|UFDC Home||myUFDC Home | Help|
This item has the following downloads:
1 INTRINSIC VARIABILIT Y AND SCALING OF THE MODERN HUMAN FOOT: S EXUAL DIMORPHISM, ECOGEOGR APHICAL PATTERNING A ND BIOMECHANICAL PERSPECTIVES By PAUL D. EMANOVSKY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSIT Y OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010
2 2010 Paul D. Emanovsky
3 To my family
4 ACKNOWLEDGMENTS I would like thank my doctoral committee and my friends and colleagues at the University of Florida, at the Joint POW/MIA Accounting CommandCentral Identification Laboratory (JPAC CIL), and beyond, for their guidance and support throughout this entire process. I owe special thanks to Mike Warren, Tom Holland and John Byrd for accommodating a schedule of intermittent attendance and departure. I have learned a great deal from all of you and feel I have developed both personally and professionally thanks to your mentorship and friendship. I thank you all for providing me with opportunities to flourish. I owe extra special thanks to my family to whom this work is dedicated. Your love and support have always encouraged me. I owe my work ethic, education, and values to all of your influences in my life, your hard work and the sacrifice s that you have made so that I could pursue my dreams. My mother in particular was always exceptionally supportive of my goals and I know she would have been extremely proud of this accomplishment. My father taught me to lead by example and showed me that diligence is a virtue; both are lessons that have served me well. To my beautiful wife Laura, you have taught me so much about myself, life, and the pursuit of happiness in our time together so far. I look forward to continuously learning from you and about you for the rest of our lives. I thank you for your love and support what a wonderful world. Many mentors, friends, and colleagues have come and gone from my immediate sphere of influence throughout this journey. Even though, you may be out of sight at times, you are never out of mind. I am particularly indebted to my friends from the University of Indianapolis and Mercyhurst College. I thank Steve Nawrocki and Dennis Dirkmaat for the invaluable education and professional op portunities you have provided
5 me. Many thanks are owed to Joe Hefner, who has been a true friend and a constant throughout my career. I thank Derek Benedix, Elias Kontanis, and Carlos Zambrano for their friendship, insight, stimulating discussions, and g enerosity.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 8 LIST OF FIGURES ........................................................................................................ 10 LIST OF ABBREVIATIONS ........................................................................................... 12 ABSTRACT ................................................................................................................... 13 CHAPTER 1 INTRODUCTION .................................................................................................... 15 2 ANATOMY AND GROWTH OF THE FOOT ........................................................... 21 Anatomy .................................................................................................................. 21 Growth .................................................................................................................... 23 3 SEXUAL DIMORPHISM ......................................................................................... 27 Size Sexual Dimorphism ......................................................................................... 28 Cube Root of Body Mass Dimorphism .................................................................... 29 Persistence of Size Sexual Dimorphism ................................................................. 29 Dimorphism in Stature ............................................................................................ 30 Dimorphism of the Foot ........................................................................................... 31 4 ECOGEOGRAPHICAL PATTERNING ................................................................... 33 Patterning at the Cellular Level ............................................................................... 38 Breadth and Scaling ............................................................................................... 40 Foot Scaling and Stature ........................................................................................ 41 Cost of Locomotion ................................................................................................. 45 Effective Mechanical Advantage ............................................................................. 47 Stress Fractures ..................................................................................................... 48 5 RELATIVE VARIATION .......................................................................................... 57 6 MATERIALS AND METHODS ................................................................................ 64 Samples .................................................................................................................. 64 Error ........................................................................................................................ 66 General Statistical Protocol ..................................................................................... 68 Proportionality of the Foot ....................................................................................... 68 Sexual Dim orphism ................................................................................................. 71
7 Allometry and Ecogeographical Patterning ............................................................. 72 Predictive M odels and S caling ................................................................................ 73 Intrinsic Variation Between Groups ......................................................................... 76 Biomechanical Environment. .................................................................................. 76 7 RESULTS ............................................................................................................... 84 Measurement Error. ................................................................................................ 84 Proportionality of the HTH Cadaver Sample Foot .................................................. 84 Proportionalit y of the HTH Skeletal Sample Foot ................................................... 86 Sexual Dimorphism ................................................................................................. 90 Allometry and Ecogeographical Patterning ............................................................. 91 Predictive Models and Scaling ................................................................................ 93 Intrinsic Variation Among Groups ........................................................................... 94 Biomechanical Environment ................................................................................... 94 8 SYNTHESIS AND APPLICATIONS ...................................................................... 140 Measurement Error ............................................................................................... 140 Relative Variability ................................................................................................ 142 Proportions of the Foot: Dimorphism and Patterning ............................................ 143 Sexual Dimorphism ............................................................................................... 145 Breadths and Scaling ............................................................................................ 148 Allometry ............................................................................................................... 150 Biomechanical Environment ................................................................................. 155 Body Mass ............................................................................................................ 157 Stature .................................................................................................................. 162 9 CONCLUSIONS ................................................................................................... 173 LIST OF REFERENCES ............................................................................................. 176 BIOGRAPHICAL SKETCH .......................................................................................... 188
