Using PCA and standard deviation analysis to evaluate the reliability of digit length impression as sound ichnotaxonomical character

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Using PCA and standard deviation analysis to evaluate the reliability of digit length impression as sound ichnotaxonomical character
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  Using PCA and standard deviation analysis to evaluate the reliability of digit length impression as sound ichnotaxonomical character  ROMANO M., CITTON P.Dipartimento di Scienze della Terra, “Sapienza” Università di Roma, Rome, Italy Introduction The relative length of digit impressions is often adopted as a binding character in ichnotaxa discrimination and trackmaker identification. The reliability of this character has been evaluated by means of Principal Component Analysis on well-preserved footprints referred to as Ichniotherium sphaerodactylum  from the Early Permian Tambach Formation (Thuringia, Germany). Materials and methods Several Ichniotherium sphaerodactylum specimens have been analyzed from the rich collection of the Museum der Natur in Gotha (MNG-1351, MNG-1515, MNG-1840, MNG-1846, MNG-2356/14, MNG-2356/15, MNG-10072). The phalangeal portion length of digits, taking as homologous points the digit tips, distally, and the center of the metapodial-phalangeal pad, proximally, has been used for measurements. The collected data have been subjected to a Principal Component Analysis (PCA) using Paleontological Statistics 2.06 (PAST) software (Hammer, 2011). The raw data have been log-transformed to fit linear models and for the correspondence of the log-transform to an isometric null hypothesis (see Smith, 1998; Chinnery, 2004; Cheng et al., 2009). In addition, for each trackway, data have been plotted on XY graphs. Conclusions Digit impression relative length has proved to be highly variable within the same trackway, due to mode of locomotion and substrate conditions. Overall, the digit relative length in manus impressions results much more variable with respect to the condition observed in pedes impressions, indicating a less biomechanically constrained front autopods, probably linked to their greater exploratory attitude during the progression of stroke. References. Cheng Y.N., Holmes R., Wu X.C. & Alfonso N. 2009. Sexual dimorphism and life history of Keichosaurus hui   (Reptilia: Sauropterygia). Journal of Vertebrate Paleontology, 29(2), 401–408. Chinnery B. 2004. Morphometric analysis of evolutionary trends in the ceratopsian postcranial skeleton. Journal of Vertebrate Paleontology, 24(3), 591–609. Hammer Ø. 2011. Paleontological Statistics (PAST) 2.06. University of Oslo, Oslo, Norway. Retrieved 7 february 2011 from http://folk.uio.no/ohammer/past/. Ősi A., Pálfy J., Makádi L., Szentesi Z., Gulyás P., Rabi M., Botfalvai G. & Hips K. 2011. Hettangian (Early Jurassic) Dinosaur Tracksites from the Mecsek Mountains, Hungary. Ichnos, 18, 79–94. Smith D.K. 1998. A morphometric analysis of  Allosaurus . Journal of Vertebrate Paleontology, 18(1), 126–142. Tucker L. & Smith M.P. 2004. A multivariate taxonomic analysis of the Late Carboniferous vertebrate ichnofauna of Alveley, southern Shropshire, England. Palaeontology, 47, 679–710. In both cases, the loads of the first principal component indicate a positive correlation of all the considered variables; however, while loads are mostly uniform in the pedes, in manus the much greater load is found in digit I length and, to a lesser extent, in the second one. In the case of pedes, the dispersion along the first principal component may indicate the dimensional parameter, while for manus the variance along the first principal component is determined by a direct correlation between the lengths of digits I and II, with greater load for the first digit (load 0.86). As regards the second component, it results, for pedes, in an inverse linear combination between the second digit length (load -0.44) and the fifth digit length (load 0.83). For the manus, the component is a linear inverse combination between the length of digit I (load -0.33) and the length of the remaining digits, with higher load found in lengths of digit four and five (loads respectively 0.51 and 0.7). Multivariate and bivariate analyses  A PCA analysis has been conducted considering simultaneously the measures for manus and pedes, while two PCA applications have been performed on manus and pedes data, separately. Each reported convex hull encloses respectively the manus and pedes of the same trackway.The analysis inclusive of manus and pedes data shows that about 67.78% of the variance is resolved into the first principal component and about 20.69% into the second one (88.47% of the total variance). Convex hulls are substantially separated along the first principal component in relation to the absolute size, which is higher in the hindfoot compared to the forefoot impression. Differently, the second principal component results from an inverse correlation between the length of the first digit (load 