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Sampling impacts the assessment of toothgrowth and replacement rates inarchosaurs implications forpaleontological studiesJens CD Kosch12 and Lindsay E Zanno12

1 Paleontology North Carolina Museum of Natural Sciences Raleigh NC USA2 Department of Biological Sciences North Carolina State University Raleigh NC USA

ABSTRACTDietary habits in extinct species cannot be directly observed thus in the absenceof extraordinary evidence they must be reconstructed with a combination ofmorphological proxies Such proxies often include information on dentalorganization and function such as tooth formation time and tooth replacementrate In extinct organisms tooth formation times and tooth replacement rate arecalculated in part via extrapolation of the space between incremental lines in dentaltissues representing daily growth (von Ebner Line Increment Width VEIW)However to date little work has been conducted testing assumptions about theprimary data underpinning these calculations specifically the potential impact ofdifferential sampling and data extrapolation protocols To address this we testeda variety of intradental intramandibular and ontogentic sampling effects oncalculations of mean VEIW tooth formation times and replacement rates usinghistological sections and CT reconstructions of a growth series of three specimensof the extant archosaurian Alligator mississippiensis We find transect position withinthe tooth and transect orientation with respect to von Ebner lines to have thegreatest impact on calculations of mean VEIWmdasha maximum number of VEIWmeasurements should be made as near to the central axis (CA) as possible Measuringin regions away from the central axis can reduce mean VEIW by up to 36 causinginflated calculations of tooth formation time We find little demonstrable impactto calculations of mean VEIW from the practice of subsampling along a transector from using mean VEIW derived from one portion of the dentition to extrapolatefor other regions of the dentition Subsampling along transects contributes onlyminor variations in mean VEIW (lt12) that are dwarfed by the standard deviation(SD) Moreover variation in VEIW with distance from the pulp cavity likely reflectsidiosyncratic patterns related to life history which are difficult to control forhowever we recommend increasing the number of VEIWmeasured to minimize thiseffect Our data reveal only a weak correlation between mean VEIW and body lengthsuggesting minimal ontogenetic impacts Finally we provide a relative SD ofmean VEIW for Alligator of 2994 which can be used by researchers to createdata-driven error bars for tooth formation times and replacement rates in fossiltaxa with small sample sizes We caution that small differences in mean VEIWcalculations resulting from non-standardized sampling protocols especially in acomparative context will produce inflated error in tooth formation time estimations

How to cite this article Kosch JCD Zanno LE 2020 Sampling impacts the assessment of tooth growth and replacement rates inarchosaurs implications for paleontological studies PeerJ 8e9918 DOI 107717peerj9918

Submitted 3 April 2020Accepted 20 August 2020Published 18 September 2020

Corresponding authorJens CD Koschtezkatlzedatfu-berlinde

Academic editorFabien Knoll

Additional Information andDeclarations can be found onpage 29

DOI 107717peerj9918

Copyright2020 Kosch and Zanno

Distributed underCreative Commons CC-BY 40

that intensify with crown height The same holds true for applications of our relativeSD to calculations of tooth formation time in extinct taxa which produce highlyvariable maximum and minimum estimates in large-toothed taxa (eg 718ndash1331days in Tyrannosaurus)

Subjects Paleontology Zoology HistologyKeywords Tooth formation Tooth replacement Archosauria Sampling effects Alligatorvon Ebner lines Error bars

INTRODUCTIONTooth replacement rate provides key information on the function and evolution of thedentition (Edmund 1960 Osborn 1970 1975 Richman Whitlock amp Abramyan 2013Whitlock amp Richman 2013 Schwarz et al 2015 LeBlanc et al 2016 Bramble et al 2017)Such data can be used to infer aspects of the paleobiology of extinct taxa includingmetabolic activityinvestment dietary preferences and behavior (Johnston 1979Barrett 2014 Salakka 2014 DrsquoEmic et al 2013 2019 DrsquoEmic amp Carrano 2019 Brinket al 2015 Button et al 2017 DrsquoEmic et al 2019) However tooth growth and exfoliationcannot be directly observed in extinct species therefore tooth replacement rate must beestimated via growth lines preserved within dentin (von Ebner Lines) andor incrementalgrowth lines of enamel that record different rhythms (see Smith (2004) for a review)Within living crocodilians von Ebner lines are known to represent daily dentin deposition(Erickson 1992 1996a) Paleontological studies have therefore used direct von Ebner linecounts or estimates derived by measuring dentin thickness divided by the mean widthbetween von Ebner lines (so called ldquovon Ebner Line IncrementWidthrdquo VEIW) to estimatetooth formation times and replacement rates in extinct species (Erickson 1996b Serenoet al 2007 DrsquoEmic et al 2013 2019 Garcia amp Zurriaguz 2016 Erickson et al 2017 Ricartet al 2019) This practice makes the accurate estimation of von Ebner line counts andmean VEIW a critical consideration as errors in the calculation of either will havecascading effects ultimately resulting in erroneous paleobiological inferences andmacroevolutionary trends

The challenges of working with fossil data constrain sampling approaches for derivingvon Ebner line count and mean VEIW in extinct species For example because a researchercannot always choose the location or orientation for consumptive sampling they oftenhave to calculate mean VEIW from one region of the tooth and apply these data todifferent transect locations within the same tooth (Erickson 1992 1996b Sereno et al2007 Gren 2011 DrsquoEmic et al 2013 2019 Gren amp Lindgren 2013 Garcia amp Zurriaguz2016 Kear et al 2017 Ricart et al 2019) Likewise researchers may have to calculatemean VIEW from one tooth position within the jaw and then apply these values toother tooth positions (Kosch 2014 Schwarz et al 2015 Garcia amp Zurriaguz 2016DrsquoEmic amp Carrano 2019 DrsquoEmic et al 2019) Moreover because von Ebner lines arenot always visible along the entire transect mean VEIWs are typically derived from atransect subsample as opposed to being calculated from the entire transect length(Erickson 1992 1996a 1996b Gren 2011 Gren amp Lindgren 2013 Button et al 2017

Kosch and Zanno (2020) PeerJ DOI 107717peerj9918 233

Erickson et al 2017 Kear et al 2017 Ricart et al 2019 DrsquoEmic et al 2019)These practices rely on a series of data extrapolations that can introduce possibleintradental and intramandibular sampling effects

Intradental data extrapolations are often based on one or multiple of the followingassumptions (1) mean VEIW is constant regardless of the developmental age of the tooth(ie does not vary significantly or consistently with distance from the pulp cavity)(2) the maximum number of von Ebner lines are preserved at any transect location(ie a transect taken anywhere on the tooth from pulp cavity to crown will capture all vonEbner lines reflecting the maximum age of the tooth) and (3) mean VEIW is consistentregardless of the transect position used for sampling (ie does not vary across thetooth) Assumption 1 forms the basis for using a subsection of a transect to derive a meanVEIW for a tooth (Erickson 1992 1996a 1996b Gren 2011 Gren amp Lindgren 2013Erickson et al 2017 Kear et al 2017 Ricart et al 2019 DrsquoEmic et al 2019) but contrastswith a competing hypothesis that teeth have different growth rates during their formationwhich would result in wider VEIWs depending on distance from the pulp cavity(Y-H Wu 2018 personal communication Lawson Wake amp Beck 1971Hanai amp Tsuihiji2018 Finger Thomson amp Isberg 2019) as well as with observations of flexible replacementrates coupled with metabolic activity (often seasonally influenced) in extant reptiles(Cooper (1966) in Anguis fragilis Delgado Davit-Beal amp Sire (2003) in Chalcidessexlineatus and Chalcides viridanus) and mammals (Klevezal 1996 66f) Assumption 2forms the basis for the use of transverse sections to derive tooth formation times (Serenoet al 2007 Gren 2011 Gren amp Lindgren 2013 Kear et al 2017 Ricart et al 2019)This assumption was criticized by DrsquoEmic et al (2013) on grounds that not all von Ebnerlines present in a tooth are exposed in transverse section Assumption three forms thebasis for approaches that measure VEIWs and calculate a mean VEIW based on transectsthat stretch from the toothrsquos center near the pulp cavity to the marginal parts of thetooth either in transverse sections of the tooth (Gren 2011 Gren amp Lindgren 2013 Kearet al 2017 Ricart et al 2019) or multiple groups of measurements in a longitudinalsection (ldquozig-zag patternrdquo Erickson 1992 1996a 1996bDrsquoEmic et al 2013 2019 (in part))

Not only is it difficult to mitigate intradental sampling effects one cannot generallysample all teeth in a tooth row therefore many studies rely on the assumption that VEIWis constant across the tooth row and between upper and lower arcades For exampleprevious studies of fossil archosaurs utilizing von Ebner line counts andor mean VEIW toderive tooth formation times and replacement rates base these estimates on teethwithin a single respective tooth family within the dentition (either mesial teeth (Erickson1992 1996a Sereno et al 2007 DrsquoEmic et al 2013) unspecified ldquomean-sized teethrdquo(Erickson 1996b Erickson et al 2017) molariform distal teeth (Ricart et al 2019) orisolated teeth of uncertain position within the jaw (Garcia amp Zurriaguz 2016DrsquoEmic et al2019)) The use of ldquomean sized teethrdquo (Erickson 1992 1996a 1996b) relies on theassumption that mean VEIW does not differ systematically according to tooth positionand thus is constant in all tooth positions DrsquoEmic et al (2013) derived a mean VEIW frompremaxillary teeth in sauropods however subsequent studies applied transfer functionsfor tooth length to whole dentitions to derive tooth formation times in sauropods


(Schwarz et al 2015 Kosch 2014 DrsquoEmic et al 2019) In a similar fashion DrsquoEmic et al(2019) applied mean VEIW derived from isolated teeth from various mandibular elementsof theropods to other mandibular elements to estimate tooth formation times andreplacement rates These practices have the potential to introduce intramandibularsampling effects Finally Erickson (1992 1996a 1996b) concluded that VEIW changesduring ontogeny with wider VEIWs characterizing larger individuals Such differencescould introduce ontogenetic sampling effects

Here we explore the impact of intradental intramandibular and ontogenetic samplingeffects on calculations of mean VIEW tooth formation times and replacement rates bysampling multiple teeth along the tooth row of different ontogenetic stages of the extantarchosaurian taxon Alligator mississippiensis We also explore the distribution of VEIWwithin our sample and apply standard deviations (SD) derived from an extant archosaur toexisting calculations of tooth formation time in fossil vertebrates in order to assess thepotential impact of VEIW variation The results serve to inform best practices for samplingin studies of dental organization and begin to quantify potential error in tooth growth andreplacement rate estimates in extinct taxa

MATERIALS AND METHODSSpecimens and samplingTo assess ontogenetic sampling effects we examined the dentition across an ontogeneticseries of three individuals of Alligator mississippiensis We estimated body length of ourtwo smallest specimens using the regressions of Farlow et al (2005) (femur length againstbody length) Our smallest individual (NCSM 100803) has an estimated body length of371 cm (femur length = 2455 mm) which corresponds to the size expected of youngyearling (larger than a hatchling but 33 smaller than a yearling at the end of its first year)(Khan amp Tansel 2000) (Figs 1A 1D and 1G) and our medium sized individual(NCSM 100804) has an estimated body length of 906 cm (femur length = 6158 mm)corresponding to the upper end of the size range expected of a 2 year old (Khan amp Tansel2000) (Figs 1B 1E and 1H) There was no associated femur with our largest specimen(NCSM 100805) therefore we used two methods to approximate an estimated body lengthrange (Figs 1C 1F and 1I) We used mandible length as a proxy for skull length whichwe then used to estimate total length from the regressions in Farlow et al (2005)We also used mandible length to estimate Snout-Vent length and then derive totalbody length using regression equations derived by Wu et al (2006) for the congenerA sinensis These produced an estimated body length of between 36 and 39 m whichcorresponds to an age of more than 16 years according to Khan amp Tansel (2000) No lifehistory data were available for specimens the estimated ages correspond to the size rangegiven for age categories in Table 3 of Khan amp Tansel (2000) following Neill (1971)

