Hemiptera, the fifth most diverse insect order, are characterized by their high diversity in deep time, with 145 known extinct families. However, the precise timing of the origin of Hemiptera lineages has remained uncertain. Traditional approaches, molecular clock analyses and fossil calibrations, have overlooked much of this extinct diversity by failing to incorporate key fossil data. Furthermore, no estimates have been proposed for the timing of the extinction of Hemiptera's fossil lineages. In this study, we use the recently developed Bayesian Brownian Bridge model, which estimates the timing of lineage origin and extinction through fossil-based Bayesian modelling, to provide a temporal framework for the rise and fall of 310 major hemipteran lineages. Our results support an early Pennsylvanian origin of Hemiptera, and indicate that the major hemipteran lineages originated between the late Carboniferous and Late Permian (Pennsylvanian-Lopingian). Additionally, our analyses reveal a radiation of Hemiptera during the Permian (Guadalupian), followed by multiple extinctions of ancient hemipteran lineages from the Permo-Triassic boundary to the mid-Triassic. A second major radiation occurred during the Cretaceous, coinciding with numerous extinctions of relic and newly emerging Cretaceous lineages, highlighting a faunal turnover. Our study provides a holistic fossil-based picture of the evolutionary history of Hemiptera.

Department Paleontology Bonn Institute of Organismic Biology University of Bonn Bonn 53115 Germany

Institut de Systématique Évolution Biodiversité Muséum national d'Histoire naturelle CNRS Sorbonne Université EPHE PSL Université des Antilles Paris F 75005 France

Institute of Geology and Paleontology Charles University Prague 12843 Czech Republic

Laboratoire Traitement du Signal et de l'Image Université de Rennes INSERM Rennes F 35000 France

Oxford University Museum of Natural History University of Oxford Parks Road Oxford OX1 3PW UK

Senckenberg Forschungsstation Grube Messel Senckenberg Forschungsinstitut und Naturmuseum Frankfurt M Messel Germany

State Key Laboratory of Palaeobiology and Stratigraphy Nanjing Institute of Geology and Palaeontology Chinese Academy of Sciences Nanjing People's Republic of China

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Bayesian modelling of the fossil record enlightens the evolutionary history of Hemiptera