8 LIST OF TABLES Table page 6 1 Mean age, mass, and stature of the HTH cadaver sample ................................. 78 6 2 Mean age, mass, and stature of the HTH skeletal sample ................................. 78 6 4 Correlation coefficients for selected tarsals, and phalanges and foot length ...... 81 6 5 Correlation coefficients for metatarsal length and foot length ............................. 82 6 6 Correlation coefficients for the metatarsal breadths vs. foot length .................... 82 7 1 Technical error of measurement and coefficient of variation of error ................. 97 7 2 Percent measurement error (%ME) of eight variables ........................................ 97 7 3 HTH cadaver sample foot length, breadth and foot length to statur e descriptive statistics ............................................................................................ 98 7 4 HTH skeletal sample foot length, breadth and foot length to stature descriptive statistics ............................................................................................ 98 7 5 Two way ANOVA results for skeletal variables ................................................... 99 7 6 Descriptive statistics for the maximum lengths of the metatarsals .................... 100 7 7 Descriptive statistics for breadth measurements of the metatarsals ................. 102 7 8 Descriptive statistics for length and breadth measurements of the calcaneus 106 7 9 Descriptive statistics minimum breadth of the talus and the maximum lengths of the talus, cuboid and navicular ..................................................................... 106 7 10 Descriptive statistics of t he lengths of the first pedal ray proximal and distal phalanges ......................................................................................................... 109 7 11 Descriptive statistics for selected ratios (variable / foot length) ........................ 111 7 12 Two way ANOVA of metatarsal to metatarsal ratios ......................................... 112 7 13 Two way ANOVA results for metatarsal to stature ratios .................................. 113 7 14 Two way ANOVA results for metatarsals to foot length ratios .......................... 113 7 16 Two way ANOVA of robusticity indices ............................................................ 116 7 17 Results of the Quick Test analysis o f metatarsal robusticity ............................. 116
9 7 18 Bias corrected coefficients of variation (V*) for pooled groups ......................... 117 7 19 Bias corrected coefficients of variation (V*) for sub groups ............................... 117 7 20 Results of t tests for coefficients of variation of correlated variables ................ 118 7 21 Observed ratios of dimorphism versus expected based on the cube root of body mass dimorphism ..................................................................................... 118 7 22 Indices of sexual dimorphis m for selected variables of the HTH skeletal sample .............................................................................................................. 119 7 23 HTH cadaver sample RMA regressions on foot length ..................................... 120 7 24 HTH skeletal sample RMA regressions on stature ........................................... 122 7 25 HTH skeletal sample RMA regressions on foot length ..................................... 123 7 26 HTH skeletal sample RMA regressions on body mass ..................................... 124 7 27 Summary of deviations from isometry after log log bivariate RMA regressions 125 7 28 LS regression equations for predicting stature from foot length ........................ 127 7 29 LS regression equations for predicting stature from the metatarsals ................ 127 7 30 LS regression equations for predicting foot length from the metatarsals, calcaneus, and cuboid ...................................................................................... 128 7 31 LS regression equations for predicting body mass from calcaneus and talus .. 129 7 32 Eco groups RMA regressions of predicted foot length on predicted tibia and predicted femur lengths .................................................................................... 132 7 33 Results of F test comparisons of V2 between groups ....................................... 132 7 34 Descriptive statistics for the effective mechanical advantage ........................... 134 7 35 Results of calculated muscle force (in N) to counter ground reaction force ...... 137 7 36 Descriptive statistics for the calculated ankle joint force ................................... 138 7 37 RMA regressions of talar and calcaneal dimensions and joint reaction force ... 1 39 8 1 Indices of sexual dimorphism for selected variables from v arious populations. 168 8 2 Demographics for HTH test of efficacy sample for body mass predictive equations .......................................................................................................... 172
10 LIST OF FIGURES Figure page 2 1 Three major regions of the foot as related to their bony morphology. ................. 26 2 2 Illustration of the windlass mechanism .............................................................. 26 4 1 Relationship of predicted limb lengths calculated for hypothetical statures for Black and White males and Black and White females. ....................................... 51 4 2 Least squares regression residuals of the sum of CUBMAX + CALMAX + 3MTMAX on Foot length for combined Black and White males .......................... 52 4 3 Theoretical scenarios for scaling of the foot and its relationship to the bending moment arms of ground reaction force at heel strike ........................... 53 4 4 Theoretical scenarios for scaling of the foot ...................................................... 54 4 5 Theoretical effect of positive allometry of foot length to stature .......................... 55 4 6 Schematic representation of foot and components for calculating effective mechanical advantage (EMA). ............................................................................ 56 6 1 Histogram illustrating the age distribution of the HTH skeletal sample. .............. 80 6 2 Diagram of force vecto rs acting on the ankle joint. ........................................... 83 7 1 Box plots of the maximum lengths of the five metatarsals. .............................. 101 7 2 Box plots of medial to later al breadths of the head and base of the first metatarsal. ........................................................................................................ 103 7 3 Box plots of medial to lateral breadths of the base of metatarsals two through five .................................................................................................................... 104 7 4 Box plot of ratio of first metatarsal head width to length ................................... 105 7 5 Box plots of length and breadth measurements of the calcaneus. ................... 107 7 6 Box plots of minimum breadth of the talus and the maximum lengths of the talus, cuboid and navicular ............................................................................... 108 7 7 Box plots of maximum lengths of the first pedal ray proximal and distal phalanges ......................................................................................................... 109 7 8 Box plot of ratios of the first toe, the first metatarsal, the calcaneus and the posterior calcaneus length, to foot length ......................................................... 110 7 9 Ratio values of metatarsals compared to one another. .................................... 111