All material was scanned at Duke University in a micro-CT Nikon XTH 225 ST CTimages were taken with a setting of 170 kV and 86 mA and slice thickness of 317 microm forthe small Alligator The skull of the medium sized Alligator was scanned in two scanprocesses one with 135 kV and154 mA and one with 130 kV and 170 mA both with a slice


thickness of 452 microm For the large Alligator the upper tooth row was scanned with 150 kVand 134 to 139 mA and the lower tooth row with 150 kV to 139 to 144 mA using a slicethickness of 613 microm All files were saved in tif format Data reconstruction was donewith a RECO1 workstation Composite files for the entire skulls or complete elements(upper and lower tooth rows of the large Alligator) were constructed in AVIZO 90 Thosefiles were used for two different purposes an initial inspection that aided in the decisionwhich alveoli should be sampled for histological sections of teeth and surrounding hardtissue and to create digital models of the teeth in order to ascertain measurements offunctional and replacement teeth of the quadrant of the jaw from which histologicalsamples would be taken Foremost among these measurements was central axis height(CAH) the distance between the tip of the pulp cavity and the crown apex which equalsthe sum of all VEIWs measured along the central axis (plus apical enamel thickness)The combination of resolution and contrast of the X-ray micro-CT scans does not allowfor the clear distinction of the enamel dentin junction in all teeth (Jones et al 2018)

We chose 12 tooth positions that exhibited both a functional tooth and replacementteeth for sampling (Pmx 1 Pmx3 Mx 6 Mx 7 Mx 12 Mx 13 Dent 2 Dent 4 Dent 11Dent 12 Dent 18 Dent 19) The distalmost teeth of the largest specimen were notpreserved therefore we approximated these tooth positions by sampling the 15th and16th alveolus Sampling of multiple tooth positions across the length of each dentaryhelped to access intramandibular sampling effects Some of our data collection requiredsampling of the same position across multiple individuals In these cases we chose a subsetof tooth positions that possessed at least one functional tooth and at least one replacementtooth (mesial dentition only as distal dentition often lacked replacement teeth) andalso represented a widespread distribution across the tooth row and dentigerous elements(mesial premaxillary teeth mesial and distal maxillary teeth and their counterparts in thedentary) across all three individuals

Figure 1 Dental anatomy of Alligator used in this study (A D G) NCSM 100803 (B E H) NCSM100804 and (C F I) NCSM 100805 Segmented dentition showing (AndashC) functional teeth in color and(DndashF) replacement teeth in color Replacement teeth and functional tooth of each position are presentedin different shades of the same color Segmented dentition not to scale skulls (GndashI) to scale Scale bar5 cm Full-size DOI 107717peerj9918fig-1


HistologyHistological slides were prepared following standard thin-sectioning protocols (Lamm2013) First the respective areas of interest were separated using a diamond bladedISOMET 1000 precision saw The segments were prepared for embedding by dehydrationin progressive ethanol baths (70 90 and 100) and defatted in acetone Sampleswere not demineralized which is known to cause shrinkage (Dean 1998 Smith 2004) andcan impact tooth measurements Next the samples were embedded in Epo-Tek 301 EpoxyResin No staining was performed The embedded jaw elements were cut close to theintended plane of the section (Fig 2) and ground using silica carbide paper (120ndash1200grit) before being fixed to a slide cut again and ground down to 013ndash056 mm thicknessThe sections were studied with a Nikon Eclipse Ci POL microscope equipped with apolarizer and a lambda filter and photographed using an iPhone 7 camera or a RolleiPowerflex 470 camera

Figure 2 Schematic representation of section planes and transects Schematic representation of dif-ferent sectioning planes with examples of raw data for different transect locations Blue von Ebner lines(VEL) appear in transverse section taken in the blue plane Red VEL appear in a transverse section in thered plane A section in the plane of the central axis (green with brackets) will cross all VELs

Full-size DOI 107717peerj9918fig-2


Identification of daily growth linesWe observed incremental growth lines ranging 5ndash39 microm within the sample and 6ndash38 micromwithin a single tooth We found no smaller incremental lines even between the von Ebnerline with the widest distance As the incremental lines observed by us conform to thewidth of daily deposited von Ebner lines reported from other archosaurs (Allison et al2019 DrsquoEmic et al 2013 2019 Erickson 1992 1996a 1996b Gren amp Lindgren 2013Ricart et al 2019 Sokolskyi Zanno amp Kosch 2019) we conclude that we did not observeintradian (Smith 2004) or ultradian (Ohtsuka amp Shinoda 1995 Klevezal 1996) linesthat might occur as bands subdividing daily lines The range of incremental line widthobserved in our sample also falls in similar range to the VEIW observed in the ever-growing incisors of rodents (Rosenberg amp Simmons 1980 Ohtsuka amp Shinoda 1995Klevezal 1996 Smith 2004) Under the assumption that the observed incremental linesare longer period Andresen lines the formation times and replacement rates becomeunrealistically long exceeding observed exfoliation rates (Erickson 1996a) by 7ndash13 timesThe presumed daily growth lines also are more similar to the short period growth linesobserved in mosasaur teeth that also sow longer period Andresen lines (Gren amp Lindgren2013) Therefore we interpret all our von Ebner line as daily incremental growth lines

Von Ebner line count and measurementsPhotographs were either stitched together into a composite within Adobe Photoshop 2015or directly opened in Image J whereupon a transect line was applied and the sectionsof the von Ebner lines crossing the transect were marked with an arrow symbol Incrementwidths were measured using the Image J inbuilt measurement tool and measurementswere exported to Excel 2015 to compute averages Minimum and maximum VEIW in agiven transect were used in combination with the transect length and the CAH to computeabsolute maximum and minimum tooth ages represented by the measured transectand the tooth respectively Upper and lower limits of tooth formation time were computedby subtracting (for maximum ages) and adding (for minimum ages) the SD of the VEIWfrom the mean VEIW and applying these values to the transect length and the CAHThis strategy of measuring VEIWs allowed us to test the assumptions that data derivedfrom one tooth position can reliably be applied to a tooth from a different tooth positionand that mean VEIW does not vary significantly or consistently with distance from thepulp cavity

Hierarchically there are three different mean VEIWs used in different steps The meanVEIW of a transect as described above the mean VEIW of all transects of a toothwhich was used in calculating the tooth formation time used to determine replacementrate the mean VEIW of a specimen was used to compare VEIW through ontogeny andwith other datasets Tooth height and CAH were measured in AVIZO 90 (Fig 1)

In the large Alligator some tooth crowns were damaged with small chips of the apicesmissing and cracks running through parts of the crown Some also showed a considerabledegree of tooth wear In these cases the crowns were digitally reconstructed to theirfull height in Avizo Cracks and missing chips were digitally infilled with voxels assigned as


reconstructed dentin up to a point where tooth wear was visible if signs of wear could beidentified Further reconstruction followed the curvature of the crownrsquos shape coveringevery exposed dentin surface with a layer at least two voxels deep that were assignedto a different material that represents dentin and enamel lost in tooth wear Thesereconstructed crowns were used when measuring CAH and tooth height for these teethThe original values without reconstruction are presented in the Data S1

Our raw measurement of CAH and tooth height include both enamel and dentinthickness The enamel layer in extant crocodylians is thin (Enax et al 2013) and scalesnearly isometrically (Schmiegelow Sellers amp Holliday 2016 Sellers Schmiegelow ampHolliday 2019) with minor changes related to tooth shape (intrafamilial heterodonty)(Osborn 1975 Kieser et al 1993 Gignac 2010 DrsquoAmore et al 2019) as opposed to sizeTo calculate CAH as a measure of dentin only we subtracted the average enamel thicknessvalue and used this corrected CAH value in our calculations The average enamelthickness was derived from measurements perpendicular to the enamel dentin junctiontaken from photographs of thin sections of representative teeth using the measurementtool in ImageJ For the small and medium sized specimens three photographs with up tofour measurements around the apical half of the crown in each photograph were usedto calculate an average enamel thickness for the large specimen two photographs wereused

We could directly measure VEIW in all but two-sampled teeth (first Pmx and 11th Mxteeth in the small Alligator) these teeth were not considered further We reconstructedtooth formation time and replacement rate from mean VEIW taken from directmeasurements of the remaining samples

Transect orientationTo determine the impact of sectioning strategy (intradental sampling effects) oncalculation of von Ebner line counts and specifically to test the assumption that meanVEIW is consistent regardless of the transect position used for sampling we counted vonEbner lines across transects taken at multiple angles from the 12th Mx 12th Dent and18th Dent tooth of the medium-sized Alligator Transect positions were categorized asbase-apex (Fig 3A from the tip of the pulp cavity to the crow apex (this is equal tothe full CAH)) near-crown-apex (Fig 3B measured at the tooth apex yet not alongthe central axis) mid-crown (Fig 3C measured in the central part of the crown) crownbase (Fig 3D transect from the tip of the pulp cavity to enamel dentin junction almostperpendicular to the central axis) root-base (Fig 3E measured from the pulp cavity nearthe root base to the lateral dentin border) mid-root (Fig 3F measured from the pulpcavity at the mid root to the lateral dentin border) root-apex (Fig 3G measured fromthe pulp cavity near the root tip to the lateral dentin border) Although all of our transectswere derived from longitudinal sections transverse transects in longitudinal section areeffectively equivalent to taking a transverse section itself as long as the transverse sectionbisects the central axis (semi-)perpendicularly


Figure 3 Schematic representation of transect orientations and examples Schematic representation ofdifferent transect orientations Transect orientations are represented by colored lines (A) base-apextransect along the central axis (CA) from the tip of the pulp cavity to the crow apex representing CAH(red) (B) near-crown-apex transect measured at the tooth apex yet not along the CA (yellow-green)(C) mid-crown transect measured in the central part of the crown (pink) (D) crown base transect fromthe tip of the pulp cavity to enamel dentin junction (EDJ) almost perpendicular to the CA (salmon)(E) root-base transect measured from the pulp cavity near the root base to the lateral dentin border(violet) (F) mid-root transect measured from the pulp cavity at the mid root to the lateral dentin border(sky blue) (G) root-apex transect measured from the pulp cavity near the root tip to the lateral dentinborder (darker blue) Numbers next to the transects are the von Ebner lines crossed and the numbersvisible under a hypothetical view through a microscope Full-size DOI 107717peerj9918fig-3


Hypotheses testing

(1) We tested the hypothesis that sampling transects taken in different orientations tovon Ebner lines will not produce significantly different calculations of formation timeby comparing VEIWs from transects taken perpendicular and oblique to von Ebnerlines We present the difference in formation time in days and in percent differencesand performed a paired t-test to test for significance

(2) We tested the hypothesis that measuring VEIWs at different distances from the pulpcavity will not result in significantly different mean VEIWs by comparing mean VEIWand resulting formation time calculations derived from eight distinct subsamplesalong the same transect in Dent 11 of the large specimen and mean VEIWs of threedifferent sections along this transect Subsamples were taken along the central axisat different distances from the pulp cavity (one apical one basal and six in various partsof the mid crown region) using all recognizable VEIWs in each subsample Thisapproach attempts to capture variation in growth rate during the formation of a toothusing a central axis transect only An ANOVA was performed to test the significanceof the differences between the means of apical basal and mid crown VEIWs andfollowed by a post-hoc TukeyndashKramer test comparing the VEIWs of the apical vs midcrown apical vs basal and mid crown vs basal sections

(3) We tested the hypothesis that sampling transects taken in different regions of the tooth(with regard to the tooth from root to apex) will not produce significantly differentVEIWs or different formation times (TFT) using multiple approaches We assessedthe impact of calculating formation time from transects located at regions around thetooth other than the central axis by calculating alternative formation times using amean VEIW and transect length from a region of the tooth off the central axis anddividing this by a formation time derived from a central axis transect (= true formationtime where both mean VEIW and CAH were derived along the central axis) A meanof these values was used to determine what percentage of the true formation timewas captured by formation times taken from transects not on the central axis

TFT ethaTHORN frac14 transect ethaTHORN=meanVEIW ethregion aTHORN a n

TFT ethtrueTHORN frac14 CAH=meanVEIWethCAHTHORNTFT etha nTHORN=TFTethtrueTHORN frac14 YY 100 frac14 frac12

We also assessed the impact of subsampling along transects not located along thecentral axis For this we calculated mean VEIW from subsamples of three transects closestand most distant from the central axis and calculated formation times using CAH derivedfrom a central axis transect These mean VEIWs represent extreme end members forVEIW thickness primarily related to tooth geometry We express the difference in theformation time estimates as a percent calculated by dividing the formation time based onthe portion furthest from the central axis by the formation time obtained from theportion closest to the central axis We test the significance of the difference between the


