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Journal of Paleontology 91(5):919–932


correction with the geometric mean provides more useful characters with smaller confidence intervals (Tables 4, 5) for differentiating them. Particularly, importance of the length and width of the occipital ring and the relative size of the cranidium could be revealed. These two characters could not otherwise be identified in the analysis with the ratios. A possible explanation for this result may be the fact that the geometric mean is a more holistic measurement because it includes all the variables to calculate a size estimator for the specimen. However, ratio variables can be affected by the relationship between the two original variables, if they co-vary. An example of this situation could be the width of the interocular genae. This character is not recovered as important to distinguish both genera when data were corrected by the geometric mean. However, when using ratios, the width of the interocular genae related to the width of the glabella (at the eye line) is strongly correlated with PC1. Through the combination of both results, the width of glabella (at the eye line) is shown to be the character that differentiates both genera, instead of the width of the interocular genae. Even if the size effect could not be completely eliminated from the analyses, both corrections applied to reducing size effects proved to be equally effective in the sense that they revealed the morphological differences of both genera. This study also confirms that the general morphology of the


cranidium of Parabolinella differs from that of Bienvillia in having a more-developed preglabellar area (sag.) and pregla- bellar field (sag.), wider posterior fixigenae (tr.), larger glabella and cranidium, and higher ratio between the width of the interocular genae and the width of glabella (at the eye line) (tr.) (Fig. 4). The first three characters have been used to justify the inclusion of P.? triarthroides in Parabolinella (e.g., Harrington and Leanza, 1957). In addition, the types of P.? triarthroides show a similar morphology to the genus Parabolinella, and they are located far from the overlapping zone. Therefore, the morphology of P.? triarthroides cannot be considered as inter- mediate, as proposed by Harrington and Leanza (1957). These authors arrived at this conclusion based on the original description of P.? triarthroides made by Harrington (1938), who reported the presence of a simple preoccipital furrow (S1) in this species. Indeed, in a previous phylogenetic analysis, this character was also identified the most significant difference between P.? triarthroides and the rest of the species of Parabolinella (Monti and Confalonieri, 2013). However, despite the importance of this character for the genus diagnosis, the correction of the original matrix regarding this particular character (from simple to bifurcated for P. triarthroides) does not produce a substantial change in the results of the cladistics analysis compared with the previous work (tree not shown). In this context, the combination between the codification of the continuous characters and the inclusion of more species of Bienvillia were key strategies to solve the position of P.? triarthroides. Therefore, the implementation of different methodologies (morphometric and phylogenetic approaches, based on raw and corrected data) gave a better understanding of how the quantitative characters and their codification may affect the proposed relationships between the species, as well as the clue to observe with more detail more specimens, and to uncover possible reasons of the discrepancies: the


misidentification of one character (simple instead of bifurcated furrow). Both types of continuous partitions recovered as synapo-


morphies of Parabolinella the following characters: larger preglabellar area (sag.) and preglabellar field (sag.), and shorter glabella (sag.). One more character was recovered as a syna- pomorphy of the genus, but it is different according to the type of coding. When quantitative characters are coded as ratio variables, there is more consistency between the qualitative and quantitative partitions, but characters coded as geometric means gave better-supported clades. Many authors have pointed out that the use of ratios may fail to eliminate the allometric effect, and at the same time can create new relationships between previously uncorrelated characters (e.g., Corruccini, 1977; Albrecht et al., 1993). Another problem could be that some measurements can be


repeated in more than one character, violating the fundamental principle of character independence. There is a long debate in the scientific literature about the best way of coding quantitative characters, but no consensus on how to solve this problem has been yet reached (e.g., Corruccini, 1977; Hills, 1978; Albrecht et al., 1993; MacLeod, 2002; Rae, 2002; Jansen, 2003; Clouse et al., 2010; De Bivort et al., 2010). For instance, different techniques were proposed to adjust ratios that maximize the reduction of size information (Corruccini, 1977; Hills, 1978; Albrecht et al., 1993), and to eliminate co-varying continuous characters from the data matrix (Clouse et al., 2010; De Bivort et al., 2010). In the present study, the main difference between both ways of coding is that the use of geometric means has the primary function to eliminate size effect while the use of ratios reflects shapes; relative proportions or positions of different structures of the cranidium morphology (see Albrecht et al., 1993 for a similar distinction). Likewise, both types of coding used here are intuitive and easily understandable, being an advantage when interpreting results. Their performance was very similar. Therefore, there is not definite answer on how to code characters and which way will be better in each case, so further research will be necessary to explore the best way of coding in every particular dataset. Finally, some characters of importance to distinguish the


two genera in the morphometric analysis also have evolutionary importance because they are recovered as synapomorphies of Parabolinella (e.g., the length of the preglabellar area [Ch. 3], the length of the preglabellar field [Ch. 4], and the length of the glabella [Ch.1]), both expressed as ratios or as data corrected by the geometric mean (Table 2, Figs. 5, 6). The width of the glabella at the base (Ch. 7) is also added to the list of synapomorphies when using CPGM. Regarding the width of the posterior fixigenae (Ch. 5) and the length of the cranidium (Ch. 0), they show some phylogenetic signal because they are recovered as synapomorphies of all of the Parabolinella species, except P. prolata (Figs. 5, 6). Lastly, the other char- acters that emerge from the morphometric analysis are those that change in their ranges on the basal nodes of the Parabolinella clade (for CPR, Ch. 10 [WPF/WOR] and for CPMG Ch. 2 [LOR]; see Table 2; Figs. 5, 6), although they are not recovered as synapomorphies. In this sense, the two types of analysis are complementary: the range of the morphological variation for each genus and the position of the type material of


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