11 7 11. Box plots of robusticity indices for metatarsals one through fi ve ...................... 115 7 11 Bivariate plot of HTH skeletal sample foot length to stature ............................. 121 7 12 Bivariate plot of HTH skeletal sample foot l ength to body mass ....................... 121 7 13 Box plot of the ratio of the medial to lateral breadth of the head of the first metatarsal to the maximum length of the first metatarsal ................................. 126 7 14 Relationship of predicted foot lengths calculated for hypothetical statures for Black and White males and Black and White females. ..................................... 129 7 15 Relationship of predicted foot lengths calculated for hypothetical first metat arsalsfor Black and White males and Black and White females .............. 130 7 16 Relationship of predicted foot lengths calc ulated for hypothetical maximum lengths of the calcaneus for Black and White males and Black and White females. ............................................................................................................ 131 7 17 Box plot of EMA calculated using the third metatarsal. ..................................... 133 7 18 LS regression of the effective mechanical advantage (calculated using the thrid metatarsal as a component of the out lever) versus body mass (in kg). ... 134 7 19 Combined sample LS regression of PCAL on Rthrdmax (CALMAX PCAL) + CUBMAX + 3RDMAX. ...................................................................................... 135 7 20 Sub sample LS regressions of PCAL on Rthrdmax = (C ALMAX PCAL) + CUBMAX + 3RDMAX ....................................................................................... 136 7 21 Muscle force (in N) required to counter GRF ................................................... 137 7 22 LS regression of body mass (in kg) and calcul ated ankle joint forces .............. 138 8 1 Log Log plot of foot length to stature for the HTH cadaver sample ................. 169 8 2 Log Log plot of f oot length to body mass for the HTH cadaver sample ........... 170 8 3 Illustration of the consequence of positive allometry relative to stature. ........... 170 8 4 Box plots of the Body Mass Index (BMI ) for the HTH skeletal sample. ............. 171 8 5 Box plots of the robusticity index for short and long first metatarsals .......... 171
12 LIST OF ABBREVIATION S ANOVA Analysis of Variance AER apical ectodermal ridge CMNH Cleveland Museum of Natural History COL cost of locomotion COP center of pressure COT cost of transport EMA effective mechanical advantage FGFs fibroblas t growth factors GRF ground reaction force HTH HamannTodd Collection ISD i ndex of sexual dimorphism JSD joint size dimorphism Le effective limb length LR linear regression LS l east squares regression MT metatarsal OLS Ordinary l east squares PZ progress zone RMA r educed m ajor a xis regression V coefficients of variation
13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INTRINSIC VARIABILIT Y AND SCALING OF THE MODERN HUMAN FOOT: S EXUAL DIMORPHISM, ECOGEOGR APHICAL PATTERNING A ND BIOMECHANICAL PERSPECTIVES By Paul D. Emanovsky December 2010 Chair : Michael Warren Major: Anthropology The current study examines the variability of foot dimensions and foot elements from an allometric perspective utilizing differences in size between the sexes and proportional differences among modern humans from disti nct ecogeographical backgrounds to examine intrinsic variability and withinfoot scaling. Allometry of foot length to stature, as well as proportions of foot length to limb length; foot elements to foot length; and foot elements to body mass was investigated for a sample of American Black and White males and females. These groups are known to vary in their body proportions due to sexual dimorphism and ecogeographical ancestry. C orrelation analyses, analysis of variance (ANOVA), coefficients of variation (as well as derivatives thereof), and bivariate linear regression of logari thmic transformed variables are used to investigate deviations from isometry (allometric scaling), intrinsic variability, and other issues rel ated to human sexual dimorphism, the ecogeographical pattern, and the biomechanical environment. Results of this study show that t he female foot is dimorphic in both absolute terms and proportionally to stature. Allometric analysis reveals that only the White female group scales with isometry for foot length to stature. All other groups scale positively, that is, t hey have larger feet than expected based on
14 the principle of geometric similarity. The foot conforms to the expected ecogeographical pattern among both males and females as the ancestrally tropically adapted group have longer feet for a given stature. It was found that it is the meta tarsal region that is driving most of the variation in the foots conformance to the ecogeographical pattern. Proximo distal and length to breadth variability was explored using coefficients of variation and their derivatives comparing the calcaneus to the first metatarsal. It was found that the more distal element was not more variable, nor was it more positively allometric. These findings are contra to what other researchers have found with regard to relative variability and allometric scaling of the major long bones of the limbs. Effective mechanical advantage at the ankle was found to be similar for all groups. Modeling of the joint force reactions at the ankle indicate that that the joint surfaces scale isometrically f or body mass. L inear regression models are presented for estimation of body mass, stature, and foot length from various pedal elements. E quations for predicting body mass from the calcaneus and talus were found to be an improvement upon existing methods for estimation of body mass in human populations based on femoral head dimensions. Furthermore, equations presented here for estimating stature from metatarsals provide an important tool for forensic and bioarchaeological analyses, as previously published methods are based on inadequate sample si zes for Black males and females.
15 CHAPTER 1 INTRODUCTION In this study I investigate the proportions of the human foot skeleton relative to foot length (fleshed), cadaveric stature and body mass The sample used in the study is drawn from four groups : American Black and White males and females. C orrelation analyses analysis of variance (ANOVA), coefficients of variation, and bivariate linear regression of logarithmic transformed variables are used to invest igate deviations from isometry ( geometric similarity ) and intrinsic variability in relation to human size sexual dimorphism ( when one sex within a species is, on average, larger than the other ) and the ecogeographical patterning of human limbs Specifica lly this study examines the patterning and morphology of the human foot as it relates to A llen s (1877) ecogeographic rule, which posits that mammals in cold environments will have shorter appendages (cold adapted) than their interspecific counterparts in warm regions who should tend to have longer more narrow appendages (tropically adapted) It is not the goal of this study to establish whether a longer more narrow foot (i.e. a tropically adapted phenotype) would be advantageous from a heat shedding per spective (or conversely whether a shortened limb is advantageous in a cold environment) but rather the goal is to investigate pedal proportions from the perspective that the foot a s a functional morphological unit must covary with the limbs. This covari ation wil l be placed in the context of developm ental and phenotypic patterning within and among human groups and the influence of these factors on limb shape and proportions (particularly the lower limb ). Th e well known patterns of scaling, or allometry for the limb long bones will also be used to investigate the proportionality of the foot from a mechanical point of view. I work from the assumption that numerous factors including climatic adaptation,
