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In spite of big data and new techniques, the phylogeny and timing of cockroaches remain in dispute. Apart from sequencing more species, an alternative way to improve the phylogenetic inference and time estimation is to improve the quality of data, calibrations and analytical procedure. This study emphasizes the completeness of data, the reliability of genes (judged via alignment ambiguity and substitution saturation), and the justification for fossil calibrations. Based on published mitochondrial genomes, the Bayesian phylogeny of cockroaches and termites is recovered as: Corydiinae + (((Cryptocercidae + Isoptera) + ((Anaplectidae + Lamproblattidae) + (Tryonicidae + Blattidae))) + (Pseudophyllodromiinae + (Ectobiinae + (Blattellinae + Blaberidae)))). With two fossil calibrations, namely, Valditermes brenanae and Piniblattella yixianensis, this study dates the crown Dictyoptera to early Jurassic, and crown Blattodea to middle Jurassic. Using the ambiguous ‘roachoid’ fossils to calibrate Dictyoptera+sister pushes these times back to Permian and Triassic. This study also shows that appropriate fossil calibrations are rarer than considered in previous studies.

The incorrect generic name Perisphaeria Burmeister, 1838 results from a mistake by Princis (1947). Perisphaeria is an incorrect spelling by Burmeister referring to Perisphaerus Serville, 1831. Princis (1947) incorrectly regarded Perisphaeria as proposed by Burmeister and as the senior synonym of Hyposphaeria Lucas, 1863, which is valid. The subfamilial name Perisphaeriinae based on Perisphaeria should be corrected to Perisphaerinae Brunner von Wattenwyl, 1865 based on Perisphaerus; but note Princis' Perisphaeriinae is based on his Perisphaeria Burmeister. The taxa involved are listed. [ABSTRACT FROM AUTHOR]