Zoological Journal of the Linnean Society (2000), 129: 489–514. With 6 figures doi:10.1006/zjls.1999.0215, available online at http://www.idealibrary.com on The braincases of mosasaurs and Varanus, and the relationships of snakes OLIVIER RIEPPEL FMLS* Dept. of Geology, The Field Museum, Roosevelt Road at Lake Shore Drive, Chicago, IL 60605–2496, U.S.A. HUSSAM ZAHER Departemento de Zoologia, Instituto de Biocie ´ncias, Universidade de Sa ´o Paulo, Caixa Postal 11461, 05422–970 Sa ´o Paulo, SP, Brasil Received March 1999; accepted for publication August 1999 The braincase structure of the mosasaur Platecarpus is described in detail and compared to that of Varanus and snakes. The braincase of mosasaurs and Varanus is found to be closely similar in most respects other than the consequences of obliteration of the metakinetic axis in mosasaurs. Neither Varanus, nor mosasaurs, approach snakes in braincase structure. The hypothesis of a sister-group relationship of snakes and mosasauroids is discussed in the light of how hypotheses of homology, or synapomorphy, can be established on an empirical, i.e. testable and potentially falsifiable basis. The establishment of homology qua synapomorphy is recognized as a procedure involving at least two levels of generalization. The most basic level is the conjecture of similarity of constituent elements of two or more organisms. Such conjectures of similarity maintain their testability, and falsifiability, only if established by reference to topographical equivalence, or equivalence of connectivity.  2000 The Linnean Society of London ADDITIONAL KEYWORDS:—Squamata – Mosasauroidea – Serpentes – phylogeny – evolution. CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . 490 Material . . . . . . . . . . . . . . . . . . . . . . . . 491 Comparison of the braincase structure of Platecarpus and Varanus . . . . . . 491 The relation of the parietal to the prootic . . . . . . . . . . . 492 The relation of the parietal to the supraoccipital . . . . . . . . . 494 The relationship of the supratemporal to the paroccipital process . . . . 495 The palatobasal articulation . . . . . . . . . . . . . . . . 497 The basicranium . . . . . . . . . . . . . . . . . . . . 497 * Corresponding author. E-mail: rieppel@fmppr.fmnh.org 489 0024–4082/00/080489+26 $35.00/0  2000 The Linnean Society of London