16 developmental limitations, safety factors, and selec tion for tissue economy, to name a few, have worked in conjunction with and possibly in opposition to one another to create the phenotypical patterns observed among modern human groups. I also assume the ontogeny of these morpholog ies and their persiste nce in modern populations are due to genetic conservation. I n addition I discuss how the detection of deviations from isometry that is, deviations from geometric similarity, is dependent on the choice of the comparative size measure a nd the composition of the sample P ractical applications such as estimation of body mass, stature, and foot length from tarsals and metatarsals are also discussed. The human foot has been the focus of anthropological investigation for sometime (Morton 1922 1924 1927). Early researchers focused on the comparative anatomy of the human foot to other primates in an effort to glean evolutionary transitions and to identify morphological indicators useful for interpreting the fossil record; they were also hoping to gain an ap preciation of modern human variation. To that end, researchers also focused on comparisons between different races or geographical populations. For example, Davenport (1932) summarizes several anthropometric investigations : In relation to stature s ome Melanesians have longer feet than most Europeans, while the Amerindians and the Chinese have relatively short feet. In general, all anthropometrists who have measured in the field have found that Negroes [sic] have long feet. .The equatorial Negro is said to have relatively narrow feet, while those of the Amerindian are broad. (Davenport 1932: 172 ) Although such generalizations are antiquated and are not conclusively meaningful, they do demonstrate an important aspect of the study of human variati on w hen anthropologists and biologists describe a population or group as long er or short er in some character the comparison is necessarily with respect to another
17 variable ( e.g., stature) or group ( e.g., Melanesians versus Europeans). These comparisons, leg lengths, for example, are only informative in the context of the other variables and groups. In human studies the standardizing variable is usually a measure of size such as ov erall stature, skeletal trunk length, body mass, or a proxy for body mas s ( e.g., using the geometric mean of the variables under scrutiny ) Current research on scaling utilizes t he allometric method, which is the study of how organisms scale with size and whether shape changes occur with changes in size. If there is no change in shape, then the scaling that does occur is considered isometric, or geometrically similar. In allometric studies isometry is the standard expectation. D eviations from isometry are considered positive allometry if the change is in a positive directi on (i.e. bigger than expected) and negative allometry if the change is in the negative direction ( i.e., smaller than expected). Tests of deviations from isometry are varied ( Corruccini 1983; Jolicoeur 1984) ; however bivariate plots of logarithmically transformed variables are an intuitive and commonly used method to assess allometric relationships ( Jungers et al., 1995; Temple et al., 2008; Holliday and Franciscus, 2009) To test a llometric scaling such as proportions of foot length to limb length, fo ot elements to foot length, or foot elements to body size, differences between males and females a n d differences between ancestral, ecogeographical populations are used. Explicitly, the questions asked to investigate scaling relationships among these gro ups include: 1 ) Does the foot display sexual dimorphism proportionate to stature? 2. ) Does the foot conform to the ecogeographical pattern? 3.) H ow do individual bones of the foot scale to overall length of the foot, total body stature, and body mass? 4 ) What is the intrinsic variability of foot elements within groups and among groups ? 5 ) How do
18 the various theoretical and observed configurations of these elements affect the biomechanic s of the foot during locomotion ? The current study utilizes an thropometric data collected from the Hamann Todd Collection (HTH) The HTH consists of over 3000 skeletons originating from a cadaveric dissection collection currently housed at the Cleveland Museum of Natural History (CMNH). The available anthropometric data are combined with osteometric data from the foot in order to test proportionality and scaling consequences Todd and Lindala (1928) explain that each group, although American and generally from the lower social strata, is relatively homogeneous, where the White population is typically first generation American or foreign born Europeans, very few are of French extraction, considerably more of Italian origin, many of British birth or parentage, but a greater number hail from that region of Europe ex tending from the Rhine to Riga and from the northern seas through the hinterland as far as the Danube. Occasionally Balkan people are to be found among our dead ( Todd and Lindala, 1928: 38). The Black population is comprise d mostly Southern Blacks ma ny from Alabama Todd noted that the sample was representative of American Blacks which are in turn reliably representative of the actual African dimensions of individuals inhabiting the great expanse of Africa, lying behind the Western coast (Todd an d Lindala, 1928 : 38). Throughout this study t he term White is adopted to denote an ancestrally European sample and Black to denote an ancestrally African sample. The current study also utilizes the word race interchangeably with ancestry. Following Hefner (2007:17) ancestry is a concept used to denote groups of people who historically shared a common geographic origin and thus some common genetic material. The cadaveric anthropometric data confirm that the White and Black populations utilized in this study follow an expected ecogeographical pattern : tropically adapted
19 groups exhibit longer limbs D escribing a subsample of the cadaveric population utilized in this study Todd and Lindala (1928) found that the Black sample has on average longer legs than would be expected for a White of the same stature. However, they also note that thi gh length and lower leg length show no differences in proportions between sex or ancestry (based on a standardizing factor). Todd and Lindala (1928: 74) conclud e so far as the foot is concerned breadth is strictly proportional to true leg length and no sex or stock linked differences occur. But in length of foot there is a very definite sex linkage in the White only and stock linkage in the Negro. They go on to explain that when foot length is predicted for a Black male using the White male data, the result is close to the actual observed foot length, however, between Black and White females the observed is off the predicted value by 12 mm. The White female has a short er foot even w hen compared to limb length (a feature not shared by the hand). The male data are a potential nonconformance with expected proportions based on the ecogeographical pattern. The remainder of the dissertation is organized as follows. Chapter 2 provides a brief introduction to the anatomy of the foot, with a focus on the systems under scrutiny here, as well as brief review of some of the aspects of growth and developmental timing Chapter 3 provides an introduction to discussion o f size sexual dimorphism in terms of stature and body mass and foot length proportionate to stature. Chapter 4 introduces ecogeographical patterning and potential mechanisms for the formation of th ese phenotypes as well as discusses proportionality of the foot, elements of the foot and the biomechanical environment (e.g. cost of locomotion, effective mechanical advantage, stress fractures). Chapter 5 introduces relative variability and discusses
20 how variability can shed light on developmental and evoluti onary processes. Chapter 6 presents the analytical procedures used to investigate scaling differences, while Chapter 7 reports the results of those analyses. Chapter 8 discusses the implications of those analyses and emphasizes several applications deriv ed from the analysis of the data
21 CHAPTER 2 ANATOMY AND GROWTH OF THE FOOT Anatomy This study is primarily interested in the skeletal morphology of the foot, with some emphasis on muscloskeletal interaction and locomotion. As such, a brief introduct ion to the anatomy of the foot, with a focus on the systems under scrutiny here, is warranted. Each foot consists of 26 bony elements: 7 tarsals, 5 metatarsals and 14 phalanges. T he foot is often delineated into three segmented portions : the hindfoot midfoot and the forefoot. The hindfoot includes the talus and calcaneus, the midfoot is represented by the other five tarsals, and the forefoot is the metatarsal and phalangeal region (F igure 21 ) M ost of this study focuses on the hindfoot through the analysis of the calcaneus This study also focuses on the medial forefoot via the analysis of the first metatarsal and the first toe or the hallux ( the proximal and distal phalanges). These two areas are the focus because of their roles in locomotion. T h e hindfoot bears the brunt of the impact initially during gait (heel strike) and weight is then transferred to the more lateral aspects of the midfoot as gait proceeds L ocomotory forces are buffered by soft tissue and joint mechanics, and then the medial forefoot act s as a rigid lever, transmitting the propulsive forces and ground reaction forces at toeoff (see below). Muscle actions at the foot take place via the insertion of extrinsic ( originating from the outside) muscles of the lower leg as well as muscles intrinsic (within) to the foot. Extrinsic muscles of the lower leg insert ing on the foot can be divided into three components, anterior, posterior and lateral crural muscles. The anterior crural muscles ( Tibialis anterior Extensor hallucis longus Extensor digitorum longus and P eroneus teritius ) dorsiflex the foot and extend the toes. The posterior crural muscles are the