VEIWs from close and most distant to the central axis with a two-sample t-test assumingunequal variances

TFT ethnear CATHORN frac14 CAH=meanVEIWethnear CATHORNTFTethfar CATHORN frac14 CAH=meanVEIWethfar CATHORNTFT ethfar CATHORN=TFTethnear CATHORN frac14 YY 100 frac14 frac12Additionally the change in resolution of von Ebner line with increasing distance from thepulp cavity in lateral transects was tested in a theoretical framework by creating a figure(Fig 3) with von Ebner lines in the same orientations and relative distances from eachother and counting the number of von Ebner line crossed by transects drawn in the toothand the number of von Ebner line visible under a magnification that mimics the resolutionachieved under a microscope

(4) We tested the hypothesis that sampling VEIW at different tooth positions within thejaw will not produce different calculations of formation time in two ways First themean VEIWs for all sampled tooth positions obtained from transects with a similarorientation were subjected to an ANOVA to test for significant differences betweentheir means To test the amount of error a researcher could encounter if using the meanVEIW derived randomly from anywhere in the dentition to calculate the formationtimes of the remainder of the dentition we calculated the grand mean standarddeviation of the VEIW derived from all transects taken along the central axis and appliedthis SD range to the VEIWs used to calculate formation times The grand mean standarddeviation is subtracted from the mean VEIW of the tooth to obtain a minimumVEIW and added to obtain a maximum VEIW Tooth formation time is derivedfrom dividing the CAH (from the tip of the pulp cavity to crown apex) by those VEIWsThe fit of the minimum and maximum mean VEIW based on formation times wascompared to the true formation times of the sampled teeth by performing a two-samplet-test for unequal variances in MS Excel (Excel for Office 365 1601132820362)The difference between the true formation time and the minimum and maximumformation times are shown in days and percent differences

(5) We tested the hypothesis that sampling during different growth stages of an organismrsquoslife history will result in different calculations of mean VEIW by investigating therelationship between VEIW and body length and tooth replacement rate and bodylength using reduced major axis regression utilizing the RSQ function to derive R2 andthe FDIST function to arrive at a significance p For other plots the coefficient ofdetermination (R2) was determined using the inbuilt functionality of MS Excel (Excelfor Office 365 1601132820362) for charts Additionally we performed an ANOVA onthe same dataset created for testing hypothesis 4 but here grouped by ontogeneticstage Using the specimens as groups we can make inferences about the presence orabsence of differences in the mean VEIW during ontogeny

Application to fossil taxaWe used the mean standard deviation of Alligator to derive an estimated SD forthe tooth formation times calculated for archosaurs in Erickson (1996b) and


Garcia amp Zurriaguz (2016) both of which reported VEIW ranges but no SDs We also usedthe reported SD for several theropods in DrsquoEmic et al (2019) as an opportunity to test theefficacy of applying the relative standard deviation of Alligator to other archosaurs whennot enough data on VEIW is available to confidently derive SD on the raw data For thiswe compared actual SD values calculated in DrsquoEmic (control values) for the theropodsMajungasaurus Ceratosaurus and Allosaurus to SD estimates for those same taxa that wederived by applying the relative standard deviation from Alligator (approximated values)CAH (from the tip of the pulp cavity to the crown apex) was derived by multiplying thereported mean VEIW with the reported tooth formation time The CAH was then divided bythe VEIWplus or minus SD to derive upper and lower ends to the range of possible tooth ages

We also explore the effect of applying the relative standard deviation of Alligator oncalculations of tooth formation time and tooth replacement rate in sauropods usingmean VEIW plusmn 1SD We followed a similar approach using data from DrsquoEmic et al (2013)DrsquoEmic amp Carrano (2019) Sattler (2014) Kosch (2014) Schwarz et al (2015) For thesauropod data we calculated the resulting minimum maximum and true formation timesand replacement rates and summarized these data for each tooth position (functionalreplacement tooth one replacement tooth two etc) This representation of toothformation time and replacement rate is analogous to how these values are calculatedin DrsquoEmic et al (2013 2019) Sattler (2014) Kosch (2014) and Schwarz et al (2015)All originally reported formation times in these publications are based on the transferfunctions of tooth height to formation time of DrsquoEmic et al (2013) using the functionfor narrow crowned taxa derived from sampling Diplodocus premaxillary teeth forDicraeosaurus and Tornieria and the function for broad crowned taxa derived fromCamarasaurus premaxillary teeth for Giraffatitan and Brachiosaurus For all teeth a meanVEIW of 15 microm was assumed derived fromDrsquoEmic et al (2013) calculation of mean VEIWfor both Dipldocus and Camarasaurus

As reported tooth replacement rates represent a mean value derived from allreplacement rates that could be obtained (and might differ slightly from tooth replacementrates that are calculated subtracting the mean tooth formation times of those positionsfrom one another due to empty tooth positions in some tooth families) Tooth replacementrate max-max is derived using VEIW minus 1SD to calculate maximal formation time for bothteeth in a tooth family Replacement rate min-min is derived using VEIW + 1SD tocalculate minimal formation time for both teeth in a tooth family Replacement ratemin-max and max-min are derived by subtracting formation times calculated usingVEIW + 1SD and VEIW minus 1SD Tooth replacement rate min-max applies VEIW + 1SD tocalculate minimum tooth formation time for the oldest tooth in a successional pair of teethin a tooth family and VEIW minus 1SD for the youngest tooth in the pair whereas toothreplacement rate max-min takes the opposite approach We obtained the mean toothformation time and mean values from tooth replacement rates for each tooth position forthe completely sampled dentitions of Tornieria Giraffatitan and Dicraeosaurus Whereasfor the more sporadically sampled dentitions of Camarasaurus (UMNH 5527) andDiplodocus (YPM 4677) and Brachiosaurus (USNM 5730) we present the range of reportedformation times for each tooth position in the Pmx or Mx and Dent


RESULTSIntradental effectsSampling transects taken in different orientations to von Ebner lines

(perpendicular or obliquely oriented to von Ebner lines) (Figs 2 3 and 4) willproduce significantly different calculations of tooth formation timeOur data rejects the hypothesis that measuring oblique to von Ebner line orientation willnot significantly affect calculations of tooth formation time Transects that cross von Ebnerlines obliquely (Figs 3 and 4 File S1) (eg top of the pulp cavity to the enamel dentinjunction in areas adjacent to the apex (Fig 3B)) yield VEIWs up to twice the width asthose made perpendicular to von Ebner line trendlines Table 1 illustrates these differenceswith 33ndash20 shorter tooth formation times calculated when mean VEIW is derived fromobliquely oriented measurements compared to those based on perpendicularly orientedmeasurements when crown height is derived from the CAH for three pairs of oblique andperpendicular series of measurements This is a significant difference paired t-testt2 = 1036 (tcrit = 430) p = 0009 mean difference 64 days However if a researcher were touse the same transect to derive mean VEIW and transect length in calculations of toothformation time the effect is less Oblique transects result in both a larger mean VEIW anda longer transect whereas perpendicular transects are composed of shorter VEIWsacross a shorter transect Nevertheless both approaches underestimate age compared totransects along the true central axis because they fail to account for the apical-mostcomponent in derivations of CAH (Fig 2) (see hypothesis 3 below)

Figure 4 Oblique transect orientation Yellow lines mark transects Individual von Ebner lines (VEL)are marked with arrows where they intersect with the transect (A) Transect strongly oblique to VELreaching from the crown base near the pulp cavity to the mid-crown (with no visible VEL in the medialposition of the tooth) (B) transect perpendicular to VEL Both transects derive from the first premaxillaryalveolus of the medium sized Alligator (NCSM 100804) Full-size DOI 107717peerj9918fig-4


Measuring VEIWs at different distances from the pulp cavity along the centralaxis will not result in significantly different calculations of mean VEIWOur data support the hypothesis that there is no consistent statistically significantdifference between calculations of tooth formation times derived from measuring VEIWsat different distances from the pulp cavity along the central axis Calculations only vary by11ndash12 (Fig 5) and we find conflicting statistical results depending on approach andmethods In the case of the eight transects presented in Fig 5 an ANOVA between the86 VEIWs measured for the crown apex the 348 VEIWs of the combined six mid crowntransects and the 42 VEIWs of the crown base finds significant differences between theVEIWs in the three regions of the tooth F2 473 = 752 (Fcrit = 262) p = 00006 Howeverthe post-hoc TukeyndashKramer test of the VEIWs of the regions only finds significantdifference between the VEIWs of the apical transect and the six mid-crown transects andbetween the apical VEIWs vs basal VEIWs We find no significant difference between midcrown VEIWs and basal VEIWs (Fig 5) Sampling transects taken in different regionsof the tooth (with regard to the tooth from rop to apex) will produce significantly differentVEIWs

We find transect position critical for precise estimates of mean VEIW and toothformation time and therefore our data refutes the hypothesis that sampling transects takenin different regions of the tooth (with regard to the tooth from root tip to apex) will notproduce significantly different VEIWs These data contradict the assumption that meanVEIW is consistent regardless of the transect position used for sampling With regard tolocation on the tooth we find that sections that do not precisely section the central axis donot preserve all von Ebner lines Transverse sections omit von Ebner lines particularlythose of the crown apex (Fig 2) This combined with the lack of resolution of von Ebnerline further from the pulp cavity results in much shorter calculated tooth formation times(tooth formation times calculated with this approach are only 83 on average of thosederived from a central axis transect in the medium Alligator) We also find that meanVEIW in a tooth decreases laterally (Figs 2 and 3 File S1) when sampled perpendicular tovon Ebner line trendlines VEIWs are thickest along the central axis from above the pulpcavity to the crown apex and thinnest near the enamel dentin junction in a transversalplane The differences between these two groups are significant t80 = 540 (tcrit = 199)p = 661451Eminus07 Table 2 exemplifies this difference in VEIW thickness and resulting

Table 1 Transects oblique and perpendicular to von Ebner lines Three pairs of measurements each from the same tooth with one oblique andone perpendicular to the von Ebner lines and the resulting TFT for the tooth from applying them to central axis height

Tooth Oblique Perpendicular

Mean VEIW(microm)

SD Min Max TFT(days)

Mean VEIW(microm)


TFTdifference

Medium (NCSM 100804) Dent 18 21 5 12 34 11845 14 4 8 21 17768 5922

Large (NCSM 100805) Dent 11 21 6 12 29 23929 175 3 13 235 29559 5630

Large (NCSM 100805) Dent 11 22 6 12 36 22841 165 3 125 215 30455 7614

NoteSD standard deviation TFT tooth formation time VEIW von Ebner line increment width


estimates if tooth formation time is derived from VEIWs obtained from subsections oflateral transects other than the central axis are then applied to CAH VEIW can beincorrectly measured by up to 36 which would lead to inaccurately calculated toothformation time and replacement rates

Figure 5 Examples of transects in different distances to pulp cavity Schematic representation oftransects in different distance to the pulp cavity All transects are along the Central axis from the tip of thepulp cavity to the crown apex All examples are from Dent 11 of the large specimen (NCSM 100805)Abbreviations CA central axis CH crown height TFT tooth formation time VEIW von Ebner lineincrement width Full-size DOI 107717peerj9918fig-5

Table 2 VEIW decrease in marginal von Ebner lines Three examples of lateral transects other than the CA Each has a subsample with a numberof VELs close to the CA with their mean VEIW and a subsample of VEL furthest from the CA with their mean VEIW

Tooth Transect Mean VEIWnear CA (microm)

Based on VEL

TFT based onnear CA VEIW

Mean VEIWfar CA (microm)

Based on VEL

TFT based onfar CA VEIW

Difference in TFTestimates ()

Medium (NCSM100804) Dent 18

mid crown 175 10 14214 135 15 18426 7714

mid crown 184 10 13519 139 19 17835 7580

Large (NCSM100805) Dent 4

root base 193 26 66630 121 9 106225 6273

NoteCA central axis TFT tooth formation time VEIW von Ebner line increment width VEL von Ebner line