0.78) and the length of the fifth (load -0.56). With respect to that component, the variability of the digit I-digit V correlation results more strongly in the impressions of front autopods with respect to the hind ones. In the PCA conducted only on pedes, the first principal component expresses approximately 51.93% of the variance and the second approximately 21.29% (73.22% of the variance); in the PCA conducted only on the manus, the first component accounts for approximately 59.65% of the variance and the second approximately for 22.78% (82.43% of the variance).Such a preliminary study, obviously case-specific, should provide a greater control on ichnotaxonomy, warning about the excessive splitting based on single isolated footprints and the taxonomic differentiation rooted on minor differences in relative length of individual digits. It can also be considered an enlightening tool, if associated to biomechanical analysis, in improving and refining trackmaker identification.The obtained results clearly indicate that the use of digit relative length as an ichnotaxonomic character should be preceded by an initial exploratory analysis able to highlight the impressions less variable and therefore more reliable from a taxonomical point of view. A multivariate analysis, which has not yet found widespread use in ichnological analysis or diagnoses ( e.g  ., cluster analysis in Tucker & Smith, 2004; Principal Component  Analysis in Ősi et al., 2011), is optimal in this sense. These footprints can be referred to a unitary kind of trackmaker within Diadectidae, as suggested by a functional analysis recently performed on the same material.The quantization and the understanding of the taxonomic or simply behavioral-structural factors upon which the morphological and dimensional variability is based is considered an important key element for a correct interpretation of the relative digits length and for its reliability in ichnotaxonomic diagnosis. Ichniotherium sphaerodactylum . MNG-1351, set 7. Scale bar is 5 cm. Principal Component Analysis. Bivariate plot of first principal component against the second, considering dataset of manus and pedes in selected Ichniotherium sphaerodactylum  trackways. Component 1    C  o  m  p  o  n  e  n   t   2 -0,4-0,32-0,240,24-0,08-0,160,080,16-0,05-0,1-0,15-0,2-0,250,050,10,15MNG - 1515 MNG - 10072MNG - 1840 MNG - 1846 MNG - 1351 Principal Component Analysis. Bivariate plot of first principal component against the second, considering dataset of pedes in selected Ichniotherium sphaerodactylum  trackways. Component 1    C  o  m  p  o  n  e  n   t   2 -0,06-0,09   -0,030,060,090,030,120,06-0,06-0,08-0,1-0,04-0,020,040,02MNG - 1515 MNG - 10072 MNG - 1840MNG - 1846 MNG - 1351 Principal Component Analysis. Bivariate plot of first principal component against the second, considering dataset of manus in selected Ichniotherium sphaerodactylum  trackways. Component 1    C  o  m  p  o  n  e  n   t   2 -0,36-0,3-0,24-0,18-0,12-0,060,12   0,06-0,16-0,12-0,08-0,040,040,080,120,16MNG - 1515 MNG - 10072MNG - 1840MNG - 1846MNG - 1351 Plot of digit lengths in the individual footprints considered for each slab. (A-E) pes. (F-L) manus. 65605550454035302520IIIIIIIVV65605550454035302520656055504540353025206560555045403530252065605550454035302520705045403530252050454035302520556050403020601070504540353025205560504540353025205515IIIIIIIVVIIIIIIIVVIIIIIIIVVIIIIIIIVVIIIIIIIVVIIIIIIIVVIIIIIIIVVIIIIIIIVVIIIIIIIVV ABCDEFGHIL Ichniotherium sphaerodactylum . MNG-1351, set 6. Scale bar is 5 cm. Ichniotherium sphaerodactylum . MNG-1846, set 2. Scale bar is 5 cm. Ichniotherium sphaerodactylum . MNG-1351, set 5. Scale bar is 5 cm. PCA loadings. Loadings of first principal component in: (A) analysis conducted on both manus and pedes data; (C) analysis conducted on manus data; (E) analysis conducted on pedes data. Loadings of second principal component in: (B) analysis conducted on both manus and pedes data; (D) analysis conducted on manus data; (F) analysis conducted on pedes data. 0,80,60,40,20-0,2-0,4-0,6-0,8-1IIIIIIIVV         L      o      a        d        i      n      g 0,43640,33160,36770,42890,58720,80,60,40,20-0,2-0,4-0,6-0,8-1IIIIIIIVV         L      o      a        d        i      n      g 0,86090,36990,28640,19610,040330,80,60,40,20-0,2-0,4-0,6-0,8-1IIIIIIIVV         L      o      a        d        i      n      g 0,62610,48280,38380,38490,28180,80,60,40,20-0,2-0,4-0,6-0,8-1IIIIIIIVV         L      o      a        d        i      n      g 0,78420,18070,0052-0,198-0,56030,80,60,40,20-0,2-0,4-0,6-0,8-1IIIIIIIVV         L      o      a        d        i      n      g -0,32710,13720,36050,50720,69780,80,60,40,20-0,2-0,4-0,6-0,8-1IIIIIIIVV         L      o      a        d        i      n      g 0,01681-0,4404-0,28130,19850,829 A BCDEF Schematic drawing of the measurement method adopted in the analysis of Ichniotherium sphaerodactylum  manus (a) and pes (b) imprints. Drawing based on best preserved specimens of MNG-1351. abIVIV
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