22 superficial group ( Gastrocnemius Soleus and P l antaris ) and the deep group ( Popliteus F lexor digitorum longus Flexor hallucis longus and Tibialis posterior ) These muscles extend the foot (plantar flexion). The tendons of the superficial group insert at the posterior calcaneus ( via the tendo calcaneus or Achilles tendon) The lateral crural muscles ( Peroneus longus and Peroneus brevis) extend and evert the foot. The independent subtleties of muscle action are dependent on the origin and insertion of each of these muscles and play a more complex role in the coordinated act of locomotion than is outlined above. The series of int rinsic muscles of the foot are necessary for joint maintenance, foot posture, and efficacy of gait. The dorsal muscle is the E xtensor digitorum brevis which extends the lateral toes. The intrinsic plantar muscles are divided into four layers with res pect to the plantar surface of the foot and begin underneath t he plantar aponeurosis, a layer of tough facia at the base of the superficial fascia that extends from the calcaneal tuberosity to the digits and is continuous on both sides with the dorsal fascia The plantar aponeurosis serves to compartmentalize the plantar surface of the foot and also acts as an attachment point for many layers of the fascia blending into the periosteum of the foot bones. The first superficial layer of intrinsic plantar mus cles just under the plantar fascia, is made up of t he Abductor hallucis which abducts and flexes the first toe ; the Flexor digitorum brevis and Abductor digiti minimi which flex the lateral toes and first toe, respectively. T he second layer consists of Q uadrates plantae and L umbricales which are also involved in flexion of the toes. The third layer includes the Flex or hallucis brevis and Adductor hallucis which flex and adduct the first toe respectively and the Flexor digii minimi brevis which flexes the fifth toe. Th e fourth
23 ( and deep est ) layer includes the Interossei dorsales and Interossei plantares which are involved in abduction and adduction of the toes respectively. One of the distinguishing characteristics of the human foot is the medial longitudinal arch (Figure 2 1) The arch is formed by the medial row of foot bones (calcaneus, talus, navicular, medial cuneiform and the first metatarsal), is supported by numerous plantar ligaments and muscles. When the arch is not needed, such as dur ing weight acceptance and quiet standing the arch loosens and lowers ; however, when in use the medial longitudinal arch acts as a rigid lever during the push off phase in gait (Zipfel et al. 2009). This is accomplished by t wisting the subtalar and talonavicular joints causing a clo sedpack (immobile) arch. Maintenance of this rigid lever is also facilitated by the windlass effect (Figure 2 2) when ligaments and tendons pass under the arch to the metatarsophalangeal joints and act as a pulley or bow s tring, bringing the two ends of the arch nearer to each other (Langdon 2005). The arch, both soft tissue and hard tissue components act to absorb stress es associated with locomotion. Growth A complete review of the development of the foot from embryo to adulthood is beyond the scope of this study (for a thorough review see Scheuer and Black 2000). However, to place adult morphological and scaling patterns in perspective, a brief review of some of the aspects of growth and developmental timing is nec essary. The review begins with hind li mb bud outgrowth and patterning followed by a presentation of the broad stages of fetal foot development, juvenile foot skeletal ossification, and timing differences in cessation of growth of the foot between males an d females. Adult postcranial morphology must first be considered at the cellular level (Lovejoy et al., 1999). Patterning and the development of the hind limb bud are under
24 the initial control of the apical ectodermal ridge (AER) and the progress zone ( PZ), an area proximal to the AER of the developing limb bud where initial cells (anlage) are assigned positional identity (Summerbell et al., 1973; Double 1994; Wolpert, 2002; Richardson et al., 2004). The progress zone model specifies that time spent wit hin the PZ determines the positional information and the subsequent cascade of specification that follows Positional information received in the initial stages of limb bud development determines whether the anla ge becomes the proximal skeletal element (h umerus or femur) or the distal elements ( e.g., radius and ulna or tibia and fibula) or the autopod region (hand and foot) This specification is based on the relative time spent within, or under the influence of the PZ morphogens or signaling molecules that act directly on cells Some recent work challenges the time spent in progress zone model in favor of prespecification of early progenitor cells (Dudley et al., 2002) ; however, both models contain time components in relation to the AER (which is in turn under control of various fibroblast growth factors (FGFs)) that affect cell survival and proliferation (Niswander, 2003). Embryologically, cartilaginous precursors of all foot elements have fully developed by day 57 in utero ( Scheuer and Black 2000). Primary ossification centers for metatarsals 2 to 5 appear between 8 and 10 weeks, and at 12 weeks for the first metatarsal (Scheuer and Black 2000) Between 5 and 6 months in utero the calcaneal primary ossification develops followed by the talus T h ese are the only two tarsals at birt h that have started ossification. Following birth, additional primary and secondary ossification centers commence. Metatarsal heads 2 to 5 fuse between the ages of 11 and 13 in females and 14 and 16 in males, the first metatarsal follows the pattern of the
25 phalanges and has a secondary ossification center at its base which fuses between 13 and 15 years in females and 16 and 18 years for males The foot completes growth with the fusion of the calcaneal epiphysis between 13 and 15 years in females and 18 and 20 years in males. Differences in the timing of growth and development of the foot in males and females have been noted (Anderson et al. 1956; Hoerr et al., 1962). For instance, A nderson et al. (195 6 ) using a lar ge semi longitudinal (n = 512) and a comparative true longitudinal (n = 20) series investigated the relative growth of the foot between boys and girls between 1 and 18 years of age. Anderson et al.s (195 6 ) results were based on measurements taken from r adiographs and anthropometrics of a heterogeneous sample of children from the greater Boston area. Their major findings indicate that at all ages below 13 years the mean foot lengths were the same for males and females, and the rates of growth were the sa me. Following 12 years of age males experience an increase in the rate and amount of growth of the foot while the female slower and less, reaching completion of foot growth by 14 years (75% of sample had completed growth by 17). Male growth continued until about 16 years (70% of sample had completed growth by 16). When compared to stature, t he rates of growth and the sum of the lengths of the femur and tibia (leg length) indicate that the foot grows by a factor of 6, while the leg length increases only by a factor of 2. This rate of growth coincides wit h the adolescent growth spurt, and illustrates that foot length does not increase in tandem with the lower leg T hus interruptions in growth of the foot during childhood ( e.g., injury or pathology) have a less deleterious effect on the overall length of the foot than an interruption to the growth centers of the femur or tibia have on stature.
