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ANTOINE VERRIÈRE ET AL.
which was traditionally considered a pararep- tile, actually represents a diapsid reptile in the process of developing an anapsid skull condi- tion and is indeed closely related to the origin of turtles (Bever et al. 2015). Independent of the origin of turtles, parareptiles are of great interest due to their great ecological diversity and because, through procolophonoids, they are one of the few clades that survived the most severe extinction event in Earth history at the end of the Permian. In this paper, we assess the completeness of the parareptile fossil record, comparing various metrics to examine different aspects of specimen completeness.
Methodology Completeness Metrics.—Mannion andUpchurch
(2010) introduced two quantitative completeness metrics, the SCM and the CCM, with two different implementations, respectively desig- nated as SCM1 and CCM1 versus SCM2 and CCM2. The first implementation determines the completeness of only themost complete specimen of a taxon, while the second considers the completeness of all known specimens of this taxon. Here, only the second implementation is used, for two reasons: (1) it is considered to be more meaningful than the single-specimen approach (Mannion and Upchurch 2010), and (2) the variable importance attributed to different parts of the skeleton may complicate the definition of themost complete specimen. The CCM reflects the amount of phyloge-
netic information available for a given taxon. It is based on the number of characters from a phylogenetic data set that can be scored for each taxon. In the original article by Mannion and Upchurch (2010), the CCM was calculated by measuring the average number of characters referring to each bone in multiple matrices and by assigning the corresponding percentage to every bone actually present in the specimen. Brocklehurst et al. (2012) improved the implementation of the CCM (hereafter, Brocklehurst’s implementation is called “CCMa”): the number of characters potentially coded on a given bone is obtained by counting the number of original characters referring to this bone in as many phylogenetic
matrices as possible, unified in one single combined matrix with duplicate characters removed. Then the character completeness percentage for this bone is calculated based on the total number of characters in the matrix. For example, if a specimen has a humerus preserved, and this bone is referred to in 4 characters out of 10, then the specimen’s completeness is 40%. The sum of the percen- tages of all elements preserved gives the completeness of the taxon. In a later study, Bell et al. (2013) suggested a
simpler method for calculating the CCM (hereafter referred as “CCMb”), which only requires access to cladistic matrices, and not to descriptions of specimens or the specimens themselves. In this approach, the ratio between the number of characters scored in a taxon and the total number of characters in the matrix is calculated for all matrices in which the taxon is included. The final completeness of the taxon is the average value from all matrices in which it is included. Here, we also calculated the completeness by dividing the total number of characters scored for the taxon by the total number of characters in all the matrices in which it is included. Correlation tests showed a very high correlation between these two methods (ρ=0.969, p<0.001), and so only the latter was employed. Both CCMa and CCMb were compared in
this study. The combined character list, required for the first approach (Mannion and Upchurch 2010), was built from three lists extracted from the most recent and exhaustive phylogenetic studies on parareptiles (Tsuji et al. 2012, 2013; MacDougall et al. 2013). In the second approach (Bell et al. 2013), 13 matrices were used: one of millerosaurians (Cisneros et al. 2008), one of pareiasaurs (Tsuji 2013), two of bolosaurians (Müller et al. 2008; Falconnet 2012), three of procolophonoids (Modesto and Damiani 2007; Säilä 2008; MacDougall et al. 2013), and five general phylogenies of parareptiles (Reisz et al. 2007; Modesto and Reisz 2008; Sues and Reisz 2008; Tsuji et al. 2012;Modesto et al. 2015). These matrices were chosen because they were the most recent and because their association provided at least one value for each parareptile taxon. Older matrices were not included, since the more
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