Intramandibular effectsSampling different tooth positions within the jaw will not produce

significantly different calculations of tooth formation timeOur data supports the hypothesis that sampling different tooth positions within the jawwill not produce significantly different calculations of tooth formation time Despiteconsiderable variation in our calculations of VEIW values (ranging 5ndash39 microm within thesample and 6ndash38 microm within a single tooth) we find no statistical difference between meanVEIWs of tooth positions calculated across the tooth row (Table 3 Fig 6) one-wayANOVA F10 19 = 104 (Fcrit = 238) p = 0448 If only the alveoli with three or moresamples for an alveolus position (4 in alveolus 4 6 in alveolus 11 5 in alveolus 5 4 inalveolus 18) are taken into account there is even less of a difference recovered one-wayANOVA F3 15 = 048 (Fcrit = 329) p = 0698 The lack of systematic variation of VEIW inteeth of different mandibular quadrants or between teeth of the lower and upper toothrows supports the assumption that data derived from one tooth position can be applied toa tooth from a different tooth position with reliability

As would be expected the smaller the mean VEIW and the longer the CAH of the teethunder study the more pronounced the influence the static grand mean standard deviationhas on derived tooth formation times (Table 4 Fig 7) Thus we find it is the size ofthe tooth that makes the tooth formation time differences more or less pronounced on anabsolute scale not the position within the jaw The (grand mean) SD of all VEIWmeasurements along the central axis is 000479 mm which is 2994 of the mean VEIW of00160 mm On average tooth formation times calculated from mean VEIW minus 1SD are4878 bigger whereas those calculated from mean VEIW + 1SD are 2394 smallerWhen tooth specific SDs are used these values change to 4123 and 2062 respectively(see Table S1) Two-sample one sided t-tests between the unmodified tooth formation

Table 3 VEIW according to tooth position

Tooth position 1 2 3 4 11 12 15 16 17 18 19

Small AlligatorNCSM 100803

Functional teeth upper dentition 0019 00127 00153 00120 00117

Replacement teeth upper dentition 00115

Functional teeth lower dentition 00133 00175 00144 00145 00125

replacement teeth lower dentition 00120 00130

Medium AlligatorNCSM 100804

Functional teeth upper dentition 00156 00115 0009prime 00135prime 00094

Replacement teeth upper dentition 00246 00370 00153 00240

Functional teeth lower dentition 00115 00143 00128

Replacement teeth lower dentition 00230

Large AlligatorNCSM 100805



Functional teeth lower dentition 00167 00270


NoteMean VEIW for the sampled tooth positions in mm Only measurements with the same transect orientation were used (central axis excerpt for prime root base acombination of root base and crown base transects) Some tooth positions were sampled but had a different transect orientation from the other teeth and were excludedfrom table and analyses Second generation replacement teeth (one in the dentition of the smallest specimen four in the dentition of the medium sized specimen three inthe dentition of the largest specimen) are excluded


Figure 6 VEIW according to tooth position Tooth position on the x axis VEIW width in mm on the yaxis Each tooth position is depicted by its own point (A) Dentition of the upper jaw (B) Dentition of thelower jaw Full-size DOI 107717peerj9918fig-6


Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT

s)SDplusmn(days)show

thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow

ingthesamedifferencesin

percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the

variancet-teststatisticand

thep-valueforaon

esidedtwo-samplet-testcomparing

TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth


times and tooth formation time calculated from mean VEIW plusmn 1SD assuming unequalvariances find a significant difference between tooth formation time calculated from meanVEIW minus 1SD and the unmodified tooth formation time (p = 0041) but no significantdifference for tooth formation time calculated from mean VEIW + 1SD (Table 4)Whereas no significant differences were found when using the tooth specific SDs insteadof a grand mean standard deviation (Table S1)

Ontogenetic effects Sampling during different growth stages of anorganismrsquos life history will not result in different calculations of mean VEIWWhen we derive mean VEIW for individual teeth with the same transect orientation andlocation and compare them among the sampled individuals (Fig 6 Table 3) we do notobserve significant differences between individuals of different ages and body sizes in oursample (one-way ANOVA F2 35 = 229 (Fcrit = 327) p = 0116) This supports thehypothesis that sampling during different growth stages will not result in significantlydifferent calculations of mean VEIW When we derive mean VEIW across the wholedentition of just our sampled individuals (from smallest to largest NCSM 100803 NCSM100804 and NCSM 100805) we find a slight increase during ontogeny (Fig 5A in File S1)however three individuals are not enough for a meaningful statistical comparison Whenwe add the mean VEIW of differently sized Alligator specimens ranging in body lengthfrom 060 m to 320 m derived from Erickson (1992 1996a) we find the relationshipbetween VEIW and body length shows a weak ontogenetic signal (R2 = 0389) that stilldoes not reach the level of 95 significance (p = 0074) in an reduced major axis regression(Fig 5B in File S1 Fig 8)

Application to fossil taxaTable 5 gives the error margins for tooth formation times of various archosaurs included inthe studies of Erickson (1996b) Garcia amp Zurriaguz (2016) and DrsquoEmic et al (2019)Garcia amp Zurriaguz (2016) only reported highest and lowest mean VEIWs and highest and

Figure 7 Tooth formation time differences for extreme VEIW values For each tooth with transects along the central axis (on the x-axis with theircentral axis height) from all our specimens the deviation of the upper and lower TFT estimate (upper estimate based on mean VEIW (tooth) minus 1SD(grand mean) lower estimate based on mean VEIW (tooth) + 1SD (grand mean)) to the calculated TFTs (based on mean VEIW (tooth)) is shown inpercent (see last two rows of Table 4) Lower TFT estimates are in purple upper TFT estimates in yellow Abbreviations SD standard deviationTFT tooth formation time VEIW von Ebner line increment width Full-size DOI 107717peerj9918fig-7


lowest tooth formation times from their five-tooth sample but never made clear if thosevalues are directly related pairing the lowest mean VEIW with the highest tooth formationtime and they provided no measurements for the five teeth sampled We assume inTable 5 that the highest age corresponds to the smallest VEIW and vice versa The VEIWin these publications likely underestimate the VEIW as it would be measured along thecentral axis because Erickson (1996b) Garcia amp Zurriaguz (2016) and in part DrsquoEmic et al(2019) based their calculations of VEIW on a combination of transverse sections andormultiple measurements along transects perpendicular or semi-perpendicular to thecentral axis and the von Ebner lines (see Fig S1 Fig 1B) We did not include the fossilcrocodylians with reported VEIWs and tooth formation times from Ricart et al (2019)because they based their tooth formation time calculations on the radius of dentine in theirtransverse sections instead of the CAH which means they are not representative of actualtooth formation times whereas the tooth formation times reported by Erickson aresupported by von Ebner line counts for all regions where they were possible

As is to be expected the greater the CAH the greater the variation in tooth formationtime produced by using mean VEIW plusmn 1SD In an adult Tyrannosaurus with morethan 15 mm CAH (from the tip of the pulp cavity to the crown apex) the differencebetween minimum and maximum estimates of tooth formation time is greater than a yearand a half (613 days) Whereas in the much shorter titanosaur tooth in our sample thisdifference is little more than 5 weeks (36 days) Table 6 summarizes the comparison ofthe SD values reported by DrsquoEmic et al (2019) and the SD values based on the SD range ofAlligator we calculatedWe also explore the effect of applying the relative standarddeviation of Alligator on calculations of tooth formation time and replacement rate insauropods (Table 7) using mean VEIW plusmn 1SD Even with the range of tooth replacementrate min-min and max-max generated by using VEIW plusmn 1SD the replacement rate valuesfor narrow crowned taxa (Diplodocus Torneria Dicraeosaurus) and broad crownedtaxa (Camarasaurus Brachiosaurus Giraffatitan) barely overlap with the exception of the

Figure 8 Mean specimen VEIW by body length Mean VEIW vs body length for Alligator specimensfrom this study and Erickson (1992 1996a) The nearly linear shaped quadratic regression and thecoefficient of determination are displayed Full-size DOI 107717peerj9918fig-8


Table 5 Error margins for published Tooth formation times

Taxon Meanincrementwidth(microm)

Central axis height(from mean VEIWand TFT) (mm)

Mean toothformationtime (days)

VEIW SDbased onAlligator(microm)

TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source

Crocodilian 13 31980 246 38916 3511046 1893248 1051046 minus566752 Erickson(1996b)Leidyosuchus 19 53770 283 56877 4039131 2178005 1209131 minus651995

Adult Edmontonia 135 37665 279 40413 3982040 2147221 1192040 minus642779

Adult Triceratops 158 60198 381 47298 5437840 2932226 1627840 minus877774

InfantLambeosaurinae

11 16170 147 32929 2098064 1131331 628064 minus338669

Adult Prosaurolophus 16 51680 323 47897 4610032 2485850 1380032 minus744150

Infant Maiasaura 12 15840 132 35923 1883976 1015889 563976 minus304111

Adult Maiasaura 13 36530 281 38916 4010585 2162613 1200585 minus647387

JuvenileEdmontosaurus

14 31500 225 41910 3211323 1731629 961323 minus518371

Adult Edmontosaurus 198 67122 339 59272 4838393 2608988 1448393 minus781012

Adult Deinonychus 101 41713 413 30235 5894562 3178502 1764562 minus951498

Adult Troodon 11 39930 363 32929 5180934 2793696 1550934 minus836304

Juvenile Albertosaur 145 49155 339 43406 4838393 2608988 1448393 minus781012

Adult Albertosaur 14 72660 519 41910 7407451 3994292 2217451 minus1195708

JuvenileTyrannosaurus

14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415

Adult Tyrannosaurus 17 158610 933 50890 13316286 7180490 3986286 minus2149510

Titaosauria indet 182 11648 64 54482 913443 492552 273443 minus147448 Garcia ampZurriaguz(2016)

MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409

Majungasaurus DrsquoEmic et al(2019)FMNH PR 2100 Pmx

dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221

FMNH PR 2100 Dentdext 2

1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus

BYU 8901 Pmx dext 2 23 80500 350 68851 4995391 2693646 1495391 minus806354

BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238

BYU 2028 Dent sin 5 23 81650 355 68851 5066754 2732127 1516754 minus817873

NotePublished TFTs from Erickson (1996b) Garcia amp Zurriaguz (2016) and DrsquoEmic et al (2019) plusmn one standard deviation (SD) based on relative SD Central axis height wasnot included in the original publications and was back calculated based on mean VEIWs given in the publications The last two columns are showing just the differences ofTFT from VEIW plusmn SD to mean TFT SD standard deviation TFT tooth formation time VEIW von Ebner line increment width


younger generation teeth (r3 or younger) of Dicraeosaurus which are calculated to havelonger replacement rates than younger teeth of their tooth families Tooth formationtimes based on VEIW plusmn 1SD between broad and narrow crowned taxa have more overlapIn all cases except for the distalmost tooth position in Dicraeosaurus we derive a negativenumber for a mean tooth replacement rate using tooth replacement rate min-max(VEIW + 1SD to calculate minimum formation time for the oldest tooth in a successionalpair of teeth in a tooth family and VEIW minus 1SD for the youngest tooth in the pair)indicating that the ldquoyoungerrdquo replacement tooth (r2) would have formed before the ldquoolderrdquoreplacement tooth (r1) which is not biologically feasible We caution against seeingthis as a failure of using tooth formation times based on mean VEIWs to derive replacementrates It is rather unlikely that all VEIWs in a tooth will be at the upper end of the VEIWrange and VEIWs in the preceding tooth in the lower VEIW range Such extremelydivergent VEIWs in teeth of a tooth family are deemed highly unlikely especially if bothteeth are still growing replacement teeth subjected to the same environmental factorsaffecting the organism forming parts of both teeth at the same time

DISCUSSIONA standardized best practice protocol for calculating tooth agesBased on our sampling tests we propose the following best practices for calculating toothages applicable to both extinct and extant taxa (1) If possible obtain data on VEIWsfrom synchrotron scanning or histological sectioning (this approach is preferred overestimates of VEIW obtained from a transfer function) (2) Measure CAH from the tip ofthe pulp cavity to the crown apex for each tooth in the dentition via models obtainedfrom CT scanning prior to preparation of histological sections This approach is preferableas it is difficult to obtain a section from exactly the plane that contains both the crown apexand the tip of the pulp cavity (3) Produce histological sections along the central axisperpendicular to von Ebner lines (4) Measure VEIW between all visible von Ebner linesalong the central axis avoiding subsampling This protocol presents a challenge as vonEbner lines in this region have the least optical contrast (Ricart et al (2019) this studyM DrsquoEmic 2018 personal communication) and are not always visible If measuring vonEbner line along the central axis is not possible and transects must be taken in an alternate