26 hindfoot midfoot forefoot Figure 2 1 Three major regions of the foot as related to their bony morphology. Arrow indicates medial longitudinal arch formed by calcaneus talus, navicular, medial cuneiform, and the first metatarsal Figure 2 2 Illustration of the windlass mechanism, dotted line represents the plantar aponeurosis and the solid line is the tendon of Flexor hallucis longus The plantar aponeurosis and the tendons of the extrinsic muscles that insert in the distal foot act together to produce a pulley or bow string effect during locomotion that allows the joints of the foot to close pack and act as a single body.
27 CHAPTER 3 SEXUAL DIMORPHISM Size sexual dimorphism in this study was approached from both forensic anthropological and human biological perspectives. Forensic anthropologists, in general, focus on the elucidation of the most appropriate and informative osteometric applications, for instance, using size differences between human groups to determine the sex of an unknown skeleton. The human biological perspective focuses on examining human population variation. Both perspectives can inform paleoanthropologists and evolutionary biologists in their endeavors to explore similar types of variability in the fossil record and in the natural world. Instances of extrapolation from models using modern hu man variability to infer past biological phenomenon are c ommon in physical anthropology ( Susman et al., 1984; Holliday and Franciscus 2009) Mechanisms of and the basis for the evolution of size sexual dimorphism and its maintenance are beyond the scope of this study. However, some discussion of the ubiquity and persistence of sexual dimorphism is offered in terms of stature and body mass to put this work in context. The current studys primary interest in size sexual dimorphism of the foot is to exam ine dimorphism in the context of allometric scaling. The fact that sex can be determined from measurements of the bony foot is well established by various researchers who employ discriminant function models to classify unknown individuals into male or fem ale groups (Steele 1976, Robling and Ubelaker, 1997; Smith, 1997; Bidmos and Asala, 2003, 2004; Case and Ross, 2007). However, the utility of any method of discriminant function analysis is dependent on the sample from which the function is derived and it s applicability to the unknown sample being
28 tested. Differ ent levels of sexual dimorphism and scaling patterns can inform the choice of models for extending or expanding data into new realms and for interpolating pattering from the existing data. To th at end, a nthropometric data collected from cadavers prior to dissection w ere used to assess fleshed foot dimensions and foot length to stature ratios. Additionally 203 resampled individuals (White males, Black males, White females, and Black females) fro m the HTH were selected for an in depth analysis of bony elements of the foot (see below Materials and Methods). Inclusion of the anthropometric as well as osteometric data permits a full investigation of relative size while addressing scaling issues bet ween individual variables and different measures of body size (i.e., stature and body mass). Size Sexual Dimorphism I n terms of body size, sexual dimorphism is when one sex within a species is, on average, larger than the other Primary differences such as biomechanical adaptations of the pelvis related to obstetrics are not typically referred to as dimorphism (Plavcan, 2001). Thus sexual dimorphism usually refers to selected differences in size that are associated with evolutionary fit ness ( Plavcan and van Schaik, 1992, 1997). While humans do not display s exual dimorphism to the extent other primates do they are considered moderately dimorphic especially in terms of body mass (Plavcan, 2001) a lthough moderate body mass dimorphism does not always eq uate to moderate skeletal dimorphism. F or instance, Lague (2003) investigat ed the distal humeral and distal femoral joints of nine hominoid species and demonstrated a relatively h igh joint size dimorphism (JSD) in humans relative to other hominoids Lagu e and Jungers (1999) point out that a great deal of attention has been paid to dimorphic cranial and dental
29 differences while relatively little is known about the postcranial skeleton. Likewise, more attention has focused on the primary appendicular elem ents in humans and recent human ancestors, but only rarely have these investigations include d pedal elements. Although there is a plethora of research dedicated to sexual dimorphism of the foot in the forensic literature ( Steele 1976 ; Robling and Ubelaker, 1997; Smith, 1997; Bidmos and Asala, 2003, 2004; Case and Ross, 2007 ) t hese studies do not usually consider examining the data beyond its efficacy for the task at hand ( i.e., the utility for correctly assigning sex to an unknown skeletal element ). In this study dimorphic dimensions are examined relative to one another and within the context of allometric scaling with body mass, statu r e and foot length, and in some cases with respect to foot element length ( e.g., a breadth in relation to a length). Cube R oot of B ody M ass D imorphism D imorphism in linear skeletal measurements is generally proportional to the cube root of body mass dimorphism (Gingerich, 1981; Plavcan, 2001). That is, if a species demonstrates a body mass dimorphism ratio of 1.5 ( i.e., males 50% larger than females) the n linear skeletal dimensions are expected to show dimorphism of nearly 1.14 (males 14% larger than females ) (Plavcan, 2001). This generalization was used as a standardizing factor to assess the amount of sexual dimorphis m between the Black and White samples. R elative conformance to the expected linear dimensions (based on the cube root of body mass dimorphism) was contrasted with the observed dimensions of the bony elements of the foot. Persistence of S ize Sexual Dimor phism There is b road agreement that the persistence of size sexual dimorphism is due to adaptation to the differing reproductive roles of males and females (Fairbairn 2006)
30 Success for females is related to fecundity while success for males is related to mating success. Thus the two groups are expected to evolve toward separate sizes that maximize fitness (or optimal sizes ) (Fairbairn 2006). Dimorphism in Stature There is no doubt that human males tend to be taller than females. Gustafsson and Lind enfors (2004) analyzed male and female average heights from 126 populations; in every population the male average was greater than the female average. One question a researcher might ask is: A re there differences in the level of dimorphism among groups th at can be explained biologically? For instance, using a large series of height data for individuals from nonindustrial populations Holden and Mace (1999) investigated the effects of the division of labor, the type of subsistence and the practice of poly gny on the degree of dimorphism. Controlling for phylogenetic relatedness, they f ound that in societies where women contribute more to food production, the women are taller, than women in societies who contribute less to food production. This finding may be due to improved nutrition (Holden and Mace, 1999). Another question, in terms of differing levels of dimorphism is: do populations that are larger (in stature) exhibit greater levels of dimorphism? Gustafsson and Lindenfors (2004) analyzed differenc es in stature between males and females in 12 6 human populations, and suggest that size sexual dimorphism and stature in humans are actually independent. In other words, Renschs rule ( species with larger males than females are hyperallometric in size sexual dimorphism) is not true for humans when both comparative phylogenetic and non phylogenetic analyses are examined.
