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Using Cross-Sectional Properties to Investigate the Advent of Walking in a Sample of Central Californian Amerindian Children

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Title:
Using Cross-Sectional Properties to Investigate the Advent of Walking in a Sample of Central Californian Amerindian Children
Creator:
Le, Kim N
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
Physical Description:
1 online resource (9 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.A.)
Degree Grantor:
University of Florida
Degree Disciplines:
Anthropology
Committee Chair:
DAEGLING,DAVID
Committee Co-Chair:
TILLMAN,MARK D
Committee Members:
COLLINGS,PETER F
WALL,CHRISTINE E
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Age groups ( jstor )
Bones ( jstor )
Femur ( jstor )
Fibula ( jstor )
Humerus ( jstor )
Long bones ( jstor )
Lower extremity ( jstor )
Ruffs ( jstor )
Tibia ( jstor )
Walking ( jstor )
Anthropology -- Dissertations, Academic -- UF
biomechanics -- bipedalism -- skeletal -- strain -- stress
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Anthropology thesis, M.A.

Notes

Abstract:
This study investigated how the change in mechanical loading associated with the onset of walking affected the cross-sectional dimensions (CSDs), i.e., area moments and section moduli, of long bones in a sample of Central Californian Amerindian children. Four statistical methods (reduced major axis regressions, rigidity ratios, ANCOVA, and bootstrap estimates) analyzed how CSDs change with diaphyseal length and across age groups, 0 to 60 months (mos). CSDs and length grew the fastest during the first year, with CSDs of upper limb bones increasing faster relative to length than lower limb bones in order to be sufficiently rigid for lifting and carrying the body in crawling. The 9mos CSD growth peak in femur and tibia most likely reflects the redistribution of body weight to the lower limbs, making the estimated age range for the onset of walking to be 9-18mos. After the first year, CSD and length growth rates declined. Especially in the lower limb, length growth was of primary importance, always outpacing CSD growth to allow limbs to reach the appropriate proportions for bipedal stability. At 48-60mos, the lower limb bones experienced an increase in CSD growth, most likely to counteract the increasing bending strain as the bone lengthened. Despite its non-involvement in weight-bearing, the fibula also showed this pattern, perhaps signaling the increased use of muscles of plantarflexion and eversion as gait matured. Growth rate did not differ between AP and ML CSDs, supporting past studies showing that bone is not necessarily reinforced in the axis of maximum strain. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.A.)--University of Florida, 2014.
Local:
Adviser: DAEGLING,DAVID.
Local:
Co-adviser: TILLMAN,MARK D.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31
Statement of Responsibility:
by Kim N Le.

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Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
5/31/2015
Resource Identifier:
908645382 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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InterpretingSkeletalGrowthinthePastFroma FunctionalandPhysiologicalPerspective ChristopherB.Ruff,*EvanGarofalo,andMeganA.Holmes CenterforFunctionalAnatomyandEvolution,JohnsHopkinsUniversitySchoolofMedicine,Baltimore,MD21205 KEYWORDS stature;bodymass;longbonestructure;mandibularstructure;corticalbone ABSTRACT Thestudyofjuvenileskeletalremains canyieldimportantinsightsintothehealth,behavior, andbiologicalrelationshipsofpastpopulations.However,moststudiesofpastskeletalgrowthhavebeenlimitedtorelativelysimplemetrics.Consideringadditional skeletalparametersandtakingabroaderphysiological perspectivecanprovideamorecompleteassessmentof growthpatternsandenvironmentalandgeneticeffects onthosepatterns.Wereviewheresomealternative approachestoontogeneticstudiesofarchaeologicaland paleontologicalskeletalmaterial,includinganalysesof bodysize(statureandbodymass)andcorticalbone structureoflongbonediaphysesandthemandibular corpus.Togethersuchanalysescanshednewlighton bothsystemicandlocalizedinuencesonbonegrowth, andthemetabolicandmechanicalfactorsunderlying variationingrowth.AmJPhysAnthropol150:2937, 2013. V V C 2012WileyPeriodicals,Inc. Interpretingskeletalgrowthanddevelopmentisintegraltomanyhumanevolutionaryandbioarchaeological studies.Juvenilespecimensconstitutekeypartsofthe humanpaleontologicalrecord;justapartiallistincludes theTaung Australopithecusafricanus cranium(Dart, 1925),theModjokertoearly Homoerectus infantcalvaria (Anton,1997),andpartialskeletonsoftheMH1 Au.sediba juvenile(Bergeretal.,2010),theearly H.erectus Nariokotomeboy''(Brownetal.,1985),andtheearly H. sapiens childfromLagarVelho(Duarteetal.,1999). Eachofthesespecimenshelpedtodeneataxonomic entityoraddressanimportantphylogeneticissue.Yet, becausejuvenileandadultmorphologiesdiffer,such analysesrequireeithercomparisonstomodernindividualsofanappropriateagestage,orextrapolationtoadulthoodviaanassumedtrajectoryofcontinuinggrowth. Thus,controversiesininterpretationofsuchspecimens areoftenaresultofdisagreementsoverthenatureof growthcurvesorhowgrowthshouldbeassessed(e.g., Coqueugniotetal.,2004;HublinandCoqueugniot,2006; Leigh,2006;alsoseeSeselj,2013). Inbioarchaeologicalresearch,skeletalgrowthstudies areoftenusedtoreconstructthehealthconditionsof pastpopulations(JohnstonandZimmer,1989;Humphrey,2000;Saunders,2008).Thisisbecauseskeletal growthisknowntobesensitivetoenvironmentalperturbations(Tanner,1992;Bogin,1999).Studiesofpostcranialskeletalgrowthinarchaeologicalsampleshavebeen largelylimitedtoassessmentsoflongbonelengths (Johnston,1962;Y'Edynak,1976;MerchantandUbelaker,1977;HummertandVanGerven,1983;Jantzand Owsley,1984;Lovejoyetal.,1990;Wall,1991;Hoppa, 1992;Saundersetal.,1993;RibotandRoberts,1996; Humphrey,2000;Lewis,2002;Pinhasietal.,2006;Mays etal.,2008;Schillacietal.,2011),althoughthereare someexceptions(e.g.,Hummert,1983;Ruffetal.,1994; Pinhasietal.,2005;Maysetal.,2009).Focusingonbone lengthhassometheoreticaljustication,inthatvariationinlongbonelengthsisassociatedwithvariationin stature(e.g.,McCammon,1970;Ruff,2007),whichhas beenusedasaprimaryindexofgrowthalterationinlivingpopulations(EvelethandTanner,1990;WHO,1995). However,growthinbodymass(weight)isalsoanimportantcriterionofhealthinmodernpopulations(seereferencesabove),andconsiderationofotheraspectsofskeletalmorphologycanprovideadditionalinsightsintothe functionalandphysiologicalbasesofgrowth,asdiscussedfurtherbelow. Inthisarticle,wereviewsomeofthesealternative approachestohumanskeletalgrowthanalysis,andgive examplesoftheirapplicationtopasthumanpopulation samplesorpaleontologicalspecimens. BODYSIZE Asnotedabove,longbonelengthsarecorrelatedwith stature(orrecumbentlength).However,limblengthto statureproportionschangedramaticallyduringgrowth (McCammon,1970;EvelethandTanner,1990),sothat changesinlongbonelengtharenotexactlyequivalent tochangesinstature.Relativelimblengthtostature proportionsalsovarybetweenpopulations(Evelethand Tanner,1990;Cowgilletal.,2012).Thus,differences betweenpopulationsinlongbonelengthsatagivenage areonlyapproximationsofdifferencesinstature.Furthermore,veryfewstudiesoflongbonegrowthperse areavailableformodernlivingpopulations,severelylimitingpossibilitiesfordirectcomparisons. Toestimatestaturefromjuvenileskeletalremains,juvenile-specicequationsareneeded,becauseofchanging linearproportionsduringgrowth(Ruff,2007).Afew *Correspondenceto:Dr.ChristopherRuff,CenterforFunctional AnatomyandEvolution,JohnsHopkinsUniversitySchoolof Medicine,1830E.MonumentSt.,Baltimore,MD21205,USA. E-mail:cbruff@jhmi.edu Received28March2012;accepted21June2012 DOI10.1002/ajpa.22120 PublishedonlineinWileyOnlineLibrary (wileyonlinelibrary.com). V V C 2012WILEYPERIODICALS,INC. AMERICANJOURNALOFPHYSICALANTHROPOLOGY150:2937(2013)

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suchtechniquesweredevelopedpriorto2000,buteach hadsomesignicantlimitations(Ruff,2007).NewpredictionformulaebasedontheDenverGrowthStudy sample(McCammon,1970)wererecentlyderived(Ruff, 2007).Theseweresubsequentlytestedandshowntoprovidereasonablestatureestimatesinaforensicsampleof Ohioblackandwhitejuveniles(SciulliandBlatt,2008). Applicationoftheformulaetootherjuvenilesamples withverydivergentlinearbodyproportions,suchas tropicalpopulations,maybemoreproblematic,however (Ruff,2007);moreworkisneededinthisregard.Possiblenutritionaleffectsonrelativelimbproportionsshould alsobeconsidered(Boginetal.,2002). Smith(2007)alsodevelopedjuvenilestatureestimationformulaebasedontheDenverGrowthStudysample.However,therewereseveralproblemswiththeanalysis.First,noneofthelongbonelengthswerecorrected formagnication,whichhasbeenshowntobesignicantandage-dependentforthisradiographicsample (Ruff,2007).Thisleadstosystematicunderestimationof staturewhenappliedtoosteologicalmaterial,andmay inpartexplainwhyCardoso(2009)didinfactobtain underestimateswhenapplyingtheseformulaetoamodernsamplewithknowncadavericstatures.Second,singleequationswerederivedforacombinedagegroupof 310years.Sincechangesinlimbproportionsoccurduringthisperiod,thisdecreasestheaccuracyofpredictions (Ruff,2007).Finally,allmeasurementsofallchildren withinthisagerangewerecombinedforderivingequations,greatlyinatingdegreesoffreedombecauseof non-independenceofdatapoints.Whiletheauthorlater attemptedtoaddressthisissuethroughsomesampling techniques,theresultsusingthefull''(combined)data setwererecommended.However,estimatederrorranges usingtheseequationsarenotstatisticallyvalid. Bodymassestimationfromjuvenileskeletalremains hasreceivedlessattention,butagain,formulaewere recentlyderivedfromDenverGrowthStudydata(Ruff, 2007).Themethodsdescribedthereinarebasedonarticulardimensionsofthelowerlimbbones(specically, mediolateralbreadthofthedistalfemoralmetaphysisin youngerjuveniles,andsuperoinferiorbreadthofthefemoralheadinolderjuveniles).Predictionerrorsare greaterthaninstatureestimation,aswouldbeexpected, andincreasewithage,againnotunexpectedly.These formulaewerealsotestedinthemodernOhioforensic sample(SciulliandBlatt,2008)andfoundtoprovide reasonableestimates,exceptforobeseindividuals(which wouldlikelynotbefrequentlyencounteredinarchaeologicalorpaleontologicalsamples).Anothersetofbody massestimationequationswerederivedfromthesame (Denver)dataset,usingmidshaftfemoralpolarsecond momentofarea(ameasureofbending/torsional strength)(Robbinsetal.,2010).Predictionerrorswere comparabletothoseusingarticularbreadths,both withintheDenversampleandwhenappliedtothesame Ohioforensicsample.However,astheauthorsnote,diaphysealcross-sectionalgeometryisalsostronglyaffected bymechanicalloadingsotherthanjustbodymass,that is,activitylevelandmuscularity(e.g.,Ruffetal.,2006). Thus,thegeneralappropriatenessoftheseequationsfor archaeologicalorpaleontologicalsamplesisquestionable. Therearemanypotentialbioarchaeologicalapplicationsofbodysizeestimationmethods.Theeffectsof factorsasvariedassocioeconomicstatus,rural-urban differences,nutritionallevel,overalldiseasestress,and specicpathogenshaveallbeenaddressedthroughanalysesofjuvenileskeletalgrowth(JantzandOwsley,1984; Lovejoyetal.,1990;Hoppa,1992;Saundersetal.,1993; RibotandRoberts,1996;Lewis,2002;Pinhasietal., 2006;Maysetal.,2008;Schillacietal.,2011).Convertingskeletaldimensionstoanthropometricdimensions (statureandbodymass)allowssuchcomparisonstobe carriedoutwithamuchbroaderrangeofmodernpopulationswithknownvariationsindemographicandepidemiologicalcharacteristics.Historicalanalysesthatcombinearchaeologicalwithmodernlivingdata,forexample toexamineseculartrends,arealsodependentonsuch conversions;todate,studiesofthiskindhavebeenlimitedtoadults(e.g.,Jaegeretal.,1998;BoginandKeep, 1999;Steckel,2004),butcouldbeappliedtojuvenilesas well.Aswithanyestimationprocedure,statureand bodymasspredictioncarrieswithitincreasedmeasurementerrorcomparedtodirectuseofskeletaldimensions.However,thisisbalancedbytheincreasedpower andscopeofcomparativeanalysesthataremadepossiblebythisapproach. Anexampleofanontogeneticcomparisonofstature andbodymassintwoarchaeologicalsamplesandthe DenverGrowthStudysampleisshowninFigure1.The twoarchaeologicalsamplesarederivedfromprotohistoricArikarafromtheSully,SouthDakotasite(Jantz andOwsley,1984),andtheearlyNeolithicC atalho yu k siteincentralTurkey(Garofaloetal.,2011;Hillson etal.,inpress).Forthesetwosamples,bodymassand staturewerecalculatedfromfemoralarticularbreadths andlength,respectively(Ruff,2007).Agesweredeterminedfromtoothlengthregressionequationsanddental development(Smith,1991;Liversidge,1994,2008;LiversidgeandMolleson,2004).Thearchaeologicaldataare forindividuals,whiletheDenverdatarepresentannual meansfor20individualsfollowedlongitudinally(see Ruff,2003b).Polynomialcurvesarettoeachdataset toillustrategeneralgrowth-relatedtrends.(Hereand elsewhereinthisarticle,theAkaikeInformationCriterionwasusedtoselectthemostappropriateorderof polynomialforeachdataset.) TheC atalho yu kandDenversamplesoverlapextensivelyinearlychildhood(priortosixyearsofage)in stature,butthendiverge,withtheDenversamplegrowingtaller(Fig.1a).Incontrast,theArikarasampleis shorterthantheothertwosamplesinearlychildhood, butthenconvergeswiththeC atalho yu ksampleduring adolescence.Bodymassshowssimilarpatterns(Fig.1b), althoughtheretendstobemoreoverlapbetweensamples,andless(andlater)divergencebetweentheC atalho yu kandDenversamples. Thereisevidencefromstudiesoflivingpopulations thatgrowthinbodysizeearlyindevelopment(infancy andearlychildhood)isrelativelysimilarinpopulations growingunderoptimalenvironmentalconditions,and thereforethatdeviationsingrowthduringthisperiod reectenvironmentaldifferences,thatis,malnutrition orotherhealthdisturbances(Habichtetal.,1974; GraitcerandGentry,1981;WHO,1999).Fromthisperspective,theresultsshowninFigure1indicatethatthe ArikarasampleexperiencedrelativelypoorerhealthconditionsduringearlygrowththaneitherC atalho yu kor Denver,andthattheC atalho yu ksamplewasrelatively healthy(consideringtheupper-middleclassDenver sampletobehealthy).TheSullyArikarasampleisfrom aperiod(ExtendedandPostcontactCoalescent)that appearstohavebeencharacterizedbyadequatedietary resources,althoughperiodicfoodshortageswerealsoa 30 C.B.RUFFETAL. AmericanJournalofPhysicalAnthropology

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possibility,especiallyearlierduringthisperiod(Jantz andOwsley,1984).Itisalsoofinterestthatlongbones fromlaterDisorganizedCoalescentsamplesinthis region(notincludedinthepresentstudy),withwelldocumentedincreasedenvironmentalstress,arelonger inearlychildhoodthanintheprecedingExtendedand PostcontactCoalescentperiods(JantzandOwsley,1984), againsuggestingthatpopulationsfromtheseearlier periodsmaynothavebeenashealthyasotherwisepresumed.Thepresentdataareconsistentwiththisinterpretation.TheresultsforC atalho yu karealsoconsistent withrecentevidenceindicatinggenerallygoodhealth amonginhabitantsofthesite(Hillsonetal.,inpress). Genetic(orpopulation-specic)differencesingrowth inbodysizemaybemoreclearlymanifestedduringadolescence(Johnstonetal.,1976;Frisanchoetal.,1980). Thiswouldsuggestthatthedifferencesinstatureand bodymassbetweentheC atalho yu kandDenversamples thatdevelopduringlaterchildhoodandadolescence (Fig.1)arearesultofgeneticdifferencesbetweenthe twopopulations,ratherthanincreasedenvironmental stressatC atalho yu k.TheArikaraappeartoovertake andperhapsevensurpasstheC atalho yu ksampleduring thisdevelopmentalperiod,whichcouldbeinterpretedas aresultofamelioratingenvironmentalconditionsafter earlychildhood,orageneticpredispositionforgreater growthinbodysizeamongtheArikarathatbecomesevidentduringadolescence.GreatPlains(adult)populationsasawholeareamongthetallestandheaviestof NativeNorthAmericaninhabitants(Auerbach,2007; AuerbachandRuff,2010),supportingthesecondinterpretation,althoughbothfactorsmayplayapart.C atalho yu kadultsareofaveragebodysize(statureandbody mass)forearlyNeolithicpopulationsinEuropeandthe NearEast(Hillsonetal.,inpress).Similarontogenetic studiesofsuchpopulationsmayhelptoidentifytowhat extentenvironmentversusgenetics(populationhistory) contributedtoobservedpatternsofvariationamong adults. Juvenilebodysizeestimationalsohasapplicabilityto paleontologicalremains.BoththeDenverstatureand bodymassestimationequations(thelatterarticular only)wereusedtoestimatebodysizeinthejuvenile H. erectus KNM-WT15000(theNariokotomeBoy'';Ruff, 2007).Estimatesweresimilartothoseobtainedearlier usingdifferentmethods(RuffandWalker,1993), althoughestimatedbodymasswasslightlyhigher.The lattermaybearesultofapelvicbreadth(usedinthe earlieranalysis)thatwassomewhathigherthanoriginallyreconstructedforthisspecimen(Ruff,2010a).StatureestimatesforKNM-WT15000werecomplicatedby hisapparentlyverytropical''(i.e.,elongatedlimb)proportions.Theextenttowhichrecognizedecogeographic differencesinadultlinearbodyproportions(Roberts, 1978;Ruff,1994)characterizejuvenilesfromthesame populationsisanimportantissuethathasguredinto interpretationsofbothKNM-WT15000aswellasthe LagarVelhojuvenile(RuffandWalker,1993;Ruffetal., 2002).Arecentstudyofabroadrangeofrecenthuman samplesindicatesthatpopulationaldifferencesinintralimblinearproportions(aswellasbodybreadth)arein factpresentamongevenyoungjuveniles(Cowgilletal., 2012). LONGBONECORTICES Skeletalgrowthinvolvesmorethansimplyincreases inoverallsize,ofcourse.Modelingandremodelingof externalandinternalsurfacesoccurcontinuously throughoutlifethroughboneappositionandresorption andareaffectedbyvariousphysiologicalfactors(Enlow, 1963;Martinetal.,1998).Thedynamicnatureofthis processcanbeexploitedtoyieldfurtherinsightsintothe environmentunderwhichthebonegrewandtheindividuallived. Oneaspectofbonemorphologythathasreceivedsome attentioninthisregardinthepaleontologicalandbioarchaeologicalliteratureistherelativeproportionof endostealtoperiostealdimensionsoflongbonediaphyses,thatis,relativecorticalthicknessorarea.Theprimaryfocusofthesestudieshasbeenonadultmorphology(e.g.,Kennedy,1985;Ruffetal.,1993;Ruff,1999), withaparticularemphasisonadultagingpatterns Fig.1. Agechangesin( a )stature,and( b )bodymassin threepopulationsamples:protohistoricArikara(circlesand dashedline),earlyNeolithicC atalho yu k(lleddiamondsand solidline),andthemodernDenverGrowthStudysample(asterisksanddottedline).Staturecalculatedfromfemorallength, andbodymassfromfemoraldistalmetaphysealandhead breadthinthetwoarchaeologicalsamples.ArikaraandC atalho yu kdatathrough20yearsareforindividuals;Denverdata aremeansof20individuals.Adultdata(plottedat23yearsof age)aremaleandfemalesamplemeans.Lineequations: Stature,Denver:68.28 1 7.9382 x 2 0.02 x 2 2 0.0053 x 3 ,Arikara: 53.60 1 9.9692 x 2 0.2311 x 2 ,C atalho yu k:61.75 1 9.038 x 2 0.2057 x 2 ;Bodymass,Denver:12.35 2 1.2996 x 1 0.4827 x 2 2 0.0142 x 3 ,Arikara:8.81 2 0.5618 x 1 0.392 x 2 2 0.0115 x 3 ,and C atalho yu k:8.95 1 0.1476 x 1 0.2815 x 2 2 0.0083 x 3 31 NEWAPPROACHESTOPASTSKELETALGROWTH AmericanJournalofPhysicalAnthropology