Table 6 Error margin differences for theropod VEIWs

Taxon MeanVEIW (microm)

transects measuredVEIWs

Previously reportedVEIW SD (microm)

Alligator basedVEIW SD (microm)

Difference oldndashnewVEIW SD ()

Alligator average 1600 87 4654 ndash 479 ndash

Majungasaurus average 1755 54 544 515 525 204

Ceratosaurus average 1446 9 54 326 433 2473

Allosaurus average 2300 4 12 082 689 8814

NoteStandard deviations of VEIW based on DrsquoEmic et al (2019) and the relative standard deviation based on Alligator (this study) are compared for MajungasaurusCeratosaurus and Allosaurus transects and measured VEIW are the numbers of transects and VEIWs measured in those transects to derive the mean VEIW and itsstandard deviation Difference oldndashnew VEIW SD () denotes how much the previously reported and the Alligator based SD differ (((old VEIW SDAlligator VEIW SD)minus 1) 100 no difference would be 0) SD standard deviation VEIW von Ebner line increment width


Table 7 Impact of VEIW plusmn 1SD on tooth formation time and replacement rate of sauropods

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

Diplodocus YPM 4677 I 187ndash183 2640421 1423784 DrsquoEmic et al(2013)

pmx II 178ndash145 2305016 1242925 36 513812 277061 minus673231 1464104

Average for tooth postion III 144ndash113 1893491 1021020 33 470994 253972 minus479298 1204264

IV 110 1569980 846574

Camarasaurus UMNH 5527 I 130ndash113 1734114 935080


Average for tooth position III 253 3610954 1947121 63 899170 484856 minus764663 2148689

IV 190 2711784 1462265 60 856353 461768 minus393166 1711287

Tornieria aficana MBR2345 I Sattler(2014)

mx sin II 13523 1930124 1040774

Average for tooth position III 14893 2125539 1146146

MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907

Giraffatitan brancai I 21634 3087749 1664995 Kosch(2014)

MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306

first 5 alveoli III 13285 1896081 1022416

MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I

dent dext II 23683 3380197 1822691 10414 1486316 801461 minus193872 2481649


Brachiosaurus sp USNM 5730 I 280 3998147 2155906 5288 754768 406999065 minus1087473 2249232 DrsquoEmic ampCarrano(2019)

mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667

Average for tooth postion III 162ndash153 2245698 1210939

dent I 258ndash242 3585753 1933532 8372 1194828 644283 minus457393 2296503

Average for tooth postion II 185ndash150 2390925 1289249

Dicraeosaurus hansemanni I Kosch(2010)Schwarzet al(2015)

MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007

pmx dext III 17400 2483423 1339127 3467 494782 266799 minus621017 1382598

IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738

first 5 alveoli III 14900 2126609 1146724 6275 895602 482932 minus141827 1520362

IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071


location VEIW should be calculated perpendicular to von Ebner line orientation as near tothe central axis as possible and CAHmeasured along the true central axis used to calculatetooth formation time Precise measurement of the CAH is important as it significantlyinfluences calculation of tooth formation times and replacement rates (5) SD from theaverage VEIW should be used to incorporate uncertainty into estimates Our analysesindicate increasing similarity of the relative standard deviations derived in this and previousstudies with increasing sample size suggesting convergence on a confident measure of errorthat is widely applicable to archosaur datasets Specifically our relative standard deviation(derived from the mean standard deviation values of 87 individual transects with 4654VEIWs) most closely approximates relative standard deviations of Majungasaurus fromDrsquoEmic et al (2019) (which was based on 54 transects with 544 VEIWs) and differs mostfrom the relative standard deviation of Allosaurus which was calculated using only 4transects with 12 VEIWs (DrsquoEmic et al 2019) (Table 6) This suggests that applying therelative standard deviation of Alligator we provide herein is a better approach forgenerating confidence intervals around mean VEIW for taxa in which only a limitednumber of VEIW can be directly measured than calculating SD from such a smallnumber of measured VEIW In addition the Alligator based relative standard deviationcan be applied to tooth formation times calculated based on a transfer function like thetransfer functions for tooth length to tooth formation time form DrsquoEmic et al (20132019) We advise to take the intradental VEIW variability we document here intoaccount also when calculating and discussing tooth replacement rates This can be doneby comparing those based on minimum and maximum tooth formation times (minus2304and +4273 in our sample respectively) for both adjacent tooth positions to thecalculated baseline value This introduces a margin of error to reports of tooth formationtime and replacement rate (6) In homodont to weakly heterodont taxa researchers canbe confident in applying mean VEIWs derived from transects perpendicular to vonEbner lines to derive calculations of tooth formation time and replacement rate in otherregions of the tooth rows and despite growth stage

Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550

first 5 alveoli III 10380 1481490 798858 6160 879189 474082 196557 1156714

IV 4220 602301 324777

NoteRanges of mean tooth formation times (TFTs) for tooth positions of the sauropods Diplodocus sp Camarasaurus sp Torneria africana Giraffatitan brancaiBrachiosaurus sp and Dicraeosaurus hansemanni and resultant tooth replacement rates (TRR) based on TFT from VEIW plusmn 1SD DrsquoEmic et al (2013) DrsquoEmic amp Carrano(2019) only give TFT for some teeth so the full range of TFTs found in the position is displayed for other tooth positions the mean TFT found in this position in the jawelement is displayed For explanation of TRR TRR max-max TRR min-min TRR min-max TRR max-min see methods SD standard deviation


Tooth geometry is more impactful on VEIW than growthCurrently our data do not support a straightforward trend in VEIW variation that can belinked to tooth growth over time Within our sample significant differences in meanVEIW occur between the apicalmost and thus oldest subsection of the tooth central axisand sections grown later Therefore it is tempting to suggest that subsampling VEIW eitherin the apicalmost or basalmost region of the tooth will lead to over or underestimatesof tooth formation time respectively However our sample contains a few replacementteeth (equivalents to the oldest and most apical crown parts of more mature teeth) thathave wider mean VEIWs than the functional teeth in their respective alveoli (Table 7)which is at odds with the pattern we document of thinner VEIWs in the apical areaMoreover when we compare multiple teeth of the same individual we observe consistentpatterns in VEIW that suggest external factors are influencing VEIW similarly within allteeth of the dentition These conflicting data suggest the crowded von Ebner lines weobserve in our sample are not reflective of a general pattern related to tooth growth that isconsistent across all individuals but rather is likely related to changing levels of metabolicactivity of the individual we sampled during tooth growth Such an interpretation fitswith other studies documenting variations in metabolic activity to tooth formation timeand replacement rate and thus daily tooth growth documented by VEIW across a widearray of tetrapods including squamates (Anguis fragilis Chalcides sexlineatus andChalcides viridanus) (Cooper 1966 Delgado Davit-Beal amp Sire 2003) and mammals(Klevezal 1996 66f) Future research into the underlying factors of tooth growth undercontrolled conditions (Wu et al 2013) might provide more conclusive explanations foractual intradental VEIW variation Thus we caution that researchers should not interpretthe pattern we document here of more crowded von Ebner lines early in tooth growth asapplicable widely to Alligator or transferable to other archosaurs What the data onsubsampling do suggest is that subsampling VEIW anywhere along the central axis of thecrown as opposed to measuring VEIW along the entire central axis can impact toothformation time calculation by up to 12 We deem this an acceptable deviation as it lieswithin the margin of error created by applying VEIW plusmn 1SD (grand mean) but note that thepractice of sampling all visible VIEWs reduces this variation and should be preferred

Variation in VEIW and observed von Ebner lines evident along transects off the centralaxis are more a function of tooth geometry than tooth growth and can have moreextreme effects on calculations of tooth formation time and tooth replacement rateWe document that tooth formation times derived from mean VEIW of all von Ebner linesalong transects lateral to the pulp cavity only capture about 83 of the age represented bythe von Ebner lines along the CAH Reasons for this are not only that fewer discerniblevon Ebner lines are represented along such transects but also that VEIW decreases inlateral transects by more than a third due to tooth shape Measuring VEIW as close to thecentral axis as possible mitigates problems introduced by other transect orientations andshould be preferred over other methods such as measuring VEIWs in multiple transversesections of the same tooth (Erickson 1992) particularly in high-crowned taxa MeanVEIWs obtained by multiple transverse sections or a zig-zag pattern (Fig 1B in File S1)


systematically underestimate the mean VEIW by conflating VEIWs of varying distancelateral of the pulp cavity however they are to be favored compared to transects thatintroduce error by measuring VEIW oblique to the von Ebner lines Future research canmake attempts to expand the dataset for crocodylians to include species with varyingtooth geometry including globidont taxa to see how tooth shape impacts VEIW and ifdifferent potential error margins have to be used when utilizing VEIW measurements inteeth with morphology distinct from our Alligator mississippienisis sample

Ontogeny and VEIWInvestigating ontogenetic sampling effects on mean VEIW is hampered by the smallsample size of this study but the ontogenetic development of dental organization we finddiffers from previously reported patterns (Edmund 1962 Erickson 1992 Hanai ampTsuihiji 2018) Erickson (1992) found a significant relationship between mean VEIW andbody length in Alligator however we find no such strong evidence for ontogeneticsampling effects on mean VEIWWhen we combine our data with that of Ericksonrsquos (19921996a) data the relationship between mean VEIW and body length does not reach alevel of 95 of significance However we note that a caveat of using the specimen levelmean VEIWs from Erickson (1992 1996a) is that his VEIWs were derived from a ldquozig-zagrdquopattern of measurement (Fig 1B in Fig S1) (ie reported mean VEIWs combine VEIWsfrom near the central axis and marginal measurements) Our data indicate that thistechnique leads to a systematic underestimation of VEIW compared to our centralaxis-based measurements Preliminary corrections for reported VEIWs of Erickson (19921996a) by adding 26667 to the reported width (following the assumption that 15 of thetransects used by Erickson are using VEIWs that are 33 too short) do increase thecorrelation of body length to specimen mean VEIW to a significant value with a better fitfor a quadratic regression (reduced major axis regression p = 00455 R2 = 0457 R2 = 0680for a quadratic regression) (Fig 6 in File S1 Table 1) However we do not deem thisad hoc correction of Erickson (1992 1996a) mean VEIWs precise enough to confidentlyapply it to all of his measurements obtained from Ericksonrsquos zig-zag counting andmeasuring method (eg in Table 5)

It is unclear if the addition of more data or a more reliable method to account for thesystematically underestimated mean VEIWs of Erickson (1992 1996a) will exacerbatethe lack of correlation or will more conclusively link mean VEIW and ontogenetic statusThe former is consistent with the mostly small and non-systematic variation in meanVEIW of hadrosaur and theropod dinosaur species of different ontogenetic status reportedin Erickson (1996b) and the constant VEIW in a juvenile and adult baurusuchidcrocodylian reported by Ricart et al (2019) As of now our data cannot confidentlysupport a simple trend of increasing VEIW during ontogeny that is strong enough toproduce significant differences (a = 93 or more) in the mean VEIWs of our sampledteeth but do suggest a slight ontogenetic increase in specimen mean VEIW Due to thelack of significance of both of our statistical tests our preliminary assessment is that VEIWdoes not change systematically and uniformly during ontogeny making it possible to


apply mean VEIWs obtained to various ontogenetic stages of a species without introducingan ontogenetic scaling factor

Although we find no substantive impact on mean VIEW across ontogeny otherresearch indicates that tooth formation time and tooth replacement ratemdashand thus toothlongevitymdashdo increase ontogenetically (File S1 Erickson 1992 1996a) Therefore otherfactors related to tooth size and jaw size likely account for this observation These couldinclude size increase of new teeth before eruptionreplacement in later tooth generationsmore space for replacement teeth in the alveolar ramusalveolidental crypts longertime required to dissolve the roots of larger teeth before they are shed andor more spacein the pulp cavityclose to the functional tooth Such a trend is supported by allometrictooth size increase compared to skull length reported by Brown et al (2015)

Our study uses data from three individuals at different ontogenetic stages to reconstructontogenetic changes and growth patterns that are hypothesized to occur in a singleindividual in a similar mannermdasha method used often in paleontology (Erickson 2014)mdashincontrast to longitudinal studies that chronicle ontogenetic trajectories of individuals overtime No longitudinal study measuring VEIW have been carried out for archosaurs todate Edmund (1962) did not measure VEIWs and Erickson (1992 1996a) did rearalligators for labeling studies of von Ebner lines but used them as single data points forVEIW