31 D imorphism of the F oot T he tendency for males to be larger than females begs investigation of dimorphism of the foot in terms of relat ive size. For instance, relative to stature, do females have smaller feet than males? S exual dimorphism in the fleshed foot is noted in a large sample (2208 females and 1774 males) of living U.S. military members (Parham et al., 1992). Using Parham et al.s data, Wunderlich and Cavanagh (1999, 2001) have shown, that male feet are longer and broader than females when relative size (stature) is controlled. Moreover, u sing several soft tissue anthropometric measurements the authors demonstrate that female feet are not isometrically scaled versions of the male foot but rather the female foot displays shape differences as well Fessler et al. (2005) call into question foot size dimorphi sm ( relative to stature) by establishing contradictions in several studi es For instance, among the 20 populations ( studied or synthesized by Hr 1925, 1928, 1935; as reported in Fessler et al. 2005:46) females in five populations presented foot to stature ratios equal to or greater than the males (4 were greater; 1 was equal). Fessler et al. (2005) point out that Baba (1975) and Anil et al .s (1997) foot length to stature ratios (FL:STAT) between males and females are not constant. Fessler et al. (2005) claim to have definitively put [ th e] question to rest (Fessler et al. 2005: 51) regarding h uman foot sexual dimorphi sm A fter a re analysis of three published datasets (Davis 1990; Parham et al. 1992; and Ozalslan et al., 2003) and after conducting an analysis of the Steggerda collection foot tracings using ANOVA Fessler et al. (2005) conclude that the relationship of foot length t o stature is linear and proportionate to staturefemale feet are just smaller.
32 What such proportional differences do not indicate is whether the foot is scaling isometrically with stature in males and negatively for females, or if the foot is negatively allometr icly scaled relative to stature in males but isometrically in females, or positively relative to stature in males and either negative or isometric scaling in females Or perhaps the foot is scaling to another feature entirely. Among modern humans, t he smaller foot size relative to stature in females has led some authors to argue for a preference by males to select smaller females T he smaller foot observed among modern females could potentially be indic ative of this phenomenon (Barber 1995; Fes sler et al. 2005).
33 CHAPTER 4 ECOGEOGRAPHICAL PATT ERNING Ecogeographical patterning first pointed out by Bergmann (1847) and Allen (1877), refers to patterns of biological variation found among species inhabiting similar environmental or geographical niches. Bergmanns rule states that, if two mammals are of similar shape but different in body size the smaller animal will lose heat more efficiently (and thus are better adapted to hot climates) Allens rule is an extension/ corollary to Bergman n s and applie s to limbs in colder climates mammals should have shorter, broader limbs Recently the universality of Bergman ns rule has been questioned (reviewed in Ashton et al. 2000; and Blackburn et al. 1999). Ashton et al. (2000) nevertheless found br oad support for the rule, temperature and latitude being nearly equally strong predictors of body size. However, the proposed mechanism of cold adaptation due to the smaller surface areato volume ratio is not entirely realized, because smaller mammals ar e not conforming any more strongly to the rule than larger animals. Blackburn et al. (1999:69) suggest a modification of the rule: Bergmann s rule is the tendency for a positive association between the body mass of species in a monophyletic higher taxon and the latitude inhabited by those species Less attention has been paid to Allen s rule directly. Hanna and Brown (1983) review human heat tolerance and mention an observation by Whittow (1973) that pigs reared outdoors in a cold environment have short er legs than littermates reared indoors. Blood flow during development is believed to be the causative mechanism as blood flow reduct ion may lead to a less than ideal realization of genetic potential. Investigation into foot or appendage proportions is n ot typically undertaken w ith testing the possible
34 benef its of thermoregulation in mind. T hat is an explicit test of surf ace areato mass ratios are often not the focus, but locomotion, digging, flight, and climbing are. Thus very few direct tests for Alle ns rule exist However, Stevenson (1986) explicitly tested Allens rule for North American rabbits and hares. Using the relationship of ear tail and hind foot lengths to basilar skull length Stevenson (1986) plotted these against average air temperature and found a negative correlation between foot length, which he interpreted as non conformance to Allens r ule. Functional hypotheses for larger feet in cold er climes, e.g. snow shoes may trump the thermoregulatory benefits. Nudds and Oswald (2007) c ontend that Allens rule remain s largely unsupported. In fact, they question whether the thermoregulatory benefits of such a mechanism are beneficial enough to be considered adaptive. In humans, ecogeographical patterning includes relatively narrow bodied and long limbed (i.e., increased linearity) individuals from warmer climes and stouter bodied and stouter limbed individuals from colder climes. For recent Europeans the shift in ecogeographical patterning is believed to have occurred approximately 20,000 years before present ( Holliday, 1995; Holliday and Ruff, 2001) During the Early Upper Paleolithic period Europeans limb proportions were similar to recent SubSaharan Africans, but during the Late Upper Paleolithic period European and Early Holocene Mesolithic individuals fall within the range of modern European variation (Holliday, 1995; Holliday and Falsetti, 1995). B ody proportions have been investigated extensively from many perspectives, all toward a variety of goals including understanding the influence of proportions on thermoregulation, biomechanics, human evolution, growth and development, and
35 human identification (Ruff, 1991, 1994; Bindon and Baker, 1997; Holliday, 1997a,b; Ruff et al., 1997; Holliday and Falsetti, 1999; Warren et al., 2002; Haeusler and McHenry, 2004; et al., 2007). Proportional variation in both modern humans and their early ancestors and this relationship to thermoregulation is an influential factor in human evolution research. Studies of proportional variation and these consequences center around changes in a groups surface areato mass (SA/M) ratio. For instance having more surface area relative to mass helps shed excess heat (through perspiration and evaporation) while less surface area better retains heat Vie wed this way, researchers conceptualize the body as a cylinder where pelvic breadths combine with stature information to gauge linearity (Ruff, 1991, 1994). Ruff (1991) has shown that despite variations in stature, populations living in similar climates maintain similar SA/M ratios by limiting variation in body breadth. Studies of proportionality for the limb bones t ypically focus on long bone measurements and ratios ( e.g., crural and brachial indices) to compare ratios These are reflective of limb prop ortions and the variation there of ( Holliday, 1999; Holliday and Ruff 2001) In a recent experimental study of Allens rule, Tilkens et al. ( 2007) tested the effects of limb length on the metabolic cost of temperature maintenance, and found that short lim bs reduce metabolic cost (measured by resting metabolic rates) while longer limbs resulted in greater heat dissipation. The persistence of the phenotypic pattern in modern groups is a wellrecognized phenomena that also has consequences in terms of practi cal applications such as estimation of stature for the skeletal remains of an unknown individual. P opulation specific e quations must be used or the target stature for the individual will be incorrect. This can be graphically illustrated by plotting predicted limb lengths (femur + tibia) for
36 any given stature using population and sex specific regression formulae following Trotter (1970) (Figure 41). Recently cross sectional geometry studies of long bones have been incorporated to relate activity and ro busticity (muscle mass) i nferences o f lifestyle and subsistence patterns (Ruff et al., 1993; Ruff, 2000; Stock, 2006; Carlson et al., 2007) drawn from this line of research seem promising since they incorporate local stimuli affecting bone growth and proportional variation. Proportionality studies typically focus on the limbs and long bone measurements relative to height and trunk length. Some attention has been given to body size and scaling of the hands and feet of lesser primates (see Lemelin and Jungers 2007), but far fewer studies have focused on allometry of the foot in anatomically modern Homo In this study I am not evaluating whether the persistence of the ecogeographical pattern in limb lengthening /shorting is truly adaptive for heat dissipat ion /retention For example, m echanisms involved in the persistence of long limbedness in individuals and groups who have left the tropical environment are outside the scope of this work. I work under the assumption that numerous factors, including climat ic adaptation, morphological constraints, safety factors, selection for tissue economy, susceptibility to epigenetic influences, to name a few have contribute d to the original development of this morphology and maintain its persistence in modern populations on the basis of genetic conservation. In this study I am investigating how the bones of the foot scale in relation to the limbs (as inferred from stature) and body mass. When anthropologists describe limb length they do so with respect to another var iable or group (see above). T ypically the variable is a nother measure of size such as
37 stature or skeletal trunk length. The lower limb is a direct contributor to stature and thus when we say the leg is long compared to stature; we are saying that there i s a proportional difference relative to a size variable or in reference to another group ( e.g., a White male versus White female) Long limbs in tropically adapted groups are long relative to stature ( the trunk plus the lower limb) ; however, the lower lim b as a component of stature may confound the comparison. Nevertheless, i n tropically adapted groups the upper limbs are also proportionally longer a biological scaling difference, since they are not a component of stature. If the foot scales in the sam e manner as the other long bones ( i.e., proportionally) the foot should be longer in ancestral tropically adapted groups. However, if a functional or mechanical reason is the cause, and the foot scales to absolute stature or to body mass, ( or to something else ) then there is no a priori reason to assume that the foot would be elongated in a tropically adapted sample. Early research into foot length to stature ratios yielded conflicting results. Giles and Vallandigham (1991:1135) point out that Topinard ( 1876) provides ratios of foot length to stature for various populations ranging from 14.9% to 18.1%, while Martin (1914) suggests that there is not great variation of foot length to height within the human races, and suggests a ratio of 15% for all Fes sler et al. ( 2005:46) compile published data for 32 populations of varying ancestry and from various time periods and report foot length as a percent of stature between 13.5 % an d 15.9% Todd and Lindala (1928) investigating a subsample of the same cadav eric population used here, found that the feet of White and Black males were the same length for any given stature, while the feet of White female s feet scaled differently White female feet were smaller. This variability in scaling may indicate that foot length
38 and the foot elements are under varying selective pressures and developmental pathways and are free to vary ( within the bounds of reason) I hypothesize that the tropically adapted sample will be elongated relative to stature, however, I am not suggesting that this is due to an increased advantage for shedding heat, or is even necessary from a mechanical standpoint, but rather this increase is based initially on patterning at the cellular level. That is, scaling of the foot with long bones (ver sus stature or body mass) is due to the pleiotropic effects of the scaling of the long bones. Pleiotropy is when a single gene influences multiple phenotypic traits. Patterning at the C ellular L evel We can gain perspective on the m echanism that can create th ese phenotypes, by examining and adapting advances in the fields of developmental biology and evolutionary developmental biology with respect to development and patterning of the human limbs The initial patterning of proximodistal limb buds are deter mined at the cellular level and very early in development ( Summerbell et al., 1973; Double 1994; Wolpert 2002). Positional information attained during the initial stages of limb bud development determine whether the anlagen becomes the proximal skeletal element (humerus or femur) versus the distal elements ( e.g., radius and ulna or tibia and fibula) or the autopod region (hand and foot). This specification is due to relative time spent within or under the influence of the PZ morphogens. Investigation in to the genetic basis for diversity of morphology has led to the realization that co option of th ese developmental mechanism s, in terms of timing and signaling is what has allowed the diversification of the tetrapod limb ( Lovejoy et al. 1999; