods with squamate tooth and diet data. 63We analysed cusp number and diet data for 545 squamate species spanning all ...