CONCLUSIONSOur results indicate that the greatest challenges to accurately estimating tooth formationtime and calculating tooth replacement rate for extinct taxa rests in (1) generating atransect perpendicular to von Ebner line orientation for the measurement of VEIW(oblique measurements reduce tooth formation time estimates by up to a third inAlligator) and (2) measuring VEIW and crown height along a transect that bisects thecentral axis as opposed to other regions of the tooth VEIW decreases with increasingdistance from the central axis (up to 36) and use of mean VEIW values from theseregions will produce inflated tooth formation times the greater the crown height the moreintense the impact errors in calculations of mean VEIW Measuring VEIW along thecentral axis also helps to keep transect orientation perpendicular to von Ebner lines

We find that transects misaligned with von Ebner line orientation or with respect to thecentral axis impact the calculation of mean VEIW far more than the acts of subsamplingwithin transects applying mean VEIW from one tooth in the tooth row to crown axisheight of another tooth and ontogenetic status of the individual sampled We documentup to 12 variation in calculations of mean VEIW when derived from subsampling thecentral axis transect and note that variation in VEIW is likely an idiosyncratic patternlinked to organismal life history Therefore we cannot recommend any standardizedsubsampling location along the central axis and recommend directly measuring thedistance between all visible von Ebner lines along to minimize error However we note thatsubsampling error is within the margin of error of VEIW plusmn 1SD derived and therefore if aVEIW cannot be measured from a complete transect it is sufficient to use a subset ofmeasurements along a central axis transect to calculate a mean VEIW for a whole tooth


Intramandibular sampling effects do not significantly influence the mean VEIW as there isno systematic variation of mean VEIW associated with tooth position along the tooth rowin our sample It is sufficient to have a few samples from teeth of a dentition to makereliable prediction of the tooth formation time for other teeth provided that the CAHis known

According to our limited data ontogenetic status does not significantly affect calculationsof mean VEIW (below a confidence value of a = 93) therefore we preliminarily suggestthat a mean VEIW obtained for a specimen of a taxon can be applied to the dentition ofother specimens regardless of growth stage However we note that this factor warrants morestudy as ad hoc corrections of data for younger specimens of Alligator suggests therelationships might reach a higher degree of significance

ABBREVIATIONSCA central axis

CAH central axis height

Dent dentary tooth position

max maximum tooth formation time estimate

min minimum tooth formation time estimate

Mx maxillary tooth position

NCSM North Carolina Museum of Natural Sciences

Pmx premaxillary tooth position

SD standard deviation

TFT Tooth Formation Time

VEIW von Ebner Increment Width between von Ebner Lines

ACKNOWLEDGEMENTSWe thank Aurore Canoville for help with histological sections and training Kirstin Brinkand Yun-Hsin Wu for discussions about dental organization and tooth replacement inAlligator Appalachian State University for donations of Alligator specimens forconsumptive sampling Adam Hartstone-Rose and Edwin Dickinson for discussions ondata interpretation and assistance with statistics Mary Schweitzer Brian LangerhansMichael DrsquoEmic Christian Kammerer and the staff and students of the PaleontologyResearch Lab at the NC Museum of Natural Sciences for helpful critiques during projectdevelopment Domenic DrsquoAmore Aaron LeBlanc and Kirstin Brink for their constructivereviews of the manuscript

ADDITIONAL INFORMATION AND DECLARATIONS

FundingThis work was supported by the North Carolina Museum of Natural Sciences The fundershad no role in study design data collection and analysis decision to publish orpreparation of the manuscript


Grant DisclosuresThe following grant information was disclosed by the authorsNorth Carolina Museum of Natural Sciences

Competing InterestsThe authors declare that they have no competing interests

Author Contributions Jens CD Kosch conceived and designed the experiments performed the experimentsanalyzed the data prepared figures andor tables authored or reviewed drafts of thepaper and approved the final draft

Lindsay E Zanno conceived and designed the experiments analyzed the data authoredor reviewed drafts of the paper and approved the final draft

Data AvailabilityThe following information was supplied regarding data availability

The raw measurements of von Ebener line increment widths (VEIWs) and the raw dataof tooth length (TH) and central axis height (CAH measured from the tip of the pulpcavity to the crown apex) are available as Supplemental Files

Supplemental InformationSupplemental information for this article can be found online at httpdxdoiorg107717peerj9918supplemental-information

REFERENCESAllison B Lamaster T Avrahami HM Zanno L 2019 Buccal tooth development replacement

rate and microstructure in parksosauridae (Dinosauria Neornithischia) Journal of VertebratePaleontology Program and Abstracts 201953

Barrett PM 2014 Paleobiology of herbivorous dinosaurs Annual Review of Earth and PlanetarySciences 42(1)207ndash230 DOI 101146annurev-earth-042711-105515

Bramble K LeBlanc ARH Lamoureux DO Wosik M Currie PJ 2017 Histological evidence fora dynamic dental battery in hadrosaurid dinosaurs Scientific Reports 7(1)15787DOI 101038s41598-017-16056-3

Brink KS Reisz RR LeBlanc ARH Chang RS Lee YC Chiang CC Huang T Evans DC 2015Developmental and evolutionary novelty in the serrated teeth of theropod dinosaursScientific Reports 5(1)12338 DOI 101038srep12338

Brown CM VanBuren CS Larson DW Brink KS Campione NE Vavrek MJ Evans DC 2015Tooth counts through growth in diapsid reptiles implications for interpreting individualand size-related variation in the fossil record Journal of Anatomy 226(4)322ndash333DOI 101111joa12280

Button K You H Kirkland JI Zanno L 2017 Incremental growth of therizinosauriandental tissues implications for dietary transitions in Theropoda PeerJ 5e4129DOI 107717peerj4129

Cooper JS 1966 Tooth replacement in the slow worm (Anguis fragilis) Journal of Zoology150(2)235ndash248 DOI 101111j1469-79981966tb03006x


DrsquoAmore DC Harmon M Drumheller SK Testin JJ 2019 Quantitative heterodonty inCrocodylia assessing size and shape across modern and extinct taxa PeerJ 7(4)e6485DOI 107717peerj6485

DrsquoEmic MD Carrano MT 2019 Redescription of brachiosaurid sauropod dinosaur material fromthe Upper Jurassic morrison formation Colorado USA Anatomical Record 303(4)732ndash758DOI 101002ar24198

DrsquoEmic MD OrsquoConnor PM Pascucci TR Gavras JN Mardakhayava E Lund EK 2019Evolution of high tooth replacement rates in theropod dinosaurs PLOS ONE 14(11)e0224734DOI 101371journalpone0224734

DrsquoEmic MD Whitlock JA Smith KM Fisher DC Wilson JA 2013 Evolution of high toothreplacement rates in sauropod dinosaurs PLOS ONE 8(7)e69235DOI 101371journalpone0069235

Dean MC 1998 Comparative observations on the spacing of short-period (von Ebnerrsquos) lines indentine Archives of Oral Biology 43(12)1009ndash1021 DOI 101016S0003-9969(98)00069-7

Delgado S Davit-Beal T Sire J-Y 2003 Dentition and tooth replacement pattern in Chalcides(Squamata Scincidae) Journal of Morphology 256(2)146ndash159 DOI 101002jmor10080

Edmund AG 1960 Tooth replacement phenomena in lower vertebrates Royal Ontario MuseumLife Science Division Contribution 521ndash190

Edmund AG 1962 Sequence and rate of tooth replacement in the crocodilia Royal OntarioMuseum Life Sciences Division Contribution 561ndash42

Enax J Fabritius H-O Rack A Prymak O Raabe D Epple M 2013 Characterization ofcrocodile teeth correlation of composition microstructure and hardness Journal of StructuralBiology 184(2)155ndash163 DOI 101016jjsb201309018

Erickson GM 1992 Verification of von Ebner incremental lines in extant and fossil archosaurdentine and tooth replacement rate assessment using counts of von Ebner lines Masterrsquos thesisMontana State University Bozeman Montana

Erickson GM 1996a Daily deposition of dentine in juvenile Alligator and assessment of toothreplacement rates using incremental line counts Journal of Morphology 228189ndash194DOI 101002(SICI)1097-4687(199605)2282lt189AID-JMOR7gt30CO2-0

Erickson GM 1996b Incremental lines of von Ebner in dinosaurs and the assessment of toothreplacement rates using growth line counts Proceedings of the National Academy of Sciences93(25)14623ndash14627 DOI 101073pnas932514623

Erickson GM 2014 On dinosaur growth Annual Review of Earth and Planetary Sciences2014(42)675ndash697 DOI 101146annurev-earth-060313-054858

Erickson GM Zelenitsky DK Kay DI Norell MA 2017 Dinosaur incubation periods directlydetermined from growth-line counts in embryonic teeth show reptilian-grade developmentProceedings of the National Academy of Sciences 114(3)540ndash545 DOI 101073pnas1613716114

Farlow JO Hurlburt GR Elsey RM Britton ARC Langston W 2005 Femoral dimensionsand body size of Alligator mississippiensis estimating the size of extinct MesoeucrocodyliansJournal of Vertebrate Paleontology 25(2)354ndash369DOI 1016710272-4634(2005)025[0354FDABSO]20CO2

Finger JW Jr Thomson PC Isberg SR 2019 A pilot study to understand tooth replacement innear-harvest farmed saltwater crocodiles (Crocodylus porosus) implications for blemishinduction Aquaculture 504102ndash106 DOI 101016jaquaculture201901060

Garcia RA Zurriaguz V 2016 Histology of teeth and tooth attachment in titanosaurs(Dinosauria Sauropoda) Cretaceous Research 57248ndash256 DOI 101016jcretres201509006


Gignac PM 2010 Biomechanics and the ontogeny of feeding in the american alligator (AlligatorMississippiensis) reconciling factors contributing to intraspecific niche differentiation in a largebodied vertebrate Dissertation Florida State University Tallahassee

Gren JA 2011 Dental histology of Cretaceous mosasaurs (Reptilia Squamata) incrementalgrowth lines in dentine and implications for tooth replacement Masterrsquos thesis LundUniversity Lund

Gren JA Lindgren J 2013 Dental histology of mosasaurs and a marine crocodylian from theCampanian (Upper Cretaceous) of southern Sweden incremental growth lines and dentineformation rates Geological Magazine 151(1)134ndash143 DOI 101017S0016756813000526

Hanai T Tsuihiji T 2018 Description of tooth ontogeny and replacement patterns in a JuvenileTarbosaurus baatar (Dinosauria Theropoda) using CT-scan data Anatomical Record302(7)1210ndash1225 DOI 101002ar24014

Jones MEH Lucas PW Tucker ES Watson AT Sertich JJW Foster JR Wiliams R Garbe UBevitt JJ Salvemini F 2018 Neutron scanning reveals unexpected complexity in the enamelthickness of an herbivorous Jurassic reptile Journal of The Royal Society Interface15(143)20180039 DOI 101098rsif20180039

Johnston PA 1979 Growth rings in dinosaur teeth Nature 278(5705)635ndash636DOI 101038278635a0

Kear BP Larsson D Lindgren J Kundrat M 2017 Exceptionally prolonged tooth formation inelasmosaurid plesiosaurians PLOS ONE 12(2)e0172759 DOI 101371journalpone0172759

Khan B Tansel B 2000 Mercury bioconcentration factors in american alligators (Alligatormississippiensis) in the Florida Everglades Ecotoxicology and Environmental Safety 47(1)54ndash58DOI 101006eesa20001923

Kieser JA Klapsidis C Law L Marion M 1993Heterodonty and patterns of tooth replacement inCrocodylus niloticus Journal of Morphology 218(2)195ndash201 DOI 101002jmor1052180208

Klevezal GA 1996 Recording structures of mammals determination of age and reconstruction oflife history Rotterdam CRC PressBalkema [translation of 1988 book cited version is thepreprint]

Kosch JCD 2010 Bezahnung und Zahnwechsel von Dicraeosaurus hansemanni UnpublishedBachelor thesis 1ndash42

Kosch JCD 2014 Tooth replacement and dentition in Giraffatitan brancai Master thesis 1ndash192

Lamm ET 2013 Preparation and sectioning of specimens In Padian K Lamm ET eds BoneHistology of Fossil Tetrapods Berkeley University of California Press 55ndash160

Lawson R Wake DB Beck NT 1971 Tooth replacement in the red-backed salamander Plethodoncinereus Journal of Morhpology 134(3)259ndash269 DOI 101002jmor1051340302

LeBlanc ARH Reisz RR Evans DC Bailleul AM 2016 Ontogeny reveals function and evolutionof the hadrosaurid dinosaur dental battery BMC Evolutionary Biology 16(1)152DOI 101186s12862-016-0721-1

Neill WT 1971 The last of the ruling reptiles alligators crocodiles and their kin New YorkColumbia University Press 263ndash277

Osborn JW 1970 New approach to Zahnreihen Nature 225(5230)343ndash346DOI 101038225343a0

Osborn JW 1975 Tooth replacement efficiency patterns and evolution Evolution 29(1)180ndash186DOI 101111j1558-56461975tb00825x

Ohtsuka M Shinoda H 1995 Ontogeny of circadian dentinogenesis in the rat incisor Archives ofOral Biology 40(6)481ndash485 DOI 1010160003-9969(95)00002-7


Ricart RSD Santucci RM Andrade MB Oliveira CEM Nava WR Degrazia GF 2019 Dentalhistology of three notosuchians (Crocodylomorpha) from the Bauru Group Upper CretaceousHistorical Biology 661ndash12 DOI 1010800891296320191675057

Richman JM Whitlock JA Abramyan J 2013 Reptilian tooth regeneration In Huang GT-JThesleff I eds Stem Cells in Craniofacial Development and Regeneration HobokenWiley-Blackwell 135ndash151

Rosenberg GD Simmons DJ 1980 Rhythmic dentinogenesis in the rabbit incisors circadianultradian amp infradian periods Calcified Tissue International 32(1)29ndash44DOI 101007BF02408519

Salakka S 2014 Tooth replacement of Euhelopus Zdanskyi [sic] (Dinosauria Sauropoda) and theevolution of titanosaurian tooth morphology Masterrsquos thesis Uppsala University Uppsala

Sattler F 2014 Tooth replacement of the sauropod dinosaur Tornieria africana (Fraas) fromTendaguru (Late Jurassic Tanzania) Bachelor thesis 1ndash41

Schmiegelow AB Sellers KC Holliday CM 2016 Ontogeny of enamel thickness in the teeth ofAlligator and its significance for crocodyliform dental evolution FASEB Journal 30(S1)7798DOI 101096fasebj301_supplement7798

Schwarz D Kosch JCD Fritsch G Hildebrandt T 2015 Dentition and tooth replacement ofDicraeosaurus hansemanni (Dinosauria Sauropoda Diplodocoidea) from the TendaguruFormation of Tanzania Journal of Vertebrate Paleontology 35(6)e1008134DOI 1010800272463420151008134

Sellers KC Schmiegelow AB Holliday CM 2019 The significance of enamel thickness in theteeth of Alligator mississippiensis and its diversity among crocodyliforms Journal of Zoology09(3)172ndash181 DOI 101111jzo12707

Sereno PC Wilson JA Witmer LM Whitlock JA Maga A Ide O Rowe TA 2007 Structuralextremes in a cretaceous dinosaur PLOS ONE 2(11)e1230 DOI 101371journalpone0001230

Smith TM 2004 Incremental development of primate dental enamel DissertationStony Brook University New York

Sokolskyi T Zanno L Kosch JC 2019 Unusual Tooth Replacement in a New CenomanianIguanodontian from the Mussentuchit Member of the Cedar Mountain Formation Journal ofVertebrate Paleontology Program and Abstracts 2019195ndash196

Whitlock JA Richman JM 2013 Biology of tooth replacement in amniotes International Journalof Oral Science 5(2)66ndash70 DOI 101038ijos201336

Wu XB Xue H Wu LS Zhu JL Wang RP 2006 Regression analysis between body andhead measurements of Chinese alligators (Alligator sinensis) in captive populationAnimal Biodiversity and Conservation 29(1)65ndash71

Wu P Wu X Jiang T-X Elsey RM Temple BL Divers SJ Glenn TC Yuan K Chen M-HWidelitz RB Chuong C-M 2013 Specialized stem cell niche enables repetitive renewal ofalligator teeth Proceedings of the National Academy of Sciences 110(22)E2009ndashE2018DOI 101073pnas1213202110


Sampling impacts the assessment of tooth growth and replacement rates in archosaurs implications for paleontological studies

Introduction

Materials and Methods

Results

Discussion

Conclusions

Abbreviations

flink7

References

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that intensify with crown height The same holds true for applications of our relativeSD to calculations of tooth formation time in extinct taxa which produce highlyvariable maximum and minimum estimates in large-toothed taxa (eg 718ndash1331days in Tyrannosaurus)

Subjects Paleontology Zoology HistologyKeywords Tooth formation Tooth replacement Archosauria Sampling effects Alligatorvon Ebner lines Error bars

INTRODUCTIONTooth replacement rate provides key information on the function and evolution of thedentition (Edmund 1960 Osborn 1970 1975 Richman Whitlock amp Abramyan 2013Whitlock amp Richman 2013 Schwarz et al 2015 LeBlanc et al 2016 Bramble et al 2017)Such data can be used to infer aspects of the paleobiology of extinct taxa includingmetabolic activityinvestment dietary preferences and behavior (Johnston 1979Barrett 2014 Salakka 2014 DrsquoEmic et al 2013 2019 DrsquoEmic amp Carrano 2019 Brinket al 2015 Button et al 2017 DrsquoEmic et al 2019) However tooth growth and exfoliationcannot be directly observed in extinct species therefore tooth replacement rate must beestimated via growth lines preserved within dentin (von Ebner Lines) andor incrementalgrowth lines of enamel that record different rhythms (see Smith (2004) for a review)Within living crocodilians von Ebner lines are known to represent daily dentin deposition(Erickson 1992 1996a) Paleontological studies have therefore used direct von Ebner linecounts or estimates derived by measuring dentin thickness divided by the mean widthbetween von Ebner lines (so called ldquovon Ebner Line IncrementWidthrdquo VEIW) to estimatetooth formation times and replacement rates in extinct species (Erickson 1996b Serenoet al 2007 DrsquoEmic et al 2013 2019 Garcia amp Zurriaguz 2016 Erickson et al 2017 Ricartet al 2019) This practice makes the accurate estimation of von Ebner line counts andmean VEIW a critical consideration as errors in the calculation of either will havecascading effects ultimately resulting in erroneous paleobiological inferences andmacroevolutionary trends

The challenges of working with fossil data constrain sampling approaches for derivingvon Ebner line count and mean VEIW in extinct species For example because a researchercannot always choose the location or orientation for consumptive sampling they oftenhave to calculate mean VEIW from one region of the tooth and apply these data todifferent transect locations within the same tooth (Erickson 1992 1996b Sereno et al2007 Gren 2011 DrsquoEmic et al 2013 2019 Gren amp Lindgren 2013 Garcia amp Zurriaguz2016 Kear et al 2017 Ricart et al 2019) Likewise researchers may have to calculatemean VIEW from one tooth position within the jaw and then apply these values toother tooth positions (Kosch 2014 Schwarz et al 2015 Garcia amp Zurriaguz 2016DrsquoEmic amp Carrano 2019 DrsquoEmic et al 2019) Moreover because von Ebner lines arenot always visible along the entire transect mean VEIWs are typically derived from atransect subsample as opposed to being calculated from the entire transect length(Erickson 1992 1996a 1996b Gren 2011 Gren amp Lindgren 2013 Button et al 2017































Hypotheses testing


























Mean VEIW(microm)


Mean VEIW(microm)


TFTdifference

Medium (NCSM 100804) Dent 18 21 5 12 34 11845 14 4 8 21 17768 5922

Large (NCSM 100805) Dent 11 21 6 12 29 23929 175 3 13 235 29559 5630

Large (NCSM 100805) Dent 11 22 6 12 36 22841 165 3 125 215 30455 7614







Based on VEL



Based on VEL




mid crown 175 10 14214 135 15 18426 7714

mid crown 184 10 13519 139 19 17835 7580


root base 193 26 66630 121 9 106225 6273







Tooth position 1 2 3 4 11 12 15 16 17 18 19




















Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT


thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow


percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the


thep-valueforaon


TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References

ltlt ASCII85EncodePages false AllowTransparency false AutoPositionEPSFiles true AutoRotatePages None Binding Left CalGrayProfile (Dot Gain 20) CalRGBProfile (sRGB IEC61966-21) CalCMYKProfile (US Web Coated 050SWOP051 v2) sRGBProfile (sRGB IEC61966-21) CannotEmbedFontPolicy Warning CompatibilityLevel 14 CompressObjects Off CompressPages true ConvertImagesToIndexed true PassThroughJPEGImages true CreateJobTicket false DefaultRenderingIntent Default DetectBlends true DetectCurves 00000 ColorConversionStrategy LeaveColorUnchanged DoThumbnails false EmbedAllFonts true EmbedOpenType false ParseICCProfilesInComments true EmbedJobOptions true DSCReportingLevel 0 EmitDSCWarnings false EndPage -1 ImageMemory 1048576 LockDistillerParams false MaxSubsetPct 100 Optimize true OPM 1 ParseDSCComments true ParseDSCCommentsForDocInfo true PreserveCopyPage true PreserveDICMYKValues true PreserveEPSInfo true PreserveFlatness true PreserveHalftoneInfo false PreserveOPIComments false PreserveOverprintSettings true StartPage 1 SubsetFonts true TransferFunctionInfo Apply UCRandBGInfo Preserve UsePrologue false ColorSettingsFile (None) AlwaysEmbed [ true ] NeverEmbed [ true ] AntiAliasColorImages false CropColorImages true ColorImageMinResolution 300 ColorImageMinResolutionPolicy OK DownsampleColorImages false ColorImageDownsampleType Average ColorImageResolution 300 ColorImageDepth 8 ColorImageMinDownsampleDepth 1 ColorImageDownsampleThreshold 150000 EncodeColorImages true ColorImageFilter FlateEncode AutoFilterColorImages false ColorImageAutoFilterStrategy JPEG ColorACSImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt ColorImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt JPEG2000ColorACSImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt JPEG2000ColorImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt AntiAliasGrayImages false CropGrayImages true GrayImageMinResolution 300 GrayImageMinResolutionPolicy OK DownsampleGrayImages false GrayImageDownsampleType Average GrayImageResolution 300 GrayImageDepth 8 GrayImageMinDownsampleDepth 2 GrayImageDownsampleThreshold 150000 EncodeGrayImages true GrayImageFilter FlateEncode AutoFilterGrayImages false GrayImageAutoFilterStrategy JPEG GrayACSImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt GrayImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt JPEG2000GrayACSImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt JPEG2000GrayImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt AntiAliasMonoImages false CropMonoImages true MonoImageMinResolution 1200 MonoImageMinResolutionPolicy OK DownsampleMonoImages false MonoImageDownsampleType Average MonoImageResolution 1200 MonoImageDepth -1 MonoImageDownsampleThreshold 150000 EncodeMonoImages true MonoImageFilter CCITTFaxEncode MonoImageDict ltlt K -1 gtgt AllowPSXObjects false CheckCompliance [ None ] PDFX1aCheck false PDFX3Check false PDFXCompliantPDFOnly false PDFXNoTrimBoxError true PDFXTrimBoxToMediaBoxOffset [ 000000 000000 000000 000000 ] PDFXSetBleedBoxToMediaBox true PDFXBleedBoxToTrimBoxOffset [ 000000 000000 000000 000000 ] PDFXOutputIntentProfile (None) PDFXOutputConditionIdentifier () PDFXOutputCondition () PDFXRegistryName () PDFXTrapped False CreateJDFFile false Description ltlt CHS ltFEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000500044004600206587686353ef901a8fc7684c976262535370673a548c002000700072006f006f00660065007200208fdb884c9ad88d2891cf62535370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002gt CHT ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef653ef5728684c9762537088686a5f548c002000700072006f006f00660065007200204e0a73725f979ad854c18cea7684521753706548679c300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt DAN 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 DEU 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 ESP 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 FRA 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 ITA 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 JPN ltFEFF9ad854c18cea51fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e30593002537052376642306e753b8cea3092670059279650306b4fdd306430533068304c3067304d307e3059300230c730b930af30c830c330d730d730ea30f330bf3067306e53705237307e305f306f30d730eb30fc30d57528306b9069305730663044307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e30593002gt KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020b370c2a4d06cd0d10020d504b9b0d1300020bc0f0020ad50c815ae30c5d0c11c0020ace0d488c9c8b85c0020c778c1c4d560002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken voor kwaliteitsafdrukken op desktopprinters en proofers De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger) NOR ltFEFF004200720075006b00200064006900730073006500200069006e006e007300740069006c006c0069006e00670065006e0065002000740069006c002000e50020006f0070007000720065007400740065002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e00740065007200200066006f00720020007500740073006b00720069006600740020006100760020006800f800790020006b00760061006c00690074006500740020007000e500200062006f007200640073006b0072006900760065007200200065006c006c00650072002000700072006f006f006600650072002e0020005000440046002d0064006f006b0075006d0065006e00740065006e00650020006b0061006e002000e50070006e00650073002000690020004100630072006f00620061007400200065006c006c00650072002000410064006f00620065002000520065006100640065007200200035002e003000200065006c006c00650072002000730065006e006500720065002egt PTB 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 SUO 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 SVE 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 ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later) gtgt Namespace [ (Adobe) (Common) (10) ] OtherNamespaces [ ltlt AsReaderSpreads false CropImagesToFrames true ErrorControl WarnAndContinue FlattenerIgnoreSpreadOverrides false IncludeGuidesGrids false IncludeNonPrinting false IncludeSlug false Namespace [ (Adobe) (InDesign) (40) ] OmitPlacedBitmaps false OmitPlacedEPS false OmitPlacedPDF false SimulateOverprint Legacy gtgt ltlt AddBleedMarks false AddColorBars false AddCropMarks false AddPageInfo false AddRegMarks false ConvertColors NoConversion DestinationProfileName () DestinationProfileSelector NA Downsample16BitImages true FlattenerPreset ltlt PresetSelector MediumResolution gtgt FormElements false GenerateStructure true IncludeBookmarks false IncludeHyperlinks false IncludeInteractive false IncludeLayers false IncludeProfiles true MultimediaHandling UseObjectSettings Namespace [ (Adobe) (CreativeSuite) (20) ] PDFXOutputIntentProfileSelector NA PreserveEditing true UntaggedCMYKHandling LeaveUntagged UntaggedRGBHandling LeaveUntagged UseDocumentBleed false gtgt ]gtgt setdistillerparamsltlt HWResolution [2400 2400] PageSize [612000 792000]gtgt setpagedevice






























Hypotheses testing


























Mean VEIW(microm)


Mean VEIW(microm)


TFTdifference

Medium (NCSM 100804) Dent 18 21 5 12 34 11845 14 4 8 21 17768 5922

Large (NCSM 100805) Dent 11 21 6 12 29 23929 175 3 13 235 29559 5630

Large (NCSM 100805) Dent 11 22 6 12 36 22841 165 3 125 215 30455 7614







Based on VEL



Based on VEL




mid crown 175 10 14214 135 15 18426 7714

mid crown 184 10 13519 139 19 17835 7580


root base 193 26 66630 121 9 106225 6273







Tooth position 1 2 3 4 11 12 15 16 17 18 19




















Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT


thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow


percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the


thep-valueforaon


TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References




















Mean VEIW(microm)


Mean VEIW(microm)


TFTdifference

Medium (NCSM 100804) Dent 18 21 5 12 34 11845 14 4 8 21 17768 5922

Large (NCSM 100805) Dent 11 21 6 12 29 23929 175 3 13 235 29559 5630

Large (NCSM 100805) Dent 11 22 6 12 36 22841 165 3 125 215 30455 7614







Based on VEL



Based on VEL




mid crown 175 10 14214 135 15 18426 7714

mid crown 184 10 13519 139 19 17835 7580


root base 193 26 66630 121 9 106225 6273







Tooth position 1 2 3 4 11 12 15 16 17 18 19




















Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT


thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow


percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the


thep-valueforaon


TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References






Based on VEL



Based on VEL




mid crown 175 10 14214 135 15 18426 7714

mid crown 184 10 13519 139 19 17835 7580


root base 193 26 66630 121 9 106225 6273







Tooth position 1 2 3 4 11 12 15 16 17 18 19




















Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT


thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow


percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the


thep-valueforaon


TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References






Tooth position 1 2 3 4 11 12 15 16 17 18 19




















Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT


thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow


percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the


thep-valueforaon


TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References




Table

4Too

thform

ationtimes

basedon

meanVEIW

(too

th)plusmn1S

D(grandmean)

Crownheight

(mm)

0193

0203

0923

1175

1233

1563

1623

1643

1785

1793

1863

2053

2055

2063

2133

TFT

bysampled

CAsections

(days)

16067

17635

70985

90385

70446

130233

121710

131424

89250

96908

128469

175954

205500

134530

148111

VEIW

ofthetooth(m

m)

0012

0012

0013

0013

0018

0012

0013

0013

0020

0019

0015

0012

0010

0015

0014

TFT

+SD

(days)

26739

30222

112395

143112

96992

216745

189942

213065

117354

130763

191837

298502

394409

195644

221928

TFT

minusSD

(days)

11483

12450

51873

66050

55308

93081

89544

95016

72006

76978

96570

124742

138948

102510

111143

SD+(days)

10673

12587

41410

52728

26546

86511

68232

81641

28104

33855

63368

122548

188909

61113

73817

SDminus(days)

minus4583

minus5185

minus19112

minus24335

minus15138

minus37152

minus32166

minus36408

minus17244

minus19930

minus31899

minus51212

minus66552

minus32021

minus36968

SD+(

)66428

71378

58337

58337

37683

66428

56061

62120

31490

34935

49326

69648

91926

45427

49839

SDminus(

)minus28528

minus29403

minus26924

minus26924

minus21488

minus28528

minus26429

minus27703

minus19321

minus20566

minus24830

minus29105

minus32385

minus23802

minus24960

Crownheight

(mm)

2193

3475

4565

5025

5265

5655

6225

6415

8825

12865

Mean

Variance

t-statistic

p-value

TFT

bysampled

CAsections

(days)

173116

133654

249000

301500

195000

396842

364035

342133

519118

559348

194454

20739047

VEIW

ofthetooth(m

m)

0013

0026

0018

0017

0027

0014

0017

0019

0017

0023

TFT

+SD

(days)

278380

163835

337058

423087

237052

597759

505673

459516

722749

706467

280449

37706375

17786

00411

TFT

minusSD

(days)

125616

112863

197423

234197

165620

297012

284381

272519

405009

462942

150211

13402557

minus11972

01187

SD+(days)

105264

30181

88058

121587

42052

200917

141638

117383

203631

147119

SDminus(days)

minus47500

minus20791

minus51578

minus67303

minus29380

minus99831

minus79654

minus69615

0000

minus96406

SD+(

)60806

22582

35365

40327

21565

50629

38908

34309

39226

26302

SDminus(

)minus27438

minus15556

minus20714

minus22323

minus15067

minus25156

minus21881

minus20347

minus21981

minus17235

Note TFT

sbasedon

meanVEIW

sforthesampled

toothpo

sition

ssorted

byascend

ingCAHR

owsTFT

plusmnSD

show

theTFT

basedon

VEIW

plusmnSD

(grand

mean)

derivedforeach

toothTFT

+SD

show

sthe

meanVEIW

(too

th)minus1SD(grand

mean)

(TFT

+SD

asitprod

uces

bigger

TFT

s)T

FTminusSD

show

sVEIW

(too

th)+1SD(grand

mean)

(TFT

minusSD

asitprod

uces

smallerTFT


thedifferencesofTFT

plusmnSD

tothebaselin

eTFT

Row

sSD

plusmn(

)areshow


percent(seealso

Fig7)T

helastfour

columns

show

themeanTFT

the


thep-valueforaon


TFT

+SD

andTFT

minusSD

SDstand

arddeviation

TFT

tooth

form

ationtimeVEIW

von

Ebn

erlin

eincrem

entwidth
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References
















TFT +SD (days)

TFT minusSD(days)

SD +(days)

SD minus(days)

Source





11 16170 147 32929 2098064 1131331 628064 minus338669





14 31500 225 41910 3211323 1731629 961323 minus518371







14 36960 264 41910 3767952 2031779 1127952 minus608221

Sub AdTyrannosaurus

14 43960 314 41910 4481579 2416585 1341579 minus723415



MPCA-Ph 4 5 9 1319

208 11232 54 62266 770717 415591 230717 minus124409


dext 31755 51249 292 52540 4167583 2247270 1247583 minus672730

UA 9944 Mx sin 1 1755 46335 264 52540 3767952 2031779 1127952 minus608221


1755 43878 250 52540 3568137 1924033 1068137 minus575967

Ceratosaurus

BYU 12893 Mx dext 6 1446 48312 334 43300 4767030 2570508 1427030 minus7695

Allosaurus


BYU 8901 Mx dext 6 23 73600 320 68851 4567215 2462762 1367215 minus737238



















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References

















Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source




IV 110 1569980 846574




IV 190 2711784 1462265 60 856353 461768 minus393166 1711287


mx sin II 13523 1930124 1040774


MBR2346 I 156325 2231156 1203098

pmx sin II 11860 1692724 912761 3773 538432 290337 minus489626 1318395

III 10267 1465315 790136 1795 256192 138146 minus565860 960197

MBR2343 II 12578 1795130 967981 3688 526300 283795 minus543354 1353449

pmx dext III 9640 1375874 741907


MBR21801 II 22959 3276775 1766923 7346 1048392 565320 minus476400 2090113

pmx sin III 15840 2260808 12190868

MBR21811 I 28652 4089365 2205093 9143 1304938 703657 minus579334 2587929

pmx sin II 20247 2889814 1558263 6414 915460 493640 minus416091 1825190

III 13833 1974354 10646234

MBR21812 I 27968 3991709 2152434 5855 835611 450584 minus1003664 2289859

pmx dext II 2211367 3156098 1701851 8917 1272206 686284 minus273426 2232431

III 14593 2082822 1123113

MBR21802 I

mx sin II 20504 2926484 1578037 9253 1320642 712125 minus161540 2194306


MBR21803 I 13285 1896081 1022416

mx dext II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21814 I 1328481 1896081 1022416

mx sin II 17801 2540630 1369974 8068 1151522 620931 minus202138 1974591


MBR21813 I 21137

mx dext II 22410 3198521 1724726 7407 1057133 570034 minus406182 2033349


(Continued)


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References


Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR218014 I

dent sin II 22789 3252511 1753839 11420 1629986 878931 minus67549 2576466


MBR218013 I




mx II 260ndash227 3506864 1890993 9759 1392908 751092 minus283666 2427667





MBR2337 II 18850 2690375 1450721 2033 290208 156488 minus959310 1406007


IV 14100 2012429 1085155 6033 861110 464333 minus26706 1352149

V 7475 1066873 575286 7600 1084714 584906 394190 1275430

VI 2850 406768 219340

MBR2338 I

pmx sin II 18525 2643989 1425708 1900 271178 146226 minus968476 1385881

III 17525 2501264 1348747 5400 770717 415591 minus382347 1568656

IV 12325 1759091 948548 5067 723142 389937 minus74796 1187876

V 6525 931284 502173 7700 1098986 592602 382157 1309431

VI 3200 456721 246276

MBR2339 I

pmx sin II 18900 2697511 1454569 1000 128453 69265 minus1117778 1315496

III 18175 2594035 1398772 4325 617288 332858 minus577976 1528121

IV 13850 1976748 1065914 5825 831376 448300 minus79458 1359133

V 8025 1145372 617615 5650 806399 434831 283574 957656

VI 2300 328269 177011

MBR2336 I

max dext II 17600 2511968 1354519 3525 503107 271289 minus654342 1428738


IV 9500 1355892 731132 5525 788558 425211 163799 1049971

V 3860 550920 297071



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References



Table 7 (continued)

Taxon Toothposition


TFT +SD(days)

TFT minusSD(days)

TRR(count)(days)

TRRmax-max(days)

TRR min-min(days)

TRRmin-max(days)

TRRmax-min(days)

Source

MBR2371 I

dent sin II 15340 2189409 1180587 4960 707918 381728 minus300904 1390550


IV 4220 602301 324777







































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References






































































































Introduction


Results

Discussion

Conclusions

Abbreviations

flink7

References


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