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(Deweyetal.,1969;VanGervenetal.,1969;Carlson etal.,1976;Ericksen,1976;RuffandHayes,1983;Mays etal.,1998;Mays,2001,2006),butafewontogenetic studieshavealsobeencarriedout(Hummert,1983;Van Gervenetal.,1985;Ruffetal.,1994;Maysetal.,2009). Studiesoflivingchildrenprovideevidencethatmalnutritioncanleadtoanincreaseinendosteal(medullary cavity)dimensionsrelativetoperiosteal(external) dimensions,leadingtoadecreaseinrelativecortical area(corticalarea/periostealarea,%CA;Garnetal., 1969;Himesetal.,1975).Basedonabnormalage changesin%CAofthetibialmidshaft,Hummert(1983) concludedthatjuvenilesfromtheNubianMedieval ChristiancemeteryofKulubnartiwerenutritionally stressed,aninterpretationconsistentwithpaleodemographicandpaleopathologicaldatafromthesite(see summaryinVanGervenetal.,1995).However,alater studyofthesamesample(VanGervenetal.,1985)concludedthatexternalbonedimensions,includingmeasuresofbonestrength,werelessaffected.Thisimplieda differentialresponseofendostealandperiostealbone envelopestonutritionalanddiseasestress,andperhaps evensomemechanicallycompensatorychanges(greater increases)ontheperiostealsurface(alsoseeGarnetal., 1969). Mays(2009)obtainedsimilarresultsinacomparison ofhigherandlowersocioeconomicstatusjuvenilesfrom a19thcenturyEnglishchurchcemetery.HigherSES individualshadthickerfemoralmidshaftcorticesthan lowerSESindividuals,butperiostealbreadthandfemorallengthwereequivalent.Thecorticalthicknessdifferenceswerepresentintheyoungestjuveniles(undersix yearsofage),possiblyindicatingmorehealthdisparities (orgreaterskeletalsensitivity)inthisagerange.These results,andthosefortheKulubnartisample,suggest thatcomparisonofdifferentskeletalparameters,beyond simplybonesize,mayidentifymoresubtleeffectsof environmentalvariationongrowth. Considerationofnormalagechangesinendostealand periostealdiaphysealdimensionsisalsoimportantin interpretingjuvenilefossilhomininremains.Relative corticalthicknesshasplayedaprominentroleinboth functionalandtaxonomicinterpretationsofearlyhomininlongbones(Ruffetal.,1993,andreferencestherein). Therelativecorticalthicknessorareaofthelong bonesofthejuvenileKNM-WT15000wasshowntobe reducedcomparedwiththatofadultearly H.erectus (Ruffetal.,1994;Ruff,2008).However,duetogreater periostealthanendostealexpansionduringgrowth(in healthyindividuals),%CAnormallyincreaseswithage, throughearlyadulthood(Garn,1970;Ruffetal.,1994). Figure2isaplotoffemoralmidshaft%CAagainstage inthePecosPueblosample(seeRuffetal.,1994;Ruff, 2010bfordetails),withKNM-WT15000andeightadult EarlyPleistocene H.erectus included(Gilbert,2008[our calculationsfrompublishedsections];Ruff,2008;TrinkausandRuff,2012).[The%CAvalueforKNM-WT 15000of65.2%usedinFigure2isthatgiveninTrinkausandRuff,2012.Thisdiffersslightlyfromthatused inanearlierstudy(69.6%,Ruffetal.,1994)duetosome subsequentminorcorrectionsinsectioncontours.]KNMWT15000doesindeedshowalower%CAvaluethan anyoftheadult H.erectus specimens,butonethatis completelynormal''forhisage.Asnotedpreviously (Ruffetal.,1994;TrinkausandRuff,2012),adultearly Homo onaveragehaveelevated%CArelativetomodern adults,andthisisalsoclearlyshowninFigure2, althoughthereisextensiveoverlapbetweenthetwo groups.ThefactthatKNM-WT15000isnotalsohigher relativetomodernjuvenilesofhisagerangeisinteresting,andcouldindicateaslightlyalteredgrowthtrajectory,althoughthisinterpretationisinpartdependenton estimatesofhisexactdevelopmentalage,whichhave varied(Smith,1993;CleggandAiello,1999;Deanand Smith,2009).Inaddition,asnotedabove,someearly Homo adultsdooverlapinrelativecorticalareawiththe modernPecosadults,soitispossiblethatKNM-WT 15000isalsoalowoutlier.However,evenifthiswere thecase,thedatashowninFigure2donotarguefora veryshortremaininggrowthperiodinKNM-WT15000 (contraTardieu,1998;Gravesetal.,2010). Recognitionthatdifferentstructuralfeaturesoflong bonesgrowatdifferentratesandareapparentlysubject todifferentgeneticconstraintsisalsoimportantininterpretingskeletalproportionsinjuveniles(alsoseeDuren etal.,2013).Forexample,thereisabundantevidence thatlongboneepiphysesfollowadifferentgrowthtrajectorythandiaphysealcortices,andarelessdevelopmentallyplasticandmorecloselytiedtogeneralgrowthin bonesize,forexample,length(Ruffetal.,1994;Trinkausetal.,1994;Liebermanetal.,2001;Auerbachand Ruff,2006;Ruff,2007).Thishasimplicationsforinterpretingtheskeletalproportionsofspecimenssuchas KNM-WT15000,whichhaslargeepiphysesrelativeto transversediaphysealdimensionsforanadult,butthat arenormalforajuvenileofhisage(Ruffetal.,1994).It isalsoconsistentwiththestudiesreviewedabovethat indicatedmoresensitivityofcorticalbonetoenvironmentalvariablesduringgrowth. Mechanicalconsiderationsarealsoimportantininterpretingvariationinlongbonecorticalgrowth.Longbone corticescontinuetogrowforalongerperiodoftimethan longbonelengthsandarticulardimensions(Ruffetal., 1994;Humphrey,1998),andtrackgrowthinbodymass Fig.2. Agechangesinfemoralmidshaftpercentcortical area{[(corticalarea/periostealarea)/periostealarea] 3 100}in thelateprehistoricPecosPueblosample(circles),KNM-WT 15000(largelledstar),andeightadultearly Homo specimens (smalllledstars,plottedatanarbitraryageof25years). EquationoflineplottedthroughPecosPueblodata: y 5 47.85 1 1.7945 x 2 0.0251 x 2 32 C.B.RUFFETAL. AmericanJournalofPhysicalAnthropology

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morecloselythanstature,particularlyinthelowerlimb (Ruff,2003a;alsoseebelow).Thisreectstheirprimary mechanicalroleinsupportingbodymassandresisting muscularforces(SumnerandAndriacchi,1996;Ruff, 2003a,b).Differencesingrowthpatternsoflongbone corticesthereforereectacomplexinterplaybetweena numbersofenvironmentalvariables,thatis,mechanical, nutritional,etc.Considerationofdifferentcorticalbone envelopesmayhelptodistinguishbetweenthesevarious inuences.Forexample,asnotedearlier,periosteal appositionmaybemoredependentonmechanicalstimuli,whileendostealapposition(injuveniles)maybe moresensitivetonutritionalinuences(e.g.,VanGerven etal.,1985;Ruff,1999;Maysetal.,2009).Suchconsiderationsalsoarguestronglyforincludingbothperiosteal andendostealdimensionswhenassessingbonegrowth andgrowthdisturbances. SKELETALREGIONALDIFFERENCES Comparisonsofgrowthbetweendifferentregionsof thebodycanalsoshedlightonbasicgrowthmechanisms,functionalrequirements,andenvironmental inuences.Forexample,manycranialdimensionsreach adultsizeearlierthanmostpostcranialdimensions (Humphrey,1998),parallelingmoregeneralsomatic trends(Bogin,1999).However,mandibularandmaxillarydimensionsareintermediateinthisregard,likely reectingtheirdistinctiverolesinmasticationaswellas otheroralfunctions(Humphrey,1998). Tofurtherevaluatefunctionalinuencesonmandibulargrowth,wecarriedoutanontogeneticstudyofstructuralpropertiesofthemandibularcorpusintwoarchaeologicalpopulationswithcontrastingdiets:lateprehistoric TigarafromPointHopeAlaska,withamechanicallyvery demandingdiet,andthesameprotohistoricArikarasampleusedinthegrowthstudiesdescribedabove,characterizedbyalessdemandingdiet(HolmesandRuff,2011). Agesweredeterminedusingthedentalagingtechniques describedabove,aswellasepiphysealunion(Scheuer andBlack,2000)intheolderjuveniles.Cross-sectional propertiesreectingmandibularcorpusrigidityand strength(secondmomentsofareaandsectionmoduli) weredeterminedfromexternalbreadthsandbiplanarradiographs(O'NeillandRuff,2004)atthePm 4 -M 1 and M 1M 2 junctions(ortheirequivalentlocationsinjuveniles priortoeruptionofthoseteeth).Agetrendswereexaminedusingpolynomialcurvets. Resultsforonestructuralshape''indextheratioof buccolingual(transverse)tosuperoinferior(sagittal) strengthareshownforthetwomandibularlocationsin Figure3a,b.Asshownthere(alsoseeHolmesandRuff, 2011),TigaraandArikaraadultmandiblesdiffersignicantlyincross-sectionalshape,withtheTigararelativelymoretransverselybuttressed.Thisshapedifferenceisnotnearlyaswelldevelopedinyoungjuveniles, however.Whenthetotalpreadult( \ 18years)agerange isdividedintothreesix-yearintervals,theshapedifferencerstreachesstatisticalsignicance(withBonferronicorrectionformultiplecomparisons)inthe612 yearagegroupfortheM1-M2location,andinthe1218 yearagegroupforthePm 4 -M 1 location(althoughthe differenceisnearlysignicantintheprecedingage group).Thus,characteristicpopulationaldifferencesin adultmorphologyonlyappearaftereruptionoftheadult dentitionandadoptionofadultmasticatorybehavior. Thisisnotadirectresultofdifferencesintoothsize,as theTigaradidnothavelargeteethrelativetotheArikara(HolmesandRuff,2011).Itisalsonotduetoan overallincreaseinmandibularsizeamongTigara,as mandibularlengthandsuperoinferiormandibularcorpus heightwerenotlarger.Rather,itappearstobeaspecic responsetoincreasedmasticatoryloadingsamongthe Tigara(Hylander,1988;DaeglingandGrine,1991). OurresultscontrastwiththoseofFukaseandSuwa (2008),whocomparedmandibulargrowthinJomonand modernJapanesesamples,andfoundthatstructuraldistinctionsamongadultswerepresentevenasearlyas infancy.However,theiryoungeragedsampleswerequite small,andtruecross-sectionalpropertieswereonly measuredatthemandibularsymphysis,notthecorpus. Itisalsopossiblethattheirtwopopulationsamples weremoregeneticallydivergentthanourswere,allowingfortheevolutionofdifferentmandibularform, expressedpriortoanydirectfunctionalinuences.Additionalontogeneticstudiesofrelatedpopulationsundergoingknownchangesindietarybehavior,aswellas experimentalstudies,willhelptoclarifytheextentof developmentalplasticityofthemandible(orofdifferent Fig.3. Agechangesintransversetosagittalbending strength(sectionmoduli)ofthemandibularcorpusatthe(a) Pm 4 -M 1 and(b)M 1 -M 2 interdentalgapsintwoarchaeological samples:Tigara(lledcirclesandsolidline)andArikara(open trianglesanddashedline).Lineequations:Pm 4 -M 1 ,Tigara:1.39 2 0.0602 x 1 0.0014 x 2 ,andArikara:1.34 2 0.0737 x 1 0.0016 x 2 ; M 1 -M 2 ,Tigara:1.38 2 0.0192 x andArikara:1.34 2 0.029 x 33 NEWAPPROACHESTOPASTSKELETALGROWTH AmericanJournalofPhysicalAnthropology

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structuralfeaturesofthemandible).Theanswertothis questionhasimportantimplicationsforinterpretingmorphologicalvariationamongbothrecentandearlierhuman populations(Larsen,1997;MallegniandTrinkaus,1997; Paschettaetal.,2010;Antonetal.,2011).Thisisalsoa goodillustrationofthepowerofskeletalontogenetic approachestoaddresssuchfundamentalissues. Wealsocarriedoutfurthercomparisonsofmandibular withpostcranialgrowthinthesameArikarasample (Holmesetal.,2010).Figure4showsontogeneticchanges inmandibularcorpus,femoralmidshaft,andhumeral middistaldiaphysealsagittalbendingstrengthinthese sameindividuals.Mandibularstrengthwasdetermined asdescribedabove;longbonecross-sectionalstrengths weredeterminedusingbiplanarradiographscombined withmoldingofexternalcontours(O'NeillandRuff, 2004).Estimatedbodymass,calculatedfromfemoral headanddistalmetaphysealbreadths(Ruff,2007),isalso plottedforcomparison.Dataareloggedtonormalizedistributionsandpreserveproportionalityovertheentire agerange.Asinpreviousanalyses,agetrendsweret withpolynomialcurves.Theageatwhich90%ofadult size(inrawparameters)isattainedisalsoindicatedfor eachparameter,followingHumphrey(1998).Adult''here isthepredictedvaluefor20-year-olds,usingthepolynomialcurves.Severaladditionaldatapointsforneonates (under1yearofage)wereincludedherebutnotinthe mandibularcomparisonswiththeTigara(Fig.3;also HolmesandRuff,2011),becauseinthatstudynoTigara individualsinthisagerangewereavailableforcomparison.Bodymasscouldnotbeestimatedinneonatessince thereisnosignicantassociationbetweendistalfemoral metaphysealbreadthandbodymassinthisagerange (Ruff,2007). Humeralstrengthreaches90%ofadultvaluesbyabout 15yearsofage,whilefemoralstrengthdoesnotreach thispointuntilsomewhatlater,about19years.Body mass(basedonfemoralheadsize)beginstoplateau between17and18years.However,infactbodymass likelyincreasedforsometimeaftercessationoffemoral headgrowth(Ruffetal.,1991).Asnotedpreviouslyfor anothersample(Ruffetal.,1994;Ruff,2003a),the growthcurveforfemoraldiaphysealstrengthparallels thatforbodymass,reectingtheprimaryroleofthe lowerlimbinsupportingbodyweight(alsoseevander Meulenetal.,1996).Humeralstrengthalsoparallels growthinoverallbodysize,butislesshighlycorrelated (Ruff,2003a);italsoappearstoplateauearlierthanfemoralstrength(Fig.4).Someofthesetrendsareinuenced bysex(Ruff,2003a,b).Becausewecouldnotdetermine sexinmostofthespecimensinourstudy,wedidnot considerthisfactorinourgrowthanalyses,butitlikely contributedtosomescatterintheindividualdata. Mandibularstrengthfollowsanearlier,morerapid growthtrajectorythanlongbonestrengths,reaching 90%ofadultvaluesbyabout10yearsofage.Theearlier growthinstrengthofthemandibleisconsistentwith ourpreviousresults(HolmesandRuff,2011),andwith Humphrey's(1998)observations.Mandibularstrength reachesnear-adultvaluesseveralyearsaftereruptionof M 1 ,aboutthetimewhenmostoftheadultdentitionis erupting(Smith,1993),andwhenadultpatternsofmasticatorybehaviorwereprobablyoperational.Thiswas likelycriticalforingestionandprocessingofsufcient foodduringtheadolescentgrowthspurt,whenbody massmorethandoubles(Fig.1b). Thus,differentskeletalregionsaresubjecttodifferent functionalinuences,andthisisreectedinaltered growthcurves.Assessmentofmechanicallyrelevant structuralpropertieshighlightsthesedifferences,and theadaptivenatureofchangingskeletalproportions duringgrowth.Variationbetweenpopulationsorpaleospeciesinsuchagepatterningmayalsoprovideimportantfunctionalinferences,forexample,regardingdietaryoractivityleveldifferencesduringgrowth. CONCLUSIONS Studiesofgrowthanddevelopmentusingskeletalsampleshavethepotentialtoyieldmuchmoreinformation thanistypicallyacquired.Forexample,whilegrowthin bodymassandstaturehavenotbeenextensivelyinvestigatedinarchaeologicalcontexts,theskeletaldimensions neededtoestimatetheseparametersarealreadyavailableforsomesamples(e.g.,Hoppa,1992;Pinhasietal., 2005).Assessmentofsuchparametersallowsmoredirect comparisontolivingsamples,whichinturnfacilitates investigationofpossibleenvironmentalandgenetic effectsonthearchaeologicalorfossilsampleunderconsideration.Evaluationofadditionalskeletalstructural featuressuchasdistributionofcorticalboneinlongbone diaphysesinjuvenilespecimenscanprovidefurther insightsintothedynamicsofbonegrowthandthedietaryandmechanicalinuencesonthatprocess.Comparisonbetweendifferentskeletalregionscanrevealother localizedfunctionalinuences,suchasmasticatoryand locomotoreffects.Takingadvantageofthefullrangeof possibleskeletalgrowthanalysesisessentialbothfor reconstructingpasthealthandbehavior,andforinterpretingvariationinjuvenilemorphologyinthearchaeologicalandhumanfossilrecord. Fig.4. Agechangesinlog-transformedsagittalbending strengthofthemidshaftfemur(lleddiamondsandsolidline), mid-distalhumerus(crossesanddottedline),mandibularcorpus atthePm 4 -M 1 junction(circlesanddash-dottedline),andbody massdeterminedfromfemoraldistalmetaphysealandhead breadth(trianglesanddashedline)inaprotohistoricArikara sample.Datapointsat23yearsofagerepresentadultmaleand femalemeans.Humerustwithasecondorderpolynomial,all otherswithathirdorderpolynomial.Arrowsindicatetheageat which90%ofadultsize(inrawparameters)reached,with adult''determinedasthepolynomial-predictedvalueat20 yearsofage.Lineequations:femur:3.28 1 0.5216 x 2 0.0263 x 2 1 0.0005 x 3 ;mandible:2.92 1 0.5303 3 0.0289 x 2 1 0.0005 x 3 ;humerus:2.93 1 0.3445 x 2 0.0094 x 2 ;bodymass:1.83 1 0.1821 x 2 0.0019 x 2 2 0.00007 x 3 34 C.B.RUFFETAL. AmericanJournalofPhysicalAnthropology

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SteckelRH.2004.Newlightonthedarkages''.TheremarkablytallstatureofnorthernEuropeanmenduringtheMedievalperiod.SocSciHist28:211229. SumnerDR,AndriacchiTP.1996.Adaptationtodifferentialloading:comparisonofgrowth-relatedchangesincross-sectional propertiesofthehumanfemurandhumerus.Bone19:121126. TannerJM.1992.Growthasameasureofthenutritionaland hygienicstatusofapopulation.HormRes38:106115. TardieuC.1998.Shortadolescenceinearlyhominids:infantile andadolescentgrowthofthehumanfemur.AmJPhys Anthropol107:163178. TrinkausE,ChurchillSE,RuffCB.1994.Postcranialrobusticityin Homo ,II:Humeralbilateralasymmetryandboneplasticity.AmJPhysAnthropol93:134. TrinkausE,RuffCB.2012.FemoralandtibialdiaphysealcrosssectionalgeometryinPleistocene Homo .PaleoAnthropology 2012:1362. vanderMeulenMCH,AshfordMW,KiratliBJ,BachrachLK, CarterDR.1996.Determinantsoffemoralgeometryand structureduringadolescentgrowth.JOrthopRes14:2229. VanGervenDP,ArmelagosGL,BartleyMR.1969.Roentgenographicanddirectmeasurementoffemoralcorticalinvolution inaprehistoricMississippianpopulation.AmJPhysAnthropol31:2338. VanGervenDP,HummertJR,BurrDB.1985.Corticalbone maintenanceandgeometryofthetibiainprehistoricchildren fromNubia'sBatnelHajar.AmJPhysAnthropol66:275 280. VanGervenDP,SheridanSG,AdamsWY.1995.Thehealthand nutritionofamedievalNubianpopulation.AmAnthropol 97:468480. WallCE.1991.Evidenceofweaningstressandcatch-upgrowth inthelongbonesofaCentralCaliforniaAmerindiansample. AnnHumBiol18:922. WHO.1995.Physicalstatus:theuseandinterpretationof anthropometry.Geneva:WorldHealthOrganization. WHO.1999.Infantandyoungchildnutrition:theWHOmulticentregrowthreferencestudy.Geneva:WHO. Y'EdynakG.1976.LongbonegrowthinWesternEskimoand Aleutskeletons.AmJPhysAnthropol45:569574. 37 NEWAPPROACHESTOPASTSKELETALGROWTH AmericanJournalofPhysicalAnthropology



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USING CROSS SECTIONAL PROPERTIES TO INVESTIGATE THE ADVENT OF WALKING IN A SAMPLE OF CENTRAL CALIFORNIAN AMERINDIAN CHILDREN By KIM N LE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS UNIVERSITY OF FLORIDA 2014

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2014 Kim N Le

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To my parents and grandparents

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4 ACKNOWLEDGMENTS I thank Dr. Chris Wall, my undergraduate mentor, who allowed me to use her unique dataset and who first introduced me to the study of allometry and to the question explored in this thesis. Without her, this project would not have been born. I thank Dr. David Daegling, my graduate mentor, who helped me to build the structure of this thesis, especially the statistical analyses and interpretations. Without him, this project would not have developed in the way that it did. I thank my friends and colleague s especially my lab mates who have helped me with their valuable academic (and life) advice. I will know them for a long time. I thank my family for their never ending love and support even though most of time, they do not understand what I am doing.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 ABSTRACT ................................ ................................ ................................ ................................ ... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ ............. 12 2 LITERATURE REVIEW ................................ ................................ ................................ .. 16 Bone Response Models ................................ ................................ ................................ ...... 16 Cross Sectional Geometry ................................ ................................ ................................ 17 Long Bones: Allometry, Ontogeny ................................ ................................ .................... 19 Ontogeny of Walking ................................ ................................ ................................ ......... 21 The Archaeology of Central California ................................ ................................ ............. 22 3 HYPOTHESES AND PREDICTIONS ................................ ................................ ............. 24 Lower Limb ................................ ................................ ................................ ....................... 24 Upper Limb ................................ ................................ ................................ ........................ 25 4 MATERIALS AND METHODS ................................ ................................ ....................... 26 Data ................................ ................................ ................................ ................................ .... 26 Cross Sectional Properties ................................ ................................ ................................ 27 Statistical Analyses ................................ ................................ ................................ ............ 28 Reduced Major Axis (RMA) Regr ession: Residuals ................................ ............. 29 Rigidity Ratios ................................ ................................ ................................ ....... 30 Analysis of Covariance (ANCOVA) ................................ ................................ .... 30 Bootstrap Estimates ................................ ................................ ............................... 31 5 RESULTS ................................ ................................ ................................ .......................... 33 Reduced Major Axis (RMA) Regression: Residuals ................................ ......................... 33 Rigidity Ratios ................................ ................................ ................................ ................... 34 ANCOVA ................................ ................................ ................................ .......................... 36 Bootstrap Estimates ................................ ................................ ................................ ........... 38 Summary of Results ................................ ................................ ................................ ........... 39

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6 Lower Limb: Hypotheses and Results ................................ ................................ ... 40 Upper Limb: Hypotheses and Results ................................ ................................ .... 41 Patterns of Growth ................................ ................................ ................................ 42 6 DISCUSSION AND CONCLUSION ................................ ................................ ............... 92 From Crawling to Walking ................................ ................................ ................................ 93 Significance of Studying the Ontogeny of Bipedality ................................ ..................... 101 Future Directions ................................ ................................ ................................ ............. 104 LIST OF REFERENCES ................................ ................................ ................................ ............. 106 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 113

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7 LIST O F TABLES Table page 4 1 Inventory of individuals grouped by age ................................ ................................ ........... 26 4 2 Equations for calculating cross sectional dimensions ................................ ....................... 28 5 1 Means and standard deviations of midshaft diameters, area moments, and section moduli by bone (element) and age ................................ ................................ ................................ 45 5 2 Humerus ANCOVA summary ................................ ................................ ........................... 77 5 3 Radius ANCOVA summary ................................ ................................ .............................. 79 5 4 Ulna ANCOVA summary ................................ ................................ ................................ .. 81 5 5 Femur ANCOVA summary ................................ ................................ ............................... 83 5 6 Tibia ANCOVA summary ................................ ................................ ................................ 85 5 7 Fibula ANCOVA summary ................................ ................................ ............................... 87

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8 LIST OF FIGURES Figure page 5 1 Humerus area moments plotted against length before and after log transformation ......... 49 5 2 Humerus section moduli plotted against length before and after log transformation ........ 50 5 3 Radius area moments plotted against length befor e and after log transformation ............. 51 5 4 Radius section moduli plotted against length before and after log transformation ........... 52 5 5 Ulna area moments plotted against length before and after log transformation ................ 53 5 6 Ulna section moduli plotted against length before and after log transformation ............... 54 5 7 Femur area moments plotted against length before and after log transformation ............. 55 5 8 Femur section moduli plotted against length before and after log transformation ............ 56 5 9 Tibia area moments plotted against length before and after log transformation ............... 57 5 10 Tibia section moduli plotted against length before and after log transformation .............. 58 5 11 Fibula area moments plotted against length before and after log transformation .............. 59 5 12 Fibula section moduli plotted against length before and after log transformation ............ 60 5 13 Humerus RMA residuals for area moment data by age group ................................ ........... 61 5 14 Humerus RMA residuals for section modulus data by age group ................................ ..... 62 5 15 Radius RMA residuals for area moment data by age group ................................ .............. 63 5 16 Radius RMA residuals for section modulus data by age group ................................ ......... 64 5 17 Ulna RMA residuals for area moment data by age group ................................ ................. 65 5 18 Ulna RMA residuals for section modulus data by age group ................................ ............ 66

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9 5 19 Femur RMA residuals for area moment data by age group ................................ ............... 67 5 20 Femur RMA residuals for section modulus data by age group ................................ ......... 68 5 21 Tibia RMA residuals for area moment data by age group ................................ ................. 69 5 22 Tibia RMA residuals for section modulus data by age group ................................ ........... 70 5 23 Fibula RMA residuals for area moment data by age group ................................ ............... 71 5 24 Fibula RMA residuals for section modulus data by age group ................................ .......... 72 5 25 Humerus rigidity ratios by age group ................................ ................................ ................ 73 5 26 Radius rigidity ratios by age group ................................ ................................ .................... 73 5 27 Ulna rigidity ratios by age group ................................ ................................ ....................... 74 5 28 Femur rigidity ratios by age group ................................ ................................ ..................... 74 5 29 Tibia rigidity ratios by age group ................................ ................................ ....................... 75 5 30 Fibula rigidity ratios by age group ................................ ................................ ..................... 75 5 31 Mean diaphyseal length plotted against age for each bone ................................ ................ 76 5 32 Humerus bootstrap estimated slopes and intercepts ................................ .......................... 89 5 33 Ulna bootstrap estimated slopes and intercepts ................................ ................................ 90 5 34 Femur bootstrap estimated slopes and intercepts ................................ ............................... 91

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10 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Deg ree of Master of Arts USING CROSS SECTIONAL PROPERTIES TO INVESTIGATE THE ADVENT OF WALKING IN A SAMPLE OF CENTRAL CALIFORNIAN AMERINDIAN CHILDREN By Kim N Le May 2014 Chair: David Daegling Major: Anthropology This study investigated how the change in mechanical loading associated with the onset of walking affected the cross sectional dimensions (CSDs), i.e., area moments and section moduli, of long bones in a sample of Central Californian Amerindian children. Four statistical methods reduced major axis regressions, rigidity ratios, ANCOVA, and bootstrap estimates analyzed how CSDs change with diaphyseal length and across age groups, 0 to 60 months (mos). CSDs and length grew the fastest during the first year, with CSDs of upper limb bones increasing faster relative to length than lower limb bones in order to be sufficiently rigid for lifting and carrying the body in crawling. The 9mos CSD growth peak in femur and tibia most likely reflects the shift of body weight to the lower limbs, making the esti mated age range for the onset of walking to be 9 18mos. After the first year, CSD and length growth rates declined. Especially in the lower limb, length growth was of primary importance, always outpacing CSD growth to allow limbs to reach the appropriate proportions for bipedal stability. At 48 60mos, the lower limb bones experienced an increase in CSD growth, most likely to counteract the increasing bending strain as the bone lengthened. Despite its non involvement in weight bearing, the fibula also sh owed this pattern, perhaps signaling the increased use of muscles of

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11 plantarflexion and eversion as gait matured. Growth rate did not differ between AP and ML CSDs, supporting past studies showing that bone is not necessarily reinforced in the axis of ma ximum strain.

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12 CHAPTER 1 INTRODUCTION The problem under investigation in the present study is how the onset of walking (bipedality) affects the skeleton during growth. Becoming bipedal involves a change in posture that leads to a change in how body weight is carried by the skeleton. The influence of this change on the limb bones (which carry the body and are directly involved in locomotion) is the primary focus of the study. The main role of the skeleton is to give structure to an organism, pro viding support for its mass throughout its life. One can understand bone in a mechanical sense by analyzing its geometry in the same way that an engineer analyzes the geometry of building material to understand how it withstands forces. In supporting mas s, bone is exposed to mechanical loads, which are external forces acting on the bone. In response to loading, the cross sectional geometry of a bone can change. From the cross section, one can calculate measurements that reflect the rigidity and strength of bone. These measurements are appropriately called cross sectional properties, or dimensions. In numerous studies of human and animal bones, cross sectional properties have been used to infer mechanical loading in order to reconstruct activity pattern s of the subjects. Activity patterns may inform about lifestyle and health of a population. The activity pattern investigated in the present study is walking in young children. This study seeks to use cross sectional properties of long bones (i.e., the bones constituting the limbs) to infer a change in locomotory pattern in infants and young children of a pre European contact Central California n Amerindian sample. The present study uses one of the largest datasets of measurements on skeletally immature individuals from archaeological sites. Additionally, while most studies on locomotion measure only the weight bearing long bones, this study will include all long bones in analyses.

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13 Transitioning from a crawling (i.e., quadrupedal) form of locomotion t o a bipedal form of locomotion (i.e., walking) results in the redistribution of body weight to the lower limbs. I use limbs in crawling is now distributed over t wo limbs in standing and walking. I will test how this redistribution of weigh t at the onset of walking influence s the cross sectional properties of the diaphyses or shafts, of upper and lower limb long bones. I will test a few specific outcomes of thi s influence from walking. One hypothesis is that cross sectional properties relative to the length of the bone will be larger in the lower limb bones when walking begins. This is implying that these bones become stronger and more rigid as the load on the m increases. It has been shown that bone will respond by adding more bone when physical exertion on the body is increased ( e.g., Jee et al., 1991; Smith and Gilligan 1991 ; Woo et al., 1981 ) (Ideas on bone response are explored in more detail in chapter two.) It is therefore reasonable that having to carry a larger proportion of body weight would result in higher cross sectional properties in the lower limb bones during walking compared to during crawling. Hand in hand with this hypothesis is the hypo thesis that cross sectional properties will increase faster during the transition from crawling to walking in order for the bones to be relatively stronger and more rigid during bipedality. This is an interesting hypothesis to test because it focuses on h ow the normal growth trajectory of long bones (i.e., increasing in size as body size increases with age) is affected by the mechanical loading associated with bipedality. Another factor to consider is that there may be directional bias in growth, such th at cross sectional properties increase faster along one axis of the bone relative to the other. Long bones bend; that is the primary type of loading (Rubin and Lanyon, 1984). When a long bone bends, along the axis of bending, one side of the diaphysis is in compression while the other is in

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14 tension. Because bone is weaker in tension, growth is stimulated on this side (Frost, 1982), resulting in seemingly faster growth along the axis of bending. Because the primary axis of motion in walking is anterior t o posterior (i.e., anteroposterior, AP), and following the reasoning articulated by Ruff and Runestad (1992) that cross sectional properties increase faster along the axis experiencing a higher bending load, I hypothesize that the lower limb long bones wil l become stronger and more rigid at a faster rate along the AP axis. The above hypotheses for the lower limb only apply to the weight bearing long bones (femur and tibia), as I do not expect the fibula to increase in rigidity and strength relatively fast er and be especially rigid and strong at the onset of walking. I also apply these hypotheses to the upper limb bones, with the major difference being timing. In the upper limb bones, faster growth and relatively higher cross sectional properties are expe cted to be seen during an earlier age interval when the individual is predominantly using the upper limbs for raising the body and crawling (Abitbol, 1993). I have summarized all the hypotheses in chapter three.Extrapolating from geometry to activity invo lves certain assumptions about how bone responds to loading. I will therefore discuss the most relevant bone response models as well as present a brief review on the usefulness and limitations of cross sectional geometry, the growth patterns (i.e., allome try) of long bones, and the development (i.e., ontogeny) of walking. I will additionally provide a broad overview of the archaeology of Central California in order to have an anthropological context in which to place the findings from this biomechanics st udy. Because this study investigates the changes taking place in bone cross sectional properties during the ontogeny of bipedality in human children, it may contribute to our understanding of the evolution of bipedalism in hominins. Unlike many studies on bipedalism, the present study is not concerned with the emergence and development of any specific

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15 anatomical trait related to bipedal locomotion, although patterns of long bone growth (i.e., growth trajectories) discerned from this study may correspond to the timing of such developments. Growth trajectories provide a foundation of morphological data on which to investigate further the mechanical (e.g., ground reaction forces) and non mechanical factors (e.g., weaning and other life history parameters) a ffecting long bone growth during this age interval in children. Since immature gait in children is an analogy for facultative (i.e., non obligate) bipedalism in non human apes and presumably in early hominins, examining these factors in future studies wil l inform about the influences on locomotion and perhaps bridge our knowledge of two distinct areas of study in biological anthropology: bipedalism and life history.

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16 CHAPTER 2 LITERATURE REVIEW Bone Response Models Bone morphology and biomechanical pr operties are clearly influenced by mechanical forces. The literature on this topic is vast (reviewed in Ehrlich and Lanyon, 2002; Martin and Burr, 1989; Robling et al., 2006; and Ruff et al., 2006). Here I will focus on the most relevant models that expl ain how mechanical force influences bone response (i.e., modeling and of bone are laid down to form primary osteons (Currey, 1984). Remodeling is bone turnover with initial resorption, followed by formation (Frost, 1987). Unlike modeling, remodeling replaces primary bone with secondary bone, made up of secondary osteons (Currey, 1984). Since remodeling involves bone replacement, it can be assumed that this proc ess does not change geometry. The general assumption underlying bone response models is that bone is sensitive to stress and strain and will model in a way to reduce strain and maintain bone integrity. Frost (1982) states that a bone models to achieve a size and geometry that minimizes strain in the Frost, 1987 ). In appropriately to t he mechanical usage (MU) of the bone, i.e., the collective stress and strain on the bone. The mechanostat negotiates bone modeling and remodeling about some threshold 1982) model. As long as strain stays within this optimum strain range, remodeling is not necessary. It has also been suggested that bone may not be trying to minimize strain, but to keep a certain level of strain that is healthy for the structure (Rubin et al., 1990).

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17 The magnitude and frequency of mechanical stress are also important factors to consider. It has been proposed and shown that the frequency of stress plays a larger role in inducing bone response than the magnitude of stress (Rubin and Lan yon, 1984; Rubin et al., 2001, 2002; Turner, 1998). For example, Turner (1998) states that it only takes a short duration of dynamic and non typical, or non routine, loading to elicit an adaptive reaction from bone. The importance of magnitude versus fre quency is clearly not mutually exclusive. Works such as Carter et al. (1996), Frost (1987), Lanyon (1982), and Lanyon and Rubin (1985), while emphasizing the importance of stress magnitude, still demonstrate the significant influence of stress frequency. Regardless of the differences among models, it is apparent that bone response can be stimulated by increased physical activity (Drapeau and Streeter 2006; Frost 1982, 1987, 1997; Jee et al. 1991; Ruff 1984; Ruff and Hayes 1983a, 1983b; Ruff and Rune stad 1992; Ruff et al. 1993, 1994, 2006; Shaw and Ryan 2012; Smith and Gilligan 1991) or surfaces where modeling can occur: periosteal and endosteal. Studies cited in Ruff (1994) show that during young adolescence, bone is added more on the periosteal surface (i.e., periosteal apposition) than on the endosteal surface (i.e., endosteal constriction). I ncreased physical activity has been shown to stimulate increased periosteal activity in adult rats (Jee et al., 1991), human s ( Smith and Gilligan 1991 ), and pigs (Woo et al., 1981 ). Overall, this body of literature can give support to a few important assumptions: that bone cell s are sensitive to local strain; that bone will react to reduce strain ; and that bone is mechanically efficient. Cross S ectional Geometry The redistribution of body weight to the lower limbs in bipedal locomotion results in higher stress and strain on these bones. Diaphyseal cross sectional dimensions are appropriate

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18 for e valuating the effects of mechanical loading, while articular dimensions are more influenced by body mass and are therefore relatively less plastic (Ruff et al., 1993). For this study, I am investigating two cross sectional dimensions calculated from midsh aft diameters: area moment ( I ) and section modulus ( Z ). Area moment gives a measure of rigidity, while section modulus (derived from area moment) more directly reflects strength. Because under the bone response models, bone is sensitive to local strain, it is assumed that bone cross sectional geometry reflects the loading environment. Bone rigidity and strength are thus assumed to reflect differing levels and types of mechanical stresses. In comparative studies among different populations, researchers t end to attribute differences in CSDs to differences in lifestyle, or activity patterns. Higher measures of CSDs tend to reflect greater bone robusticity and more strenuous activities (Cowgill, 2010; Ruff, 2000a; Ruff and Hayes, 1983a, 1983b; Ruff et al., 1993). Such studies therefore try to directly infer type and magnitude of loading from cross sectional geometry. In the case of locomotion, t ransitioning to bipedal walking may involve significant changes in the type of stress exerted on the bones, in te rms of either axial stresses (i.e., compressive and tensile) or bending and torsional stresses. Ruff and Runestad (1992) regressed bending or torsional rigidity against axial rigidity (proportional to cortical area or cross sectional area) to determine wh ich type of stress was predominant at certain age intervals. For example, they assumed that mediolateral (ML) rigidity increases faster than anteroposterior (AP) rigidity because the ML bending load is greater than the AP bending load. In general, the ty pe of mechanical loading on long bone diaphyses is bending (Rubin and Lanyon, 1984). However, several studies show the importance of being wary about extrapolating loads from strain (Ruff, 2006). Studies on quadrupeds (Demes et al., 1998, 2001; Lieberma n et al., 2004; Schaffler et al., 1985) show long bone diaphyses to not be reinforced in the direction of

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19 maximum strain. Lieberman et a l. (2004) among other studies, showed that axial loads are always superimposed onto bending l oads and that other facto rs like limb positioning and ground reaction forces affect rigidity and strength. While I and Z can be measured precisely through any absolute values are subject t o error (Lieberman et al., 2004; Stock and Shaw, 2007). Instead, relative values are more useful for revealing meaningful patterns. In other words, one cannot determine the stress that acted on the bone solely from its cross sectional geometry. Therefor e, strain. Long Bones: Allometry, Ontogeny During development, long bones follow certain predictable patterns of growth allometry. However, variations in such allometric relationships among individuals and populations can be attributed to more extrinsic factors (e.g., nutrition, physical activity, pathology). For my study, I will be focusing on how mechanical loading from bipedal walking affects growth allometry patterns. The assumption is that variations in these patterns are reflective of skeletal adaptation to walking. S uch a drastic change i n body posture and locomotion would be expected to create shifts in body weight distribution and the orientation and magnitude of stress. Smith and Shaw (2012) as well as Shaw and Ryan (2012) among other studies, show how long bone architecture reflects humans, changes in the biomechanical properties of the lower limbs are typically indicative of the development of propulsive limbs (Robinson et al. 1972; Wells et a l. 2002). Sumner and Andriacchi (1996), Ruff (2003a, 2003b), and Gosman et al. (2013) specifically suggest the onset of walking as the source of mechanical stress affecting the morphology and cross sectional

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20 properties of the long bones in their samples. study. Studies examining the changes in cross sectional dimensions over time, as well as how these growth trajectories are correlated among the various dimensions are numerous (Cowgill 2010; Goldman et a l. 2009; Gosman et al. 2013; Harrington 2010; Ruff 2000b, 2003a, 2003b; Ruff and Hayes 1984a, 1984b; Ruff et al., 1994; Smith and Buschang 2004; Sumner and Andriacchi 1996; van der Meulen et al. 1996; Wall 1991; Wells et al. 2002). Most of these studies look at remains from an archaeological context. However, Goldman et al. (2009) did a histological study investigating how cortical bone pattern shifts during early childhood to a more adult like geometric pattern. Aside from cros s sectional dimensions, numerous allometry studies specifically focus on limb proportions. In a study on two species of capuchin monkeys, Jungers and Fleagle (1980) found that, while both are arboreal quadrupeds, relatively longer limbs in one species ref lected its more cursorial locomotory behavior. This study examined limb length relative to body mass between two animals using the same mode of locomotion. For comparing different modes of locomotion however, it is useful to examine l imb proportions in t erms of the length of the upper limb (or forelimb) relative to the lower limb (or hindlimb). This is typically expressed as an intermembral (IM) index (upper limb length to lower limb length ratio). Modes of locomotion correspond to particular intermembr al index ranges. Leapers like indrids have the lowest IM indices, while suspensory primates like gibbons have the highest indices. Jungers (1984) found that IM index tends to increase with body size. This is because relatively shorter hindlimbs (and tru nk) means less drag and a higher center of mass for suspensory primates, making it easier to move a large body around. However, large cercopithecines (e.g., baboons) are exceptions because they are mainly terrestrial quadrupeds (Jungers, 1984). In contra st to quadrupeds,

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21 humans have a lower intermembral index (i.e., shorter upper limbs relative to lower limbs). Jungers et al. (1988) demonstrated that this is achieved by having lower limbs lengthen at a faster rate than upper limbs (i.e., lower limbs are positively allometric to upper limbs). Intermembral index is thus changing during ontogeny. Ontogeny of Walking The literature on the ontogeny of walking in humans includes studies on the biomechanics of both crawling and walking. Before assessing the ef fects of walking on long bones, it is necessary to understand the biomechanics of crawling to allow for the comparison of loads between the two locomotory types. Crawling can be considered as human quadrupedalism, even though it is different from non huma n quadrupedalism, such as in the way the head is held during quadrupedal movement (Abitbol, 1993). A number of studies have explored the mechanical loading of limbs during crawling. Patrick et al. (2009) showed that crawling stance phase in the forelimbs is longer (about 16.7% longer) than in the hindlimbs, meaning that the forelimbs are supporting body weight for an overall longer duration of time. Even so, the forelimbs and hindlimbs were found to not differ significantly in vertical peak ground force (Yozu et al. 2013). Ground reaction force (GRF) is the force the ground exerts on an objec t or being in contact with it, and it appears that Yozu et al. (2013) has been the only study to measure GRFs in crawling children. Transitioning from crawling to walking requires certain morphological modifications. The correct limb proportions need to be achieved (Jungers et al., 1988), so that the body can be more stable while upright due to a lower center of mass (Adolph and Avolio, 2000). When infants begin to walk, their gait is immature. Developing a mature gait requires some important adjustments in posture and motor control. One type of adjustment is the development of motor

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22 control so that muscles can be used in a mechanically efficient way. Cowgill e t al. (2010) found that peak GRFs differed in magnitude and direction between young children and adults, and that the youngest children displayed the most variable GRF traces. This suggests that children refine their motor control over time. Additionally the immature gait of young children is partly due to the lack of a bicondylar, or intercondylar, angle of the femur. This angle is necessary for the valgus condition in humans, bringing the feet closer to the midline of the body. The transition into th e valgus angle is associated with changes in ML and AP femoral dimensions (Tardieu et al. 2006), as well as with changes in torsional stress on the femur and tibia (Tardieu 2010). This implies that cross sectional dimensions would become less variable w ith time, approaching more adult (i.e., mature gait) patterns. One such pattern may be increased asymmetry of AP and ML dimensions due to a marked difference in loading in one direction relative to the other but the loads experienced most likely become m ore normal or typical as gait matures. Thus, this asymmetry is associated with decreased variance in cross sectional dimensions and more typical loads. The implication then is that decreased variance would be observed in older children relative to younge r children. The Archaeology of Central California My sample comprises individuals representing different populations scattered across 58 archaeological sites in Central California (Wall, 1991). The sites date from Early to Late Periods of history, or 425 0 to 300 years before present (Moratto, 1984, as cited in Wall, 1991). This span of time also corresponds to the so called Pacific Period beginning 4000 years ago and ending in 1769 (which marks the establishment of San Diego as the first permanent Europe an settlement in California) (Chartkoff and Chartkoff, 1984). Regardless of period name, the remains are pre European contact. Since the cultures of this region were so diverse, I can only

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23 provide a rough sketch of these peoples. They can be characteriz ed as practicing a hunting gathering subsistence strategy (Wall, 1991). The pre contact peoples of California survived on a remarkably wide variety of easily obtainable food, from plants to insects to animals (Kroeber, 1925). Food items were seasonal, wh ich made for small, roaming groups. However, the Pacific Period also saw the emergence of larger sedentary settlements with cash economy (Chartkoff and Chartkoff, 1984). The lack of controls in the sample (e.g., cultural practices and behaviors), due to unknown population affiliation, should not be an issue as children begin walking at fairly predictable ages regardless of where they are from.

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24 CHAPTER 3 HYPOTHESES AND PREDICTIONS Lower L imb I hypothesize the transition from crawling to walking to occ ur in the 9 to 24 months (mos) age interval. Independent studies have shown walking to begin earliest at 6mos with the latest unassisted walking at about 18mos (deGroot et al., 1997; Frankenburg and Dodds, 1967; Stanitski et al., 2000). Therefore, 9mos is a more reasonable upper limit since 6mos is the earliest age with children still requiring support. Weaning takes place around 1.5 to 2 years of age (Silver, 1978; Wallace, 1978) when children are expected to be off the breast and walking, thus marking the upper limit of the hypothesized age range (24mos). Greater bending and torsional stress on the lower limbs during walking would be reflected in greater bending/torsional rigidity and strength relative to diaphyseal length in the 24mos group compared to the 9m o s group. More specifically, I expect a higher increase in rigidity and strength relative to diaphyseal length i.e., higher relative growth rates, in the 9 24mos interval compared to dur ing the 0 9mos and 24 60mos intervals. I additionally hypothesize that AP CSDs will grow faster than ML CSDs, specifically in the femur and tibia, since the primary plane of motion in walking is AP. It follows that bending is AP due to the actions of muscles (e.g., hip extensors) that help us use our lower l imbs for propulsion (Ruff and Runestad, 1992). Due to its lack of involvement in bearing body mass, I hypothesize that the fibula will have a lower relative rigidity and strength than the femur and tibia. I do not expect the fibula to display higher rela tive rigidity and strength growth rates in the 9 24mos interval compared to outside this interval.

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25 Upper L imb Because of greater forelimb (or upper limb) use for the initial lifting of the upper body and eventual crawling (Abitbol 1993), I hypothesiz e the rigidity and strength of the humerus, ulna, and radius to be highest relative to diaphyseal length and relatively higher than that of the lower limb during the 0 9m o s interval. Therefore, these bones should experience higher increase in rigidity and strength relative to diaphyseal length i.e., higher relative growth rates, in the 0 9mos interval compared to periods outside this interval I expect a lesser increase in growth of rigidity and strength relative to length after 9mos when it is hypothesi zed that the child will begin standing and walking.

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26 CHAPTER 4 MATERIALS AND METHODS Data The data consists of 224 individuals from an unidentified Central California n Amerindian population (which may actually represent several unidentified populations) with an age range of neonate to 5 years, based on standard dental aging methods (Table 4 1). Table 4 1. Inventory of individuals grouped by age. Source: Wall (1991) The collection was housed at the Lowie Museum of Anthropology (now the Phoebe A. Hearst Museum of Anthropology), Berkeley, California, but has since been repatriated under NAGPRA (Native American Graves Protection and Repatriation Act). No markers of abno rmalities (e.g., pathology) were observed in the skeletal remains (Wall, personal communication, 2014). However, the fact that these individuals died in infancy and early childhood indicates the possibility that the growth patterns they exhibit may be unr epresentative of those of the larger population (Wall, 1991), e.g., due to poor health. Without knowing the exact environments in which these individuals lived, the dataset is nonetheless informative about childhood growth in Age group (months) Number of individuals 0 50 6 21 9 21 12 24 18 24 24 16 36 20 48 33 60 15 Total 224

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27 this general population. The skeletal elements measured are the limb long bones: humerus, radius, ulna, femur, tibia, and fibula. Any one of these elements may be missing for an individual as part of the taphonomic process. The measurements were taken on the diaphysis (shaft) of th e bone, as the epiphyses (ends) are yet unfused for individuals from this age range and thus are often missing. The measurements include diaphyseal length, anteroposterior (AP) midshaft diameter, and mediolateral (ML) midshaft diameter. Cross Sectional P roperties Cross sectional properties or dimensions (CSDs), estimate bone rigidity and strength. Bone rigidity refers to resistance to deformation by mechanical stresses that can be induced through bending, torsion, compression, and tension. Rigidity is measured by area (or second) and polar moments of inertia. Area moment is designated as I Bone strength is associated with rigidity and is the measure of how much load a specimen can take before failure, i.e., the stress at fracture (Currey 1984). Ruff (2000a) defines strength as the moment of inertia (i.e., the measure of rigidity) divided by the distance, y, from the neutral axis or centroid to the outermost edge of the section. This measurement is called the section modulus (designated as Z ) To calculate area moments and section moduli from AP and ML midshaft diameters, I used equations for a solid ellipse from Roark et al. (2002) (listed in Table 4 2). Modeling the cross sectional area as a solid ellipse means viewing the bone as a so lid shaft of cortical bone with no medullary cavity. modeling can occur: periosteal and endosteal. Studies cited in Ruff (1994) show that during young adolescence, bone is added more on the periosteal surface (i.e., periosteal apposition) than on the endosteal surface (i.e., endosteal constriction). Even in adults, increased physical activity

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28 stimulated increased periosteal activity (Jee et al., 1991; Smith and Gilligan 1991). Because of t his pattern in youn g individuals I will assume that evidence of bone modeling in my sample, as measured by changes in total cross sectional area, is solely the result of periosteal apposition. This is a necessary assumption given that the sample contains no measurements f or the medullary cavity but reasonable in light of the fact that periosteal apposition is most important in augmenting bone strength and rigidity. Table 4 2. Equations for calculating cross sectional dimensions. Source: Roark et al. (2002) Note: The constant 'a' is the anteroposterior radius (AP midshaft diameter divided by 2). The constant 'b' is the mediolateral radius (ML midshaft diameter divided by 2). Statistical Analyses The goal of the statistical methods I have used is to analyze how area moments and sect ion moduli (CSDs) relate to diaphyseal length for each age group. Diaphyseal length is strongly associated with moment of inertia (Ruff, 1984) and thus assumed to be proportional to it. This allows me to determine relative rigidity and strength at each a ge and to understand how CSDs grow with increasing length and age, i.e., examine the growth trajectories of CSDs and length. Below, I describe the statistical methods in detail. All analyses were performed on log Cross sectional dimension (CSD) Equation anteroposterior area moment mediolateral area moment anteroposterior section modulus mediolateral section modulus

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29 transformed data. Log transformed data r eveals information about proportional changes (relative growth), not just absolute changes (i.e., that individuals become bigger over time). In log space, data points are arranged in a way that makes it easier to compare between groups. All analyses were performed using the statistical software, R (2013a). Reduced Major Axis (RMA) Regression: Residuals RMA regression is a model II regression, appropriate for testing functional relationships in this case, between CSD and diaphyseal length. CSD was plotte d against length for all age groups, and a RMA regression line was fitted to the data using the R (Dillon, 2003). To determine how CSD is scaled in relation to length, the empirical slope (i.e., the slope of the regression) was compared to the slope of proportionality. The slope of proportionality is the slope of isometry given the dimensions of the variables: CSD/length. The relationship between two dimensions is isometric when proportionality (shape) is preserved as size increases. For rigidity, measured by the area moment ( I ), this slope is length 4 /length = 4.0. For strength, measured by the section modulus ( Z ), this slope is length 3 /length = 3.0. The output script includes the following for both RMA and ordinary lea st squares (OLS) regressions: empirical slope (i.e, actual calculated slope of the regression), upper and lower value. If the slope of proportionality, m p falls within the confidence interval, it indicates that m p is not significantly different from the empirical slope. This means CSD is isometric to length. However, if the slope of proportionality (m p =4.0 for I m p =3.0 for Z ) is above the upper confide nce limit of slopes, CSD is negatively allometric to length. Conversely, if the slope of proportionality is below the lower confidence limit of slopes, CSD is positively allometric to length.

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30 To better examine how well diaphyseal length predicts CSD, I c alculated residuals from the RMA regression. Residuals represent the variance that is not explained by the regression and can either be positive or negative. The residual of each data point was calculated as the area of the right triangle ( ) distance from data point to regression distance from data point to regression line, or the height of the triangle). The regression line predicts a certain I or Z for a give n length. Therefore, residuals above the line belong to I or Z values that are higher than the values predicted by the regression. These values are thus underestimated. Conversely, data points below the line are lower than predicted values and are thus overestimated by the regression. Rigidity Ratios A rigidity ratio is a dimensionless ratio calculated as the ratio of maximum area moment to length 4 for each individual for all age groups. The maximum area moment is defined as either I AP or I ML dependin g on which moment is larger for that individual. Because the raw ratio value is minuscule, all raw ratio values were multiplied by a common constant (of 1.0x10 6 ), resulting in values that are easier to examine and compare. Relative magnitudes of ratios a re still preserved. Rigidity ratios give a measure of rigidity relative to diaphyseal length, and thus are often referred to as relative rigidity in the text. Analysis of Covariance (ANCOVA) An ANCOVA tests how two variables covary, i.e., change with one another, and how the covariation is influenced by some categorical factor. The strength of the covariation is reflected in the magnitude of R 2 or the coefficient of determination. In this case, the two variables are CSD and diaphyseal length, and the categorical factor is age group. The main purpose of using ANCOVA is to test the homogeneity of slopes by comparing regressions specific to age groups.

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31 This means that if one were to plot CSD against length, the slope of the regression line drawn through each age group should be homogenous across all age groups. For instance, if the variables were positively correlated in one age group, they sho uld be positively correlated in all the other age groups. Homogeneous slopes and similar R 2 values indicate that the relationship between CSD and length is consistent across age groups. The lack of homogeneity among slopes implies that age influences how CSD and length covary. One can also look for differences in intercepts. If slopes are parallel (and thus, homogeneous), differences in intercepts reflect differences in magnitude in the case of this study, the magnitude of the CSD. For the goals of the present study, differences in intercepts are not of interest because I expect older children to have higher intercepts than younger children simply due to growth in overall body size. To test homogeneity by comparing regression slopes, ordinary least squ ares (OLS) regressions (model I) were fitted to data in each age group using the R package (2013b). The output includes empirical slope with p value, intercept with p value, and R 2 Non significant regressions indicate the lack of covariation between CSD and length. Significant regression slopes show covariation. The higher the R 2 value is, the greater the covariation. Significant slopes may or may not indicate strong covariation, but a high R 2 is always associated with a significant slope. Scaling (i.e., isometry, positive allometry, negative allometry) can be determined by comparing empirical slope to the slope of proportionality, as was done for the RMA residuals previously described. Bootstrap Estimates The bootstrap resampling method (see Daegling, 1996) gives information on regression slope variance and intercept variance through the simulation of repeated sampling of the population. For each age group, 100 bootstrap samples were created by resampling from the

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32 original data wi th replacement to the size of the original sample. OLS (model I) regressions were fitted to data in each bootstrap sample using the R estimated slopes and intercepts per age group. Estimated intercepts were plott ed against estimated slopes, categorized by age group. Each age group therefore had a range of 100 possible slopes and a corresponding range of 100 possible intercepts. Ranges of slopes specific to age groups that do not overlap indicate different scalin g. Bones are judged as similarly scaled (i.e., isometric, positively allometric, or negatively isometric) at ages where both the range of slopes and the range of intercepts overlapped.

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33 CHAPTER 5 RESULTS The relationship between area moments or section moduli (from here on in called cross sectional dimensions, CSDs) and diaphyseal length during the 0 60mos interval is nonlinear. Log transformation of the data made the relationship more linear (Figures 5 1 to 5 12). However, it is apparent that the data is overall still curvilinear since sections of the dataset while individually linear differ in slope from one another. In log space, data points are arranged in a way that makes it easier to examine propor tional change and compare between groups. From Figures 5 1 to 5 12, it can be seen that as length and time increase, CSDs increase more slowly. Such trends will be shown statistically through methods previously outlined. All analyses were performed on l og transformed data. I will present results for both area moments ( I ) and section moduli ( Z ), which are expected to be congruous since Z is derived from I I gives information about rigidity, while Z gives more direct information about strength since it accounts for an additional dimension of the cross sectional area. In long bones, increased size (diameter) usually results in increased rigidity and strength (Table 5 1) If I and Z are not congruous, then it is a sign of a disconnect between size and geometry, perhaps due to an additional factor. RMA Regression Residuals Reduced major axis (RMA) regressions assessed the relationship between the CSDs and length in log space. The slope of proportionality is the slope of isometry. The relationship betw een two dimensions is isometric when proportionality (shape) is preserved as size increases. Since the slope of proportionality (m p =4.0 for I, m p =3.0 for Z) was above the upper confidence limit of slopes, there was negative allometry for all CSDs for all lower limb bones (femur, tibia, fibula), indicating that the CSDs increased at a slower rate than length. In the upper limb bones (humerus, radiu s, ulna), CSDs and length were overall isometric, i.e., that CSDs increased at

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34 about the same rate as length. However, CSDs were positively allometric to length in some bones during the first year, as were shown by ANCOVA results based on ordinary least s quares regressions (discussed in a later section). On the whole, these scaling differences are reflected in the nonlinear relationship between CSDs and length before and even after log transformation. The trends in RMA regression residuals among upper (Fi gs. 5 13 to 5 18) and lower (Figs. 5 19 to 5 24) limb bones were very similar. The horizontal line at the zero mark in these figures represents the regression line. The value of the residual along the y axis is therefore a measure of the distance from in dividual point to regression. Neonates (0mo) mostly fell below the regression line (overestimated). From 6mos to 18mos, most individuals fell above the line (underestimated). During this period, CSDs were increasing at a faster rate than the expected ra te represented by the regression slope. The 24 36mos interval was quite distinct from the earlier and later age intervals. For these two age groups, individual points were fairly balanced in distribution above and below the regression line. In the lower limb, relative to 24mos and 48mos, the 36mos range above the line tended to be greater even while the number of individuals above and below were balanced. In the upper limb, the 36mos range was more balanced, although there were more individuals falling below the line for the radius (Figs. 5 15 to 5 16) and ML ulna (Figs. 5 17 to 5 18). This period marks the beginning of the decline in CSD growth rate. At 48mos and 60mos, the majority of points fell below the line (overestimated) for all bones and CSDs. Rigidity Ratios Bone is more rigid when the area moment is higher than that predicted by length if area moment and length were isometric. Generally, regardless of the allometric relationship, if two long bones are subjected to the same load, the one wi th a higher ratio experiences less stress. If

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35 CSD is fairly isometric to length (as the RMA regressions showed), ratios and residuals will agree in terms of their relative magnitudes. High rigidity ratios (Figs. 5 25 to 5 30) were associated with positiv e residuals (Figs. 5 13 to 5 24). Relative to length, the bones displayed the highest rigidity during the first year, especially in the 6 12mos interval (Figs. 5 25 to 5 30), even though the ratio was comparatively low at birth (0mo). All bones (except f or fibula, Fig. 5 30) showed a clear increase in relative rigidity from 0mo to 6mos, although there appeared to be a greater difference from 0mo to 6mos in the upper limb bones. Meanwhile, lower limb bones had the highest ratios at birth. The femur and t ibia at 0mo were absolutely greater in diaphyseal length (Fig. 5 31), diameter, and rigidity compared to the upper limb bones (Table 5 1). Even though the difference in length among the femur, tibia, and humerus was not very large, the difference in diame ters was large enough to result in the femur and tibia having area moments that were twice as large as those for the humerus at 0mo (Table 5 1). From 0mo to 6mos, the difference in ratio was not as great in the lower limb. To illustrate, the humerus (Fig 5 25) and femur (Fig. 5 28) were essentially equal in relative rigidity (median ratio 2.0) at age 0mo, but the humerus grossly exceeded the femur in relative rigidity by 6mos onwards. In turn, rigidity ratios were the highest in the tibia compared to the other bones, peaking at 6mos and 9mos (Fig. 5 29). However, relative rigidity may look exceptionally high in the tibia at 6mos and 9mos due to a steep drop at 12mos. The humerus and tibia also showed more spread (i.e., variance) in their data compare d to the others not just for the first year but for all ages. Rigidity ratios, like the residuals, showed that while CSD and length might both be increasing quickly together during the first year, rigidity and strength were higher than predicted by lengt h. At 18mos, relative rigidity (ratio) was still high and residuals were above the regression line. 24 36mos ratios were intermediate between those of the 6 18mos interval and

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36 the 48 60mos interval. It was around this time that residuals were fairly bal anced above and below the regression line. Rigidity ratios were lowest at 48 60mos (when most residuals were negative). In the upper limb bones, relative rigidity during this interval dropped to the level that it was at 0mo. When compared on the same sc ale to the other bones, the fibula was singular in not showing much change in relative rigidity over time, although on a smaller scale, the trends were obviously similar to those of the other bones, as seen with the residuals. ANCOVA While the residuals a nd ratios describe how relative bone rigidity and strength change with age, ANCOVA slopes help to illustrate how CSDs and length change with one another, i.e., how their growth trajectories are related through time. ANCOVA slopes and intercepts were for o rdinary least squares (OLS) regressions rather than RMA regressions (from which the residuals came), but results should not be affected. The ANCOVA showed slopes to be variable in terms of significance and relation to the slope of isometry, indicating tha t growth rates of all rigidity and strength measurements (CSDs) were variable. R 2 values were also variable, meaning that covariation between CSD and length was not uniform across age groups. In order to further discern the relationship between CSD and l ength, I have included Figure 5 31 showing how mean diaphyseal length changes with age, taken from Wall (1991), which used the same dataset. A general pattern for all bones was that regression slopes and intercepts were significant during the first year for all CSDs (Tables 5 2 to 5 7). Since a non significant regression indicates absence of predictable covariance, high R 2 values will always reflect significant regressions. In the first year, diaphyseal length (Fig. 5 31) and CSDs showed high covariance and relatively high slopes. In the upper limb, particularly in the humerus (Table 5 2), there was positive allometry between CSD and length (where regression slope is greater than the slope of

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37 isometry: m reg >4.0 for I m reg >3.0 for Z ), indicating that CS Ds increased disproportionately to length in the first year. This would account for the very high rigidity ratios in the humerus compared to the radius, ulna, and even the femur (Table 5 5). In the lower limb bones, CSD was positively allometric to lengt h at 0mo (ML femur, AP fibula) and at 12mos (AP fibula). It is interesting however that all bones (except the fibula, Table 5 7) showed positive allometry at 9mos. Otherwise, CSD was negatively allometric to length (m reg <4.0 for I m reg <3.0 for Z ) at all other age groups (for significant slopes), indicating that CSD growth rate was lower than length growth rate. Overall, the first year was characterized by rapid growth in diaphyseal length relative to time (Fig. 5 31), as well as by rapid growth in rigid ity and strength with respect to length. The latter is particularly true for the humerus, in which CSD increased faster than length (Table 5 2). It is only in the first year that we see CSDs being positively allometric to length. After 12mos, length gr owth declined overall. I suspect that the non significant slopes (with corresponding low R 2 values) after 12mos were due to the first decline in length growth (Fig. 5 31) while rigidity and strength continued to increase, resulting in a loss of correlatio n between CSD and length. Hence, common among all bones was the lack of significant slopes at 18mos. Significant slopes at 24mos were present for some bones and only for mediolateral (ML) CSDs. These were most likely due to the increase in length growth rate after the 12 18mos decline (Fig. 5 31). The significant slopes at 36mos in some bones were harder to interpret. There appeared to be slightly greater variance in residuals above the line at 36mos compared to at 24mos (Figs. 5 13 to 5 24), but otherw ise, the two age groups were very similar in rigidity ratio (Figs. 5 25 to 5 30) and R 2 This suggests that significance at 36mos was most likely spurious, resulting from increased variance in the data, allowing a regression line to be drawn and falsely s howing CSD to be increasing as length is (barely) increasing. When outliers at

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38 36mos in the radius were excluded from analysis, significance was not affected however. Nonetheless, this does not exempt the significance from being spurious. It is clear th at length and CSDs scarcely increased from 24mos to 36mos, as reflected in the similar rigidity ratios for the two age groups (Figs. 5 25 to 5 30). There was a noticeable difference between upper and lower limbs for the older age groups. In the lower limb bones, regression slopes were significant and R 2 values were high throughout the older age groups (48 60mos) unlike in the upper limb. During this interval, length growth rate increased once more after the lag (Fig. 5 31). At the same time, CSDs were in creasing at a disproportionately lower rate compared to length as indicated by the mostly negative residuals, i.e., CSDs were not as high as predicted by length (Figs. 5 13 to 5 24). Therefore, CSD growth rates were reduced relative to length (i.e., negat ive allometry). It is interesting to note that growth in ML rigidity (I ML ) and strength (Z ML ) seemed to halt early in the tibia so that at 60mos, there were no regressions (i.e., non significant slopes). Bootstrap Estimates When estimated intercepts wer e plotted against estimated slopes from resampled data (Figs. 5 32 to 5 34), ranges of slopes specific to age groups that did not overlap indicated different scaling. These patterns of non overlapping slopes were consistent with the ANCOVA results. Bones were similarly scaled (i.e., isometric, positively allometric, or negatively isometric) at ages where both the range of slopes and range of intercepts overlapped. Since larger individuals have absolutely higher rigidity and strength, it is expected that, while similarly scaled, ranges of intercepts for older age groups will extend to higher values than the ranges of intercepts for younger age groups. This was supported by the data: 0ms included the lowest estimated intercepts while 60mos included the hig hest estimated intercepts. Because CSDs were

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39 positively allometric to length during the first year mainly in the humerus (Fig. 5 32) and ulna (Fig. 5 33), upper limb ranges of estimated slopes were more separated between the younger ages (i.e., the first year) and the older ages (i.e., after age 1 or 2 years). In the lower limb, this separation between younger and older ages was not seen, so that ranges of slopes were fairly consistent (i.e., overlapping) across age groups. The lower limb bones were similarly scaled across age groups (i.e., CSDs were negatively allometric to length), with a few exceptions (ML femur, AP fibula) as described in the summary of ANCOVA results. Also previously described was the interesting phenomenon that in all bones (except the fibula), CSDs were positively allometric to length at 9mos. This was reflected in the inclusion of higher slope values in the range of estimated slopes for the 9mos group. In the femur and tibia, much of the estimated slopes at 9mos were among the highest of any age group, but the range was still wide (Fig 5 34). This may be indicative of interindividual variation in lower limb usage at this age (e.g., advent of standing). In the upper limb, especially for the forearm, the range of slopes at 60mos was wider than in the lower limb, with some overlapping t he 0mo and 9mos ranges (Figs. 5 33). This may be reflecting high interindividual variation due to more cultural factors such as physical labor (e.g., carrying, gathering). Summary of Results Here I have summarized the findings from the RMA regression re siduals, rigidity ratios, ANCOVA, and bootstrap estimates in terms of how they have supported or contradicted my hypotheses. I then summarized the results in terms of periods of growth. Recall that I assumed the transition from crawling to walking to occ ur in the 9 24mos age interval.

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40 Lower Limb: Hypotheses and Results The first hypothesis was that g reater bending and torsional stress on the lower limbs during walking would be reflected in greater bending/torsional rigidity and strength relative to diaphyseal length in the 24mos group compared to the 9m o s group. In other words, relative rigidity and strength were expected to increase as children walked more. Rigidity ratios were found to be highest in the first year, specifically at 6 18mos. RMA r esiduals showed that CSDs were underestimated at 6 18mos. These tests support the hypothesis that rigidity and strength are highest during the interval of onset of walking. However, relative rigidity and strength did not increase with age, as hypothesize d. Rather they decreased due to increasing length. The second hypothesis was that a higher increase in rigidity and strength relative to diaphyseal length i.e., higher relative growth rates, would take place in the 9 24mos interval compared to dur ing the 0 9mos and 24 60mos intervals. The ANCOVAs for the lower limb bones showed negative allometry for all significant regressions except at 9mos, where CSD growth outpaced length growth (i.e., positive allometry) in the femur and tibia. The bootstrap method showed that the highest estimated slopes were in the range for the 9mos group. However, these results do not completely support the hypothesis, since the ANCOVAs demonstrated that 0 12mos is the period of fastest growth, with 9mos being the peak for CSD growth in the femur and tibia. These results support 9mos as a reasonable estimate of the lower limit of the walking age interval due to CSDs increasing relatively rapidly in the femur and tibia, the weight bearing bones. After 12mos, CSD growth rate dec lined. Positive RMA residuals showed that CSDs continued to be underestimated until after 18mos. Rigidity ratios were highest until after 18mos. These results therefore support an earlier upper limit of the walking age: 18mos instead of 24mos. Relative rigidity and strength really declined after 18mos.

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41 The third hypothesis was that AP CSDs would grow faster than ML CSDs, specifically in the femur and tibia, since AP bending is assumed. However, there were no noticeable differences among the growth patt erns of AP and ML CSDs. The ANCOVAs showed that the CSDs did not differ in how they scaled with length and in how they covaried with length (Tables 5 2 to 5 7). The relationship of CSDs to length therefore did not seem to indicate any bias towards AP gro wth. The final hypothesis for the lower limb was that due to its lack of involvement in bearing body mass, the fibula 1) would have a lower relative rigidity and strength than the femur and tibia, and 2) would not display higher relative rigi dity and strength growth rates during the onset of walking. Both parts of this hypothesis were supported. While the growth pattern for its length is consistent with that of the other bones, the ANCOVA showed the fibula to be the only bone that did not di splay high CSD growth rate throughout the first year (Table 5 7). It also did not display a peak in CSD growth rate at 9mos (positive allometry) seen in the femur and tibia (Tables 5 5 to 5 7; Fig. 5 34). The fibula had the lowest relative rigidity value s of any long bone (Fig. 5 30) due to its low CSDs but long length (comparable to tibial length). However, the fibula displayed an increase in CSD growth rate at 48 60mos, consistent with the femur and tibia. Upper Limb: Hypotheses and Results The firs t hypothesis was that the rigidity and strength of the humerus, ulna, and radius would be highest relative to diaphyseal length and relatively higher than that of the lower limb during the 0 9m o s interval. As was seen in the lower limb bones, relative rig idity was highest during 6 18mos and residuals were mostly positive. However, the increase from 0mo to 6mos

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42 was greater in the upper limb bones (Figs. 5 25 to 5 27). Relative rigidity values for the humerus were greater than those for the femur and fibul a throughout. The second hypothesis was that these bones would experience a higher increase in rigidity and strength relative to diaphyseal length i.e., higher relative growth rates, in the 0 9mos interval compared to outside this interval Results of the ANCOVAs supported this hypothesis. From 0 12mos, CSDs increased faster than length, i.e., were positively allometric to length (Tables 5 2 to 5 4). Bootstrap estimates also supported this hypothesis. The ranges of bootstrap estimated slopes for you nger age groups were distinctly separated from the ranges of older age groups. The ranges for the younger age groups spanned the higher slope range (Figs. 5 32 and 5 33). After the first year, growth in rigidity and strength declined while length continue d to follow the same growth trajectory in the other long bones, leading to a loss of covariation between CSDs and length and lower relative rigidity values (Figs. 5 25 to 5 27). RMA residuals were mostly negative in the older age groups, which was consist ent across all bones (Figs. 5 13 to 5 24). Patterns of Growth I have categorized the growth patterns discerned from statistical analyses into three broad periods of growth: high growth, static growth, and declining growth. Finally, I summarized key diffe rences in patterns found between the upper versus lower limb. Period of high growth. This is the period of 0 12mos. The ANCOVAs showed significant slopes and high R 2 values for all bones. There was positive allometry in the humerus (0 12mos), ulna (0, 9, 12mos), radius (0, 9mos), ML femur (0, 9mos), and AP fibula (0, 12mos). Positive allometry was predominant for the upper limb bones. At 9mos, all bones (except the fibula) displayed positive allometric scaling. The bootstrap method showed that ranges of

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43 estimated slopes include d very high slope values. T he highest estimated slopes were in the range for the 9mos group Diaphyseal length growth rates were highest during the first year, as indicated by the steep slopes in Figure 5 31. During the perio d 6 18mos, CSDs were underestimated by the regression, as indicated by the positive RMA residuals. Also, relative rigidity values (ratios) were highest during this time. Period of static growth. This is the period of 18 36mos. During this time, growth in CSDs and length began to decline in rate. Between 24mos and 36mos, almost no growth was observed. After 12mos, there were no more instances of positive allometry. A ll significant regressions afterwards were instances of negative allometry In the 18mo s group, regression slopes were non significant, i.e., no regression could be calculated from the data, due to length growth decreasing faster than CSD growth. The first decline in diaphyseal length growth rate was at 12 18mos. From 24 36mos, growth was fairly static. Length growth rate was at its lowest, as indicated by the lowest slope (Fig. 5 31). RMA residuals were balanced about the regression. Rigidity ratios were intermediate between those for 6 18mos and 48 60mos. Period of declined growth. T his is the period of 36 60mos. Bootstrap estimated slope s were in the lower value range. R anges of estimated slopes for age groups in this interval were separate from ranges of slopes for age groups in the 0 12mos interval During 48 60mos, CSDs were ov erestimated by the regression, as indicated by the negative RMA residuals. Relative rigidity values (ratios) were lowest at this time. CSD growth rate s were reduced r elative to length. L ength growth rate increased after the 24 36mos lag In the lower limb, regression slopes were significant (showing CSDs to be negatively allometric to length) and R 2 values were high.

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44 Upper versus lower limb. For the upper limb bones, there was separation of the ranges of estimated slopes specific to younger age group s from those of older age groups due to CSDs being positively allometric to length in the first year After 36mos, the ANCOVAs showed non significant slopes, i.e., no regressions, and low R 2 values, except for the radius at 48mos. The range of bootstrap estimated slopes at 60mos was very wide, overlapping with ranges for 0mo and 9mos (which include d the highest estimated slopes). This variability seemed pronounced for the forearm bones For the lower limb bones, the ranges of bootstrap estimated slopes were more overlapping, i.e., the ranges were more consistent. E stimated slopes in the range for 9mos were highest in the femur and tibia compared to in the other bones

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45 Table 5 1. Means and standard deviations of midshaft diameters, area moments, and section moduli by bone (element) and age. Element & Age(mos) N Length AP Diameter ML Diameter Humerus 0 46 62.13 3.44 5.08 0.59 5.04 0.52 6 18 76.64 6.54 7.19 0.99 6.78 0.91 9 19 86.92 5.68 8.08 0.78 7.87 0.86 12 20 98.74 5.38 9.17 1.16 8.79 1.12 18 23 105.07 5.52 9.42 1.13 8.94 1.01 24 13 117.58 8.64 10.06 0.98 9.66 1.03 36 16 118.97 10.14 9.99 0.85 9.64 0.63 48 26 135.40 9.48 10.56 1.05 9.86 0.92 60 12 154.81 10.26 11.41 1.08 10.85 0.72 Radius 0 36 50.87 2.93 3.31 0.36 3.75 0.47 6 15 62.08 5.98 4.83 0.67 5.20 0.70 9 15 70.23 4.87 5.14 0.59 5.92 0.80 12 18 78.31 5.15 5.44 0.42 6.57 0.63 18 15 82.98 4.75 5.50 0.40 6.61 0.65 24 12 91.23 8.32 5.80 0.36 6.93 0.62 36 16 92.52 8.30 5.79 0.42 6.86 0.58 48 23 107.93 7.46 6.21 0.43 7.75 0.66 60 9 120.94 9.22 6.86 0.87 7.85 0.94 Ulna 0 33 58.40 3.46 3.98 0.63 3.34 0.41 6 17 70.59 6.43 5.60 0.64 5.00 0.61 9 15 79.18 5.63 6.35 0.93 5.38 0.72 12 17 88.32 5.10 7.02 0.82 5.71 0.56 18 17 92.07 4.57 6.78 0.67 5.93 0.82 24 13 101.60 8.78 6.93 0.72 6.15 0.82 36 16 103.63 8.13 6.91 0.65 6.41 0.78 48 22 119.34 9.10 7.63 1.12 6.72 0.79 60 10 132.15 9.88 8.45 0.99 7.10 0.98

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46 Table 5 1. Continued Element & Age(mos) IAP ZAP IML ZML Humerus 0 33.74 13.88 22.07 6.73 34.46 15.14 22.28 7.09 6 119.3 61.68 57.18 21.66 134.53 69.30 60.70 23.14 9 204.91 87.68 85.72 26.89 214.98 89.01 87.88 26.81 12 328.01 153.92 121.88 41.21 355.48 142.54 127.10 39.90 18 350.75 138.99 129.16 38.91 390.74 151.17 136.32 40.82 24 466.03 161.58 159.81 42.48 503.61 172.61 166.21 43.42 36 446.78 100.72 155.86 26.63 484.14 141.99 161.98 32.74 48 514.88 157.56 173.86 40.62 592.91 204.19 186.40 46.48 60 724.43 149.47 224.88 35.39 811.96 223.49 237.61 46.75 Radius 0 9.19 3.99 8.02 2.64 7.11 3.17 7.06 2.33 6 36.18 18.03 22.61 8.21 31.15 14.43 20.99 7.40 9 57.00 28.60 31.28 11.61 42.55 21.55 27.05 9.91 12 78.90 25.57 39.90 9.67 53.68 15.85 32.96 7.45 18 80.79 27.26 40.65 9.89 55.43 16.06 33.73 7.35 24 97.67 31.15 47.00 10.59 67.58 16.70 39.18 7.49 36 93.70 24.88 45.75 8.79 66.53 17.14 38.57 7.11 48 146.02 43.10 62.90 13.46 92.95 23.42 50.25 9.69 60 169.33 62.82 71.36 19.09 128.96 47.04 62.26 16.07 Ulna 0 7.83 3.20 7.69 2.54 11.52 6.50 9.26 3.67 6 36.25 13.72 23.88 6.74 45.18 16.35 26.67 7.31 9 51.56 21.59 31.41 9.89 72.58 36.53 37.15 12.86 12 66.59 23.28 38.76 9.69 101.53 34.66 47.82 12.22 18 73.52 28.75 40.64 11.84 93.97 33.33 46.08 12.13 24 82.70 32.94 44.29 12.46 103.66 37.40 49.70 12.84 36 95.72 51.93 48.74 17.95 109.28 52.28 52.23 17.63 48 120.13 57.28 58.73 19.61 157.69 76.18 67.14 23.26 60 160.60 83.12 73.54 27.53 225.17 116.53 87.20 31.97

PAGE 47

47 Table 5 1. Continued Element & Age(mos) N Length AP Diameter ML Diameter Femur 0 42 72.63 4.31 5.79 0.65 6.15 0.51 6 12 94.54 9.21 7.59 0.68 8.36 0.83 9 14 108.48 6.65 8.89 0.71 9.31 1.09 12 17 126.25 6.99 9.71 0.89 10.61 0.80 18 22 132.85 8.35 9.70 0.86 10.69 0.77 24 12 153.90 13.17 10.70 1.27 11.45 1.19 36 16 158.17 13.32 11.27 0.97 11.79 0.82 48 24 183.30 18.86 12.06 1.24 12.76 1.23 60 12 215.65 18.62 13.99 0.95 14.14 1.35 Tibia 0 41 63.52 3.91 6.03 0.66 5.78 0.52 6 16 80.09 8.25 8.36 0.70 7.47 0.69 9 12 91.42 6.21 9.31 1.29 8.34 1.00 12 15 103.78 7.53 9.77 1.30 8.95 0.74 18 19 110.05 6.53 9.98 0.95 9.12 0.82 24 11 123.84 14.08 10.91 1.47 9.51 1.64 36 16 128.70 13.39 11.67 1.60 9.89 0.96 48 21 153.77 16.27 12.85 1.88 10.91 1.09 60 11 178.55 11.79 14.53 1.75 12.38 1.14 Fibula 0 34 60.44 3.54 2.55 0.32 3.28 0.55 6 9 76.61 9.51 3.85 0.67 3.90 0.43 9 10 88.98 6.14 4.18 0.42 5.29 1.57 12 11 97.11 6.82 4.40 0.40 4.87 0.68 18 13 104.63 7.98 4.43 0.51 5.12 0.47 24 9 121.47 11.38 4.92 0.65 5.69 0.82 36 10 126.73 16.85 5.33 0.68 6.13 1.05 48 17 151.34 13.71 5.91 0.75 6.48 0.76 60 11 171.14 14.35 6.44 0.64 7.59 1.02

PAGE 48

48 Table 5 1. Continued Element & Age(mos) IAP ZAP IML ZML Femur 0 68.63 23.10 37.17 9.62 61.91 24.74 35.21 10.22 6 227.50 76.00 90.31 22.85 186.60 59.12 81.84 20.01 9 373.57 163.54 131.85 40.86 333.45 115.35 125.01 33.25 12 584.80 166.31 184.49 40.04 493.99 161.14 169.32 40.26 18 597.92 171.60 187.22 39.95 496.46 169.28 170.35 40.45 24 829.68 292.31 239.82 66.14 729.43 261.52 224.71 63.33 36 929.45 243.40 264.28 52.58 855.35 254.13 253.23 54.91 48 1291.72 485.31 335.23 94.66 1160.09 461.70 317.46 92.69 60 2012.46 687.25 473.30 116.32 1945.30 552.86 466.30 100.65 Tibia 0 59.91 20.20 34.39 9.00 65.71 24.08 35.97 9.99 6 178.33 60.67 79.31 20.23 222.25 73.85 88.58 22.08 9 283.93 131.78 111.59 39.06 359.73 191.95 125.24 47.76 12 358.03 117.46 133.18 34.66 436.79 166.86 146.63 43.10 18 387.20 141.24 141.05 38.16 465.83 189.12 154.56 44.22 24 516.89 279.64 173.58 72.57 662.68 333.58 197.20 77.39 36 587.41 260.84 195.89 65.57 839.50 442.75 233.18 87.91 48 863. 54 348.43 261.61 80.30 1234.66 595.36 311.35 109.72 60 1370.76 340.13 371.68 67.46 1925.87 639.73 439.39 102.60 Fibula 0 4.87 2.63 4.76 1.86 2.85 1.37 3.65 1.29 6 12.02 5.39 10.12 3.52 12.18 6.32 10.14 3.98 9 38.81 45.60 21.04 14.59 19.61 8.47 15.60 5.64 12 26.76 11.75 17.93 5.87 21.21 7.29 16.04 4.44 18 30.35 10.92 19.69 5.21 22.87 8.39 17.07 4.68 24 48.63 24.56 27.70 10.52 35.95 16.06 23.87 8.46 36 66.83 38.59 34.86 14.18 48.72 22.59 29.93 10.45 48 82.71 34.64 42.10 12.71 69.36 30.62 38.51 12.10 60 147.20 73.57 63.34 21.05 103.24 36.41 53.30 14.37

PAGE 49

49 A B C D Figure 5 1. Humerus area moments plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appearance. A) Anteroposterior moments, or IAP, against length. B) Log IAP against log length. C) Mediolateral moments, or IML, against length. D ) Log IML against log length.

PAGE 50

50 A B C D Figure 5 2. Humerus section moduli plotted against length (mm) befor e (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the d ata an overall curvilinear appeara nce. A) Anteroposterior section moduli, or ZAP, against length. B) Log Z AP against log length. C) Mediolateral section moduli, or ZML, against length. D) Log Z ML against log length.

PAGE 51

51 A B C D Figure 5 3. Radius area moments plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age gr oups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appearance. A) Anteroposterior moments, or IAP, against length. B) Log IAP against log length. C) Mediolateral moments, or IML, against length. D) Log IML against log length.

PAGE 52

52 A B C D Figure 5 4. Radius section moduli plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note a lso the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appeara nce. A) Anteroposterior section moduli, or ZAP, again st length. B) Log Z AP against log length. C) Mediolateral section moduli, or ZML, against length. D) Log Z ML against log length.

PAGE 53

53 A B C D Figure 5 5. Ulna area moments plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appearance. A) Anteroposterior moments, or IAP, against length. B) Log IAP against log length. C) Mediolateral moments, or IML, against length. D) Log IML against log length.

PAGE 54

54 A B C D Figure 5 6. Ulna section moduli plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitte d to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differ ing slopes give the data an overall curvilinear appeara nce. A) Anteroposterior section moduli, or ZAP, against length. B) Log Z AP against log length. C) Mediolateral section moduli, or ZML, against length. D) Log Z ML against log length.

PAGE 55

55 A B C D Figure 5 7. Femur area moments plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appearance. A) Anteroposter ior moments, or IAP, against length. B) Log IAP against log length. C) Mediolateral moments, or IML, against length. D) Log IML against log length.

PAGE 56

56 A B C D Figure 5 8. Femur section moduli plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note a lso the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appeara nce. A) Anteroposterior section moduli, or ZAP, again st length. B) Log Z AP against log length. C) Mediolateral section moduli, or ZML, against length. D) Log Z ML against log length.

PAGE 57

57 A B C D Figure 5 9. Tibia area moments plotted against length (mm) before (A, C) and after (B, D) log transformat ion. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appearance. A) Anteroposterior moments, or IAP, against length. B) Log IAP against log length. C) Mediolateral moments, or IML, again st length. D) Log IML against log length.

PAGE 58

58 A B C D Figure 5 10. Tibia section moduli plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slope s give the data an overall curvilinear appeara nce. A) Anteroposterior section moduli, or ZAP, against length. B) Log Z AP against log length. C) Mediolateral section moduli, or ZML, against length. D) Log Z ML against log length.

PAGE 59

59 A B C D Figure 5 11. Fibula area moments plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appearance. A) Anteroposterior mom ents, or IAP, against length. B) Log IAP against log length. C) Mediolateral moments, or IML, against length. D) Log IML against log length.

PAGE 60

60 A B C D Figure 5 12. Fibula section moduli plotted against length (mm) before (A, C) and after (B, D) log transformation. For log transformed data : Note how a regression can be easily fitted to the data of the younger age groups compared to the more scattered data of the older age groups. Note also the steeper slope of the hypothetical line fitted to the data of the younger age groups compared to that for the older age groups. These differing slopes give the data an overall curvilinear appeara nce. A) Anteroposterior section moduli, or ZAP, against length. B) Log Z AP against log length. C) Mediolateral section moduli, or ZML, against length. D) Log Z ML against log length.

PAGE 61

61 A B Figure 5 13. Humerus RMA residuals for area moment data by age group (months). A) Anteroposterior data, IAP B) Mediolateral data. IML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the l ine) residuals, as well as the ranges for positive and negative residual values.

PAGE 62

62 A B Figure 5 14. Humerus RMA r esiduals for section modulus data by age group (months). A) Anteroposterior data, ZAP B) Mediolateral data. ZML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 63

63 A B Figure 5 15. Radius RMA residuals for area moment data by age group (months). A) Anteroposterior data, IAP B) Mediolateral data. IML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 64

64 A B Figure 5 16. Radius RMA r esiduals for section modulus data by age group (months). A) Anteroposterior data, ZAP B) Mediolateral data. ZML Line at 0 represent s the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (b elow the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 65

65 A B Figure 5 17. Ulna RMA residuals for area moment data by age group (months). A) Anteroposterior data, IAP B) Mediolateral data. IML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and ne gative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 66

66 A B Figure 5 18. Ulna RMA r esiduals for section modulus data by age group (months). A) Anteroposterior data, ZAP B) Mediolateral data. ZML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 67

67 A B Figure 5 19. Femur RMA residuals for area moment data by age group (months). A) Anteroposterior data, IAP B) Mediolateral data. IML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 68

68 A B Figure 5 20. Femur RMA r esiduals for section modulus data by age group (months). A) Anteroposterior data, ZAP B) Mediolateral data. ZML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 69

69 A B Figure 5 21. Tibia RMA residuals for area moment data by age group (months). A) Anteroposterior data, IAP B) Mediolateral data. IML Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) a nd negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 70

70 A B Figure 5 22. Tibia RMA r esiduals for section modulus data by age group (months). A) Anteroposterior data, ZAP B) Mediolateral data. ZML Li ne at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line ) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 71

71 A B Figure 5 23. Fibula RMA residuals for area moment data by age group (months). A) Anteroposterior data, IAP B) Mediolateral data. IML Li ne at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line ) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 72

72 A B Figure 5 24. Fibula RMA r esiduals for section modulus data by age group (months). A) Anteroposterior data, ZAP B) Mediolateral data. ZM L Line at 0 represents the RMA regression. Positive residuals are for area moments underestimated by the regression. Negative residuals are for area moments overestimated by the regression. The accompanying table s provide the counts of positive (above the line) and negative (below the line) residuals, as well as the ranges for positive and negative residual values.

PAGE 73

73 Figure 5 25. Humerus. Boxplots of rigidity ratios for each age group. Ratio gives measure of relative rigidity. Bold line represents median ratio for age group. Figure 5 26. Radius. Boxplots of rigidity ratios for each age group. Ratio gives measure of relative rigidity. Bold line represents median ratio for age group

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74 Figure 5 27. Ulna. Boxplots of rigidity ratios for each age group. Ratio gives measure of relative rigidity. Bold line represents median ratio for age group. Figure 5 28. Femur. Boxplots of rigidity ratios for each age group. Ratio gives measure of relative rigidity. Bold line represents median ratio for age group.

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75 Figure 5 29. Tibia. Boxplots of rigidity ratios for each age group. Ratio gives measure of relative rigidity. Bold line represents median ratio for age group. Figure 5 30 Fibula. Boxplots of rigidity ratios for each age group. Ratio gives measure of relative rigidity. Bold line represents median ratio for age group. Note that the y axis scale is different from that of Figs. 5 25 to 5 29 to enhance visualization.

PAGE 76

76 Figur e 5 31. Mean diaphyseal length (mm) plotted against age for each bone. Source: Wall (1991)

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77 Table 5 2. Humerus ANCOVA summary. Age (months) CSD Slope Significance Intercept Significance R squared All IAP 3.54 *** 10.91 *** 0.86 IML 3.65 *** 11.31 *** 0.86 ZAP 2.67 *** 7.77 *** 0.87 ZML 2.72 *** 7.97 *** 0.86 0 IAP 4.53 *** 15.24 *** 0.42 IML 5.49 *** 19.21 *** 0.55 ZAP 3.51 *** 11.46 *** 0.46 ZML 4.00 *** 13.45 *** 0.54 6 IAP 4.87 *** 16.46 *** 0.66 IML 4.12 ** 13.07 0.44 ZAP 3.56 *** 11.45 ** 0.64 ZML 3.18 ** 9.76 0.49 9 IAP 5.52 *** 19.39 *** 0.75 IML 5.06 *** 17.30 *** 0.72 ZAP 4.08 *** 13.81 *** 0.75 ZML 3.85 *** 12.77 *** 0.74 12 IAP 4.27 13.91 0.24 IML 3.33 9.50 0.13 ZAP 3.08 9.41 0.23 ZML 2.61 7.21 0.15 18 IAP 3.05 8.39 0.13 IML 3.24 9.19 0.13 ZAP 2.31 5.93 0.13 ZML 2.40 6.32 0.13 24 IAP 2.06 3.73 0.15 IML 1.59 1.44 0.10 ZAP 1.49 2.04 0.14 ZML 1.25 0.89 0.11 36 IAP 1.92 ** 3.08 0.53 IML 1.76 2.26 0.33 ZAP 1.42 ** 1.74 0.52 ZML 1.34 1.33 0.37

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78 Table 5 2. Continued Age (months) CSD Slope Significance Intercept Significance R squared 48 IAP 0.99 1.32 0.04 IML 0.53 3.71 0.01 ZAP 0.69 1.76 0.04 ZML 0.46 2.96 0.02 60 IAP 0.12 7.16 0.00 IML 1.89 2.85 0.17 ZAP 0.16 4.59 0.00 ZML 1.16 0.42 0.14 Note: Significance levels: (***) p<0.0001, (**) p<0.001, (*) p<0.05

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79 Table 5 3. Radius ANCOVA summary. Age (months) CSD Slope Significance Intercept Significance R squared All IAP 3.55 *** 11.49 *** 0.84 IML 3.34 *** 10.93 *** 0.84 ZAP 2.63 *** 8.08 *** 0.84 ZML 2.53 *** 7.80 *** 0.85 0 IAP 6.33 *** 22.76 *** 0.51 IML 5.70 *** 20.52 *** 0.54 ZAP 4.67 *** 16.32 *** 0.52 ZML 4.35 *** 15.20 *** 0.55 6 IAP 3.54 ** 11.11 0.42 IML 3.75 ** 12.16 0.43 ZAP 2.68 ** 7.99 0.43 ZML 2.79 ** 8.52 0.44 9 IAP 5.39 ** 18.96 ** 0.55 IML 5.27 *** 18.75 *** 0.68 ZAP 4.03 *** 13.72 ** 0.58 ZML 3.97 *** 13.63 ** 0.67 12 IAP 3.57 ** 11.26 0.42 IML 2.80 8.26 0.34 ZAP 2.58 ** 7.60 0.41 ZML 2.20 ** 6.10 0.36 18 IAP 2.57 6.99 0.18 IML 1.08 0.79 0.05 ZAP 1.74 4.00 0.16 ZML 1.00 0.90 0.07 24 IAP 1.28 1.24 0.16 IML 1.70 3.50 0.42 ZAP 1.01 0.75 0.19 ZML 1.22 1.87 0.37 36 IAP 1.52 2.37 0.25 IML 1.52 2.73 0.33 ZAP 1.14 1.35 0.28 ZML 1.14 1.53 0.34

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80 Table 5 3. Continued Age (months) CSD Slope Significance Intercept Significance R squared 48 IAP 1.24 0.84 0.08 IML 1.90 4.39 0.24 ZAP 1.01 0.61 0.11 ZML 1.34 2.38 0.22 60 IAP 0.02 4.97 0.00 IML 1.60 2.88 0.10 ZAP 0.21 3.21 0.00 ZML 1.00 0.71 0.08 Note: Significance levels: (***) p<0.0001, (**) p<0.001, (*) p<0.05

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81 Table 5 4. Ulna ANCOVA summary. Age (months) CSD Slope Significance Intercept Significance R squared All IAP 3.59 *** 12.24 *** 0.78 IML 3.54 *** 11.69 *** 0.79 ZAP 2.69 *** 8.64 *** 0.79 ZML 2.66 *** 8.37 *** 0.79 0 IAP 5.86 *** 21.87 *** 0.45 IML 6.41 *** 23.75 *** 0.45 ZAP 4.46 *** 16.17 *** 0.46 ZML 4.74 *** 17.11 *** 0.46 6 IAP 2.91 8.86 0.34 IML 2.94 ** 8.79 0.37 ZAP 2.19 ** 6.17 0.37 ZML 2.20 ** 6.13 0.39 9 IAP 5.88 *** 21.85 *** 0.76 IML 3.79 12.40 0.33 ZAP 4.15 *** 14.74 *** 0.73 ZML 3.11 ** 10.01 0.42 12 IAP 4.84 *** 17.54 *** 0.63 IML 5.45 *** 19.87 ** 0.58 ZAP 3.71 *** 12.98 *** 0.66 ZML 4.01 *** 14.15 ** 0.61 18 IAP 2.12 5.38 0.05 IML 3.61 11.84 0.25 ZAP 1.78 4.38 0.07 ZML 2.52 7.60 0.21 24 IAP 0.93 8.63 0.04 IML 1.34 1.58 0.13 ZAP 0.41 5.66 0.02 ZML 0.72 0.55 0.07 36 IAP 1.81 3.93 0.12 IML 1.16 0.75 0.07 ZAP 1.28 2.08 0.12 ZML 0.95 0.49 0.08

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82 Table 5 4. Continued Age (months) CSD Slope Significance Intercept Significance R squared 48 IAP 1.63 3.07 0.09 IML 2.58 7.39 0.16 ZAP 1.34 2.37 0.11 ZML 1.82 4.53 0.16 60 IAP 0.79 1.13 0.02 IML 1.50 1.98 0.07 ZAP 0.68 0.93 0.02 ZML 1.03 0.63 0.06 Note: Significance levels: (***) p<0.0001, (**) p<0.001, (*) p<0.05

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83 Table 5 5. Femur ANCOVA summary. Age (months) CSD Slope Significance Intercept Significance R squared All IAP 3.14 *** 9.12 *** 0.93 IML 3.19 *** 9.46 *** 0.93 ZAP 2.36 *** 6.41 *** 0.94 ZML 2.38 *** 6.58 *** 0.93 0 IAP 3.66 *** 11.51 *** 0.42 IML 4.72 *** 16.19 *** 0.50 ZAP 2.88 *** 8.75 *** 0.45 ZML 3.41 *** 11.09 *** 0.50 6 IAP 3.50 *** 10.55 ** 0.76 IML 2.85 ** 7.79 0.57 ZAP 2.55 *** 7.10 ** 0.74 ZML 2.22 ** 5.72 0.61 9 IAP 6.11 *** 22.78 *** 0.78 IML 4.63 *** 15.95 ** 0.67 ZAP 4.40 *** 15.76 *** 0.77 ZML 3.66 *** 12.35 ** 0.70 12 IAP 3.25 ** 9.36 0.37 IML 3.76 ** 12.02 0.40 ZAP 2.50 ** 6.89 0.39 ZML 2.75 ** 8.21 0.41 18 IAP 2.01 3.46 0.21 IML 1.65 1.89 0.11 ZAP 1.46 1.93 0.20 ZML 1.28 1.14 0.13 24 IAP 2.69 6.87 0.30 IML 3.32 10.20 0.37 ZAP 2.09 5.10 0.32 ZML 2.41 6.76 0.37 36 IAP 1.38 0.17 0.20 IML 1.66 1.70 0.23 ZAP 1.07 0.15 0.21 ZML 1.21 0.61 0.23

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84 Table 5 5. Continued Age (months) CSD Slope Significance Intercept Significance R squared 48 IAP 2.63 *** 6.60 0.55 IML 2.67 *** 6.93 0.54 ZAP 1.98 *** 4.52 0.55 ZML 2.00 *** 4.69 0.54 60 IAP 3.06 ** 8.90 0.61 IML 2.19 4.20 0.46 ZAP 2.19 ** 5.62 0.60 ZML 1.75 3.27 0.50 Note: Significance levels: (***) p<0.0001, (**) p<0.001, (*) p<0.05

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85 Table 5 6. Tibia ANCOVA summary. Age (months) CSD Slope Significance Intercept Significance R squared All IAP 2.98 *** 8.20 *** 0.90 IML 3.22 *** 9.09 *** 0.89 ZAP 2.27 *** 5.79 *** 0.90 ZML 2.39 *** 6.24 *** 0.89 0 IAP 3.39 *** 10.05 ** 0.30 IML 3.47 *** 10.28 0.25 ZAP 2.55 *** 7.10 ** 0.30 ZML 2.59 *** 7.21 0.26 6 IAP 2.99 *** 7.96 ** 0.70 IML 2.83 *** 7.03 ** 0.70 ZAP 2.22 *** 5.38 ** 0.71 ZML 2.14 *** 4.92 ** 0.70 9 IAP 5.86 *** 20.91 ** 0.70 IML 6.41 *** 23.18 ** 0.75 ZAP 4.47 *** 15.50 ** 0.72 ZML 4.74 *** 16.63 ** 0.76 12 IAP 3.27 ** 9.36 0.43 IML 3.34 9.52 0.24 ZAP 2.46 6.57 0.39 ZML 2.50 6.65 0.26 18 IAP 2.16 4.24 0.14 IML 2.48 5.57 0.18 ZAP 1.66 2.87 0.15 ZML 1.82 3.54 0.18 24 IAP 2.78 7.28 0.25 IML 2.49 5.62 0.28 ZAP 2.05 4.78 0.26 ZML 1.90 3.95 0.29 36 IAP 1.86 2.72 0.25 IML 2.54 5.72 0.33 ZAP 1.48 1.94 0.27 ZML 1.82 3.45 0.32

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86 Table 5 6. Continued Age (months) CSD Slope Significance Intercept Significance R squared 48 IAP 2.75 *** 7.14 0.53 IML 2.85 ** 7.33 0.36 ZAP 2.07 *** 4.91 0.51 ZML 2.13 ** 5.01 0.39 60 IAP 2.76 7.12 0.48 IML 2.58 5.87 0.22 ZAP 2.05 4.71 0.52 ZML 1.96 4.09 0.29 Note: Significance levels: (***) p<0.0001, (**) p<0.001, (*) p<0.05

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87 Table 5 7. Fibula ANCOVA summary. Age (months) CSD Slope Significance Intercept Significance R squared All IAP 3.25 *** 11.75 *** 0.87 IML 3.42 *** 12.88 *** 0.89 ZAP 2.46 *** 8.49 *** 0.88 ZML 2.55 *** 9.05 *** 0.90 0 IAP 5.88 *** 22.66 *** 0.34 IML 3.06 11.61 0.15 ZAP 4.05 *** 15.13 ** 0.33 ZML 2.64 ** 9.61 0.19 6 IAP 2.58 8.77 0.41 IML 2.53 8.62 0.22 ZAP 1.92 6.08 0.37 ZML 1.91 6.02 0.25 9 IAP 1.02 1.26 0.01 IML 3.17 11.34 0.26 ZAP 1.03 1.74 0.02 ZML 2.11 6.78 0.17 12 IAP 4.98 19.60 0.50 IML 2.95 10.50 0.28 ZAP 3.48 13.10 0.48 ZML 2.47 8.54 0.33 18 IAP 2.18 6.78 0.23 IML 1.36 3.28 0.06 ZAP 1.53 4.18 0.20 ZML 1.13 2.43 0.09 24 IAP 3.52 13.12 0.37 IML 4.10 16.19 0.51 ZAP 2.71 9.76 0.40 ZML 3.00 11.29 0.49 36 IAP 2.85 9.70 0.49 IML 2.08 6.26 0.37 ZAP 2.04 6.37 0.49 ZML 1.65 4.66 0.41

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88 Table 5 7. Continued Age (months) CSD Slope Significance Intercept Significance R squared 48 IAP 2.70 ** 9.21 0.38 IML 3.53 *** 13.54 ** 0.58 ZAP 2.13 ** 6.98 0.45 ZML 2.54 *** 9.14 ** 0.59 60 IAP 2.96 10.30 0.34 IML 3.13 11.51 0.52 ZAP 2.24 7.41 0.38 ZML 2.33 8.01 0.51 Note: Significance levels: (***) p<0.0001, (**) p<0.001, (*) p<0.05

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89 Figure 5 32. Humerus bootstrap estimated slopes and intercepts for AP area moment data. Note that the ranges of slopes for younger age groups are distinctly separated from the ranges of older age groups. The ranges for the younger age groups span the higher slope range (bottom right quadrant).

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90 Figure 5 33. Ulna bootstrap estimated slopes and intercepts for AP area moment data. Note that the ranges of slopes for younger age groups are distinctly separate from the ranges of older age groups. The ranges for the younger age groups span the higher slope range (bottom right quadrant). Note also the especially wide range of slopes for the 60mos age group.

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91 Figure 5 34. Femur bootstrap estimated slopes and intercepts for AP area moment data. Note that the ranges of slopes of all age groups overlap. Note also how the range of slopes for the 9mos group spans the higher slope value range (bottom right quadrant), separate from the ranges of other age groups.

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92 CHAPTER 6 DISCUSSION AND CONCLUSION In this chapter, I will discuss in detail how the growth trajectories of CSD and length (summarized in the Results chapter) reflect changes in mechanical loading during crawling and the transition to walking. I will also discuss how my results fit with th e findings of other studies. Based on my results, I estimate the advent of walking for individuals in this sample to be in the 9 18mos range, which falls into my hypothesized range of 9 24mos. Concerning the lower limb bones, the findings supported my hy pothesis that there would be a higher increase in CSD relative to length in this interval. In fact, the increase is found even earlier, at 6mos. This increase may be resulting from the generally rapid growth in infants shortly after birth. Perhaps these children are beginning to stand and walk with assistance at around 6mos, which is the earliest age that Stanitski et al. (2000) found. However, the scaling evidence is strongly suggesting 9mos as the earliest age that independent walking becomes routine. One has to assume that the morphology observed is the result of the loading event. As expected, the fibula displays the lowest relative CSDs and is less responsive to changes in loading. Contrary to what I expected, it was found that relative CSDs are higher in the earlier age groups than in the later age groups because of the greater increase in length relative to CSD. My hypothesis that AP and ML CSD growth rates will differ is however rejected, as no difference is evident in the results. For the up per limb bones, my hypotheses are all supported. Relative rigidity is highest (among all bones) during the 0 9mos period. CSD growth rates are higher relative to length in this period, declining after the first year. I will end this chapter with two s ections: 1) a brief discussion of what we can gain in our understanding of the evolution of bipedalism through studying the ontogeny of walking in

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93 children; and 2) a proposal for a future bipedalism study involving the integration of force data and morphol ogical data, with special consideration of the role of life history variables. From Crawling to Walking Determining the age at the advent of walking requires seeing signals that may indicate differentiation between the upper and lower limbs since the lower limbs have taken on the responsibility of body weight support, while the upper limbs are free. The cha nges that are expected to accompany the advent of walking may not be immediately apparent because learning good term from Cowgill et al. (2010) for referring to this learning period in which the child is standing and taking unsteady, unbalanced steps. We expect there to be 1) changes in the lower limbs to allow them to accommodate body weight during bipedal stance and locomotion and 2) changes that take place e.g., the bicondylar angle (Tardieu and Trinkaus, 1994; Tardieu et al., 2006; Tardieu, 2010), development of a longitudinal arch (Bertsch et al., 2004). If the two lower limbs are to ta ke on the weight of the body, they must first be strong enough. In the first year, bones are lengthening and strengthening very quickly with rigidity and strength growth rates peaking at around 9mos. This is not surprising given that this is generally a time of rapid somatic growth and development. Because the bone is lengthening so rapidly, rigidity and strength must also keep pace to reduce bending and torsional strain. Recall that the main type of mechanical loading on long bone diaphyses is bending (Rubin and Lanyon, 1984). The limbs would have little trouble supporting the child in crawling. The humerus becomes more rigid (relative to length) than the femur simply by increasing its diameter faster than it increases its diaphyseal length. This agr

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94 increases in strength faster than the femur during 6 12mos, with the trend reversing after the first year. The radius and ulna are also increasing in rigidity and strength faster than in length, albeit less consistently within the first year. The upper limbs are stronger earlier, which would allow the child to first lift its upper body off the ground. What is required for standing on two limbs? At the very least, it would require bones with sufficient rig idity and strength. Based on relative rigidity alone, the femur and especially the tibia are most rigid for their length at 6mos. However, it is at around 9mos that diameter growth is outpacing diaphyseal length growth in order for these bones to still b e sufficiently rigid as the child grows taller. The femur and tibia maintain high relative rigidity from 6mos to 9mos perhaps because the child is standing and beginning to take first steps. Redistributing body weight from four limbs to two limbs certain stimulate bone growth (Turner, 1998). Based on these results, an estimate of the toddling period (which encompasses the advent of standing and walking with immature gait) is 9 18mos. At 18mos, rigidity an d strength are still higher than expected for length. This is because at 18mos, length growth has slowed down more than CSD growth has, so that relative rigidity is still high and residuals are still mostly positive. By 24mos however, CSD growth really d eclines. A few studies have shown walking to begin at age intervals falling within my estimated range of 9mos to 18 mos. An early study examined the developmental progress of 1,036 children in Denver, Colorado. It found that children were able to walk a ssisted (in this case, while holding onto furniture) at around 7.3mos (25 th percentile) to 12.7mos (90 th percentile) and th percentile) to 14.3mos (90 th percentile) (Frankenburg and Dodds, 1967). deGro ot et al. (1997) set the criterion for independent walking as being able to walk 5 meters without assistance. Children who met this criterion were aged

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95 age at which the subject was able to arise from a sitting position on the floor and walk at least 6 earliest age was 6 months, the mean age was 11.3mos, and the median age was 11mos. Further supporting my estimated range is the finding that late in the first year, bicondylar angle begins to form, reaching the minimum adult angle at age 4 years (Tardieu and Trinkaus, 1994) or 7 years (Yaguramaki and Kimura, 2002). As di scussed in the Literature Review chapter, the bicondylar angle contributes to a mature walking gait. Although the lack of a bicondylar angle makes for inefficient bipedality, it causes the child to walk with legs far apart which actually creates a wide ba se for lateral stability (Yaguramaki and Kimura, 2002). A wide base however creates more mediolateral movement, but this decreases as the body stabilizes, beginning distally (i.e., ankle to knee to hip to shoulder) (Cioni et al., 1993; Yaguramaki and Kimu ra, 2002). Another outcome of a less stable body is a longer stance phase and a longer double support time (i.e., time during which the body is supported by both legs in between stance and opposite foot swing) compared to adults (Grimshaw et al., 1998). The role of the neuromotor system is also important to consider in understanding gait and posture but is beyond the scope of this study. Past 12mos, bones experience comparatively less growth in rigidity and strength. The 18 36mos interval is a fairly s tatic period of growth, even for diaphyseal length between 24mos and 36mos. Wall (1991) has attributed this 24 36mos lag to weaning stress. It is not energetically worthwhile to grow the body when there is less nutrition available to sustain it. Ethnogr aphic data for various contemporary North American Indian populations show weaning to occur during the age interval of 1.5 to 3 years (Ray, 1971; Silver, 1978; Wallace, 1978). This data does not confirm weaning as the source of the growth lag, but it cert ainly supports it.

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96 Nonetheless, even with the presence of a growth lag, it is clear that lengthening the bone is of primary importance to allow the limbs to reach the appropriate proportions. This would explain why aside from a few instances in the first year length growth rate always exceeds CSD growth rate in the lower limb bones, allowing the legs to become much longer than the arms. The upper limbs remain rigid while the child continues to rely on crawling or for support in standing up and while walki ng. However, relative rigidity declines over time as these bones lengthen. In absolute terms, the femur is the most rigid and strongest bone, which is not surprising given its role as the primary weight bearing bone. This is supported by van der Meulen et al. (1996), which found femoral cross sectional geometry to be most influenced by body mass. Body mass was the best predictor of cross sectional properties in the femur. The grossly surpassed by that of the humerus and tibia. However, this is simply informing us that the femur has always been absolutely longer than the other bones. Additionally, it is the cross sectional area rather than the length that matters for determini ng axial stress (i.e., compression, tension), which will always be present in conjunction with bending and torsional stresses. Allometry studies such as Jungers et al. (1988) found that the lower limb long bones increase in length at a faster rate than th e upper limb long bones, resulting in longer lower limbs, as seen in this study. An earlier study, Buschang (1982), attributed this pattern to upper limb buds appearing earlier in development and to the observation that upper limbs reach adult size earlie r than lower limbs. Achieving the proper proportion of long legs to short arms makes the body a stable structure down to the naval or pelvic level, since the re is so much muscle mass contributed by the lower limbs alone. A lower center of mass means less muscle force is needed to stay upright (Adolph

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97 and Avolio, 2000). Young children also lower their center of gravity for balance by employing a bent knee and bent hip posture (Hallemans et al., 2005), something reminiscent of facultative bipedalism in some non human primates. Declining relative rigidity is of less consequence for the upper limb bones once the child is habitually walking. The lower limb bone s would however be more vulnerable to bending and torsion as length increases. After the lag from 24mos to 36mos of age, length growth resumed. To counteract the increased bending strain (and consequent increased risk of fracturing), rigidity and strengt h growth had to also pick up pace after age 36mos. The observation that diaphyseal length and CSDs are correlated in this way suggests that bone can sense deviations from some optimum strain threshold (Lanyon, 1982). When the bone becomes too long and th e risk of fracture increases, the proper response would be to increase diameter. Among all the bones, fibular growth trajectories are the least consistent. Its irregular cross sectional shape and little to no involvement in weight bearing are the primar y factors contributing to the inconsistent growth patterns. This is to say that, for the fibula, AP and ML diameters and CSDs do not reflect geometry very well. Growth in the fibula is mainly in length. At 48 60mos however, its rigidity and strength gro wth rates increase relative to length like in the femur and tibia and for the same reason (i.e., to counteract increased bending strain). Even though the fibula is not directly weight bearing, it is a site of attachment for muscles that plantarflex and ev ert the foot at the ankle (i.e., Soleus, Peroneus longus and brevis) (Agur and Aside from muscle action, propulsion is also made possible by the longitudin al arch of the foot, which develops until age 6 years (Bertsch et al., 2004). Evidence for a developed arch and

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98 to midfoot arch to forefoot toe off that c an be traced on a pressure pad or a simple ink imprint of the forefoot and hindfoot, as reflected in the increase in maximum ground reaction force (GRF) fo r these parts (Bertsch et al., 2004). For an immature gait, hip flexors are actually used more than plantarflexors for propulsion (Sutherland, 1997). Therefore, we should expect greater action in plantarflexors in children with mature gait. Aside from propulsion created in stance phase through plantarflexion, stability is also needed in stance phase. The Soleus is important during stance because it restrains dorsiflexion and brings the knee into extension (Jonkers et al., 2003). It can be seen as a st abilizing plantarflexor. The other two muscles attached to the fibula are Peroneus longus and Peroneus brevis, the everters of the foot. As the heel leaves contact with the ground as the foot rolls forward, the ankle (specifically, subtalar) joint invert s about 15 degrees (Anderson and Pandy, 2001). This implies that the everters would be active to keep the ankle from over inverting, causing injury. So from immature gait to mature gait, it is implied that plantarflexors increase in activity, and it is o nly when proper roll over and greater propulsion has been achieved does over inversion become a problem, thus requiring increased action of everters. Therefore, the faster increase in rigidity and strength observed at 48 60mos in the fibula can perhaps be attributed primarily to the increased actions of Peroneus longus and brevis. So despite the lack of attention to the fibula in most studies on locomotion, its analysis is valuable in this case for showing that changes in biomechanical properties (reflect ed by CSDs) do indicate the development of the lower limbs into propulsive limbs (Robinson et al., 1972; Wells et al., 2002) as gait matures. There is no evidence of any substantial differences in growth trajectories between AP and ML dimensions, contrary to what I had predicted, specifically for the femur and tibia. Despite

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99 the AP axis being the primary axis of motion for walking and running, the bones are surrounded on all sides by muscles that move the limb in more than one plane. The lack of differen ce between AP and ML growth trajectories helps to show how unreliable cross sectional geometry can be in reconstructing the loading environment since the bone is not reinforced in rigidity or strength along the AP axis, which is the axis of bending. Cross sectional geometry studies on quadrupeds like macaques (Demes et al., 1998, 2001; Schaffler et al., 1985) and sheep (Lieberman et al., 2004) likewise found no correlation between the axis of maximum rigidity and the axis of maximum strain. Ruff et al. (2 006) suggested that perhaps this is due to the bone having already adapted to the maximum loading by remodeling, similar to what Frost (1982) outlined. For example, they showed that ML in vivo strains were higher than AP in vivo strains during walking eve n though maximum loading was actually in the AP direction. The bone may have already adapted to AP loading. Additionally, the fact that not all bones are circular in cross section like the humerus and femur does not make it necessary for growth rates alon g different axes to differ. At any age or length, AP and ML CSDs may differ in magnitude, but the magnitude of increase in CSD may be equal along both axes. This demonstrates that cross sectional shape is more or less preserved: a newborn humerus is iden tifiable as a humerus and will continue to be humerus like throughout life. This agrees with Gosman et al. (2013), which found femoral and tibial shape to be preserved throughout growth. Frost (1987) explained how long bone shape is maintained as size in cal processes such as the actions of proteins. Bone morphogenetic proteins (BMPs) are especially important because

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100 they are highly involved in the development of cartilage and bone, e.g., inducing and regulating formation from mesoderm (Xiao et al., 2007) Geometry can also be attributed to mechanical forces. If we accept that the biomechanical properties of bones can be affected by mechanical forces after birth, then it also makes sense that these forces would have been shaping the bone since its format ion. Early involuntary muscle contractions and later voluntary movements by the fetus generate forces on bone that influence cartilage formation and ossification (Carter et al., 1996). In support, Carter and Beaupre (2007, p. 78) showed how inadequate mu scle contractions in utero can lead to a relatively weaker, less developed bone. Both biochemical and mechanical processes play a role in bone formation and therefore not mutually exclusive. in rigidity and strength in the lower limbs during the later ages after the child has been habitually walking for some time, having more or less developed a bicondylar angle and mature gait. Additionally, for its length, the humerus becomes rigid and str ong quite early in life at a pace unmatched by either the femur or tibia until 9mos and at 9mos only. While human crawling may be the closest we can get to comparing human quadrupedalism and non human quadrupedalism, crawling is different in a few ways fr om non human quadrupedalism. While body weight is more evenly distributed over four limbs, it is actually the upper limbs that are responsible for supporting the body during the stance phase in crawling (Patrick et al., 2009). The stance phase involves o ne limb supporting the body as the other limb is picked up and repositioned in front in order to move the body forward. In walking, one leg supports the weight of the entire body in stance phase. The upper limbs therefore experience a different kind of l oading as part of their role in crawling stance phase. Another difference that is more obvious is the fact that human infants crawl on their knees, which really reflects the longer lower limb in humans (i.e., lower intermembral index).

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101 The femora are the primary weight bearing lower limb bones during crawling. It is not until around 9mos that CSD becomes positively allometric in both the femur and tibia, indicating the bearing once the child is standing. The uppe r limb loses its involvement in body weight support once the child is habitually walking upright. This means that the upper limbs can be involved in other forms of physical activities. In the upper limb bones, there appears to be high variance in rigidit y and strength growth around 60mos. This high variance is perhaps reflecting the fact that some individuals are exerting more force on their upper limbs, particularly the forearm, resulting in an expanded diameter, thus increasing relative rigidity and st rength. While geometry is overall preserved, such that a humerus will always look like a humerus, bone is fairly plastic in response to mechanical loading, depending on such factors as magnitude and frequency. The introduction of a new physical activity and the prolongation of the activity can lead to increased rigidity and strength via periosteal apposition (to increase diaphyseal diameter) or endosteal contraction (to add cortex) (Jee et al., 1991; Ruff et al., 1994; Woo et al., 1981). It is not uncomm on for young children in numerous societies today and certainly in this Amerindian population to participate in physical labor. In these societies, children are considered economic capital, capable of assisting the community in foraging or agricultural la bor. Carrying goods, gathering food, and holding younger siblings are a few such activities that would have been suitable for social development and cultura l education (Bock, 2002). Significance of Studying the Ontogeny of Bipedality We can infer bipedality in fossil hominins because bipedalism is associated with certain morphological signatures seen directly on the skeleton. Specific anatomical modificati ons have

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102 taken place over the course of hominin evolution, resulting in efficient obligate bipeds. One of the many important questions we can ask is how did later hominins become such efficient bipeds? One route to take in the exploration of this complic ated question is to study the ontogeny of bipedality in children through the use of cross sectional data, in my case. Studying the ontogeny of bipedality is informative of the evolution of bipedalism for a few reasons. From birth to crawling to walking, children experience a number of necessary musculoskeletal changes. These changes can and have been investigated to understand how they contribute to bipedal efficiency. Likewise, we can investigate how forces change during the transition from crawling (q uadrupedalism) to walking (bipedalism). While we may be able to discern the morphological traits of bipedal animals, ontogenetic studies provide a more dynamic view of the factors shaping bipedal locomotion, which can help us to make inferences about past circumstances (e.g., environments, processes) leading to the bipedal form. When trying to understand past organisms and environments, it is valuable to use the facultative (i.e., non habitual) bipedalism displayed by some extant non human primates and presumably by the earliest hominins. Macaques trained to walk bipedally over the course of a decade showed a gait pattern similar to the immature gait pattern of children, mainly due to an undeveloped bicondylar angle (Nakatsukasa et al., 1995). In the early walking stage, children adopt a bent knee and bent hip posture. The adoption of this posture is similar to the compliant gait used by some arboreal quadr uped monkeys to lower vertical peak reaction forces while moving on branches (Schmitt, 1999). Additionally, finding that pressure peaks are lower in the li mb loading compared to mature walking. This may explain the sudden increase in CSD growth

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103 rate at 48 60mos. The posture associated with mature gait, while providing stability and efficiency, is costly in terms of the high load incurred on the lower limbs A point that should be emphasized from Cowgill et al. (2010) is that going from crawling to toddling to walking, the skeleton is not simply progressing from an underdeveloped form to a developed, adult form. Instead, the authors propose that we should view the whole ontogeny of walking as involving distinct phases of morphological and developmental (e.g., neurophysiological) changes. When reviewing the findings of bipedalism studies, this idea is apparent in that certain specific morphological features need to develop before children become mature walkers. Once these features arise, the fine tuning of them can be more progressive. Regardless of how long the macaques were trained to walk, their bipedality was constrained by their body structure. My fi ndings show distinct periods of change corresponding to postural changes. While relative rigidity and strength decreased over time for all bones as length increased, growth in length and CSD were not constant throughout development. As explained by the b one response models of such authors as Frost (1987) and Lanyon (1982), bone is a fairly (but not perfectly) efficient tissue, remodeling only under certain circumstances. It therefore follows that CSD growth should increase (via increased shaft diameter) in response to increased loading rather than maintain some constant rate of change. If we apply this view to the evolution of hominin bipedalism, we can think of bipedalism as arising from the appearance of a few key anatomical features. These features mu st be in place, and it must be somehow energetically worthwhile to be at least a facultative biped, even if energy efficiency was not the original selective force driving the evolution of bipedalism. Thinking about the evolution of bipedalism in this way would allow us to better appreciate the

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104 possibility that bipedal locomotion can correspond to varied body structures (i.e., suites of morphological features) and that body structures of early hominins need not resemble our own. Future Directions To expand upon the present study, the next step would be to carry out in vivo studies of children in the crawling and walking phases. Cross sectional data is useful for studying allometry and mapping growth trajectories, as demonstrated in this project. From such analyses, I have attempted to make inferences about the timing of a specific loading event: bipedal walking. However, even concluding anything about the loading history is problematic because strain is not always going to directly reflect the di rection and magnitude of stress, as I have previously emphasized. On the other hand, an in vivo study would allow me to directly measure the direction and magnitude of forces acting on the body. Specifically, I want to measure the ground reaction force ( GRF), the equal and opposite force that the ground exerts on the body in contact with it. GRFs measure the forces that the body (specifically the limbs) experiences during both rest and movement. As I have discussed in the Literature Review chapter, Yozu et al. (2013) is the only study to date that has measured GRFs during crawling in children. Hallemans et al. (2005) measured GRFs in toddlers only a few months after the onset of walking to compare with adult gait patterns. Cowgill et al. (2010) compare d GRFs between young and mature walkers (in reference to immature and mature gait patterns, respectively). In order to provide a more fluid view of kinematic changes over time, I propose measuring GRFS through all phases: crawling, toddling, and walking. This would necessitate that the study be a longitudinal one since all phases should be analyzed in the same individual. In addition to GRFs, I also propose measuring pressure distribution to analyze how force is distributed by the limbs as limb posture c hanges, which can provide insight into balance, high stress regions, etc. Because

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105 force data can provide information that cannot be extracted from cross sectional data alone, it is valuable in adding a new dimension to interpretations of morphological dat a. Aside from morphology, we may also think about approaching the study of bipedalism from the standpoint of life history. In light of the possible effect of weaning stress on long bone growth for this sample of Amerindian children, it seems a worthwhil e endeavor to further investigate how weaning affects growth and activity patterns among human populations. Timing of weaning and its effects can then be compared among the apes. We already know that the timing of events has an influence on morphology, b ut the connection to bipedalism should be further explored. An integration of experimental data on early walking in children with life history data collected for extant apes and in ferred from fossil hominins may add some insight into the evolutionary hist ory of bipedalism.

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112 Wells JP, Hyler Both DL, Danley TD, and Wallace GH. 2002. Biomechanics of growth and development in the healthy human infant: a pilot study. J Am Osteopath Assoc 102(6):313 319. Woo SL, Kuei SC, Amiel D, Gomez MA, Hayes WC, White FC, and Akeson WH. 1981. The effect of prolonged p hysical training on the properties of long bone: a study of Wolff's law. J Bone Joint Surg 63(5):780 787. Xiao Y T, Xiang L X, and Shao J Z. 2007. Mini Review: Bone morphogenetic protein. Biochemical and Biophysical Research Communications 362:550 553. Y aguramaki N, and Kimura T. 2002. Acquirement of stability and mobility in infant gait. Gait & Posture 16:69 77. Yozu A, Haga N, Tojima M, Zhang Y, Sumitani M, and Otake Y. 2013. Vertical peak ground force in human infant crawling. Gait Posture 37:293 295.

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113 BIOGRAPHICAL SKETCH Kim N Le earned her Bachelor of Science degree in Evolutionary Anthropology from Duke University in spring 2012. Her senior thesis, Sexual dimorphism in the human mandible and its biomechanical implications was supervised by Dr. Chris Wall. At the 82 nd annual American Association of Physical Anthropologists (AAPA) conference, she presented a project on bone biomechanics: Spatial variation in mandibular bone stiffness and its effect on structura l bending stiffness: a test case using the Ta Forest monkeys She earned her Master of Arts in Anthropology fro m the University of Florida in s Using cross sectional properties to investigate the advent of walking in a sa mple of Central Californian Amerindian children was supervised by Dr. David Daegling. Kim will continue onto a doctoral degree in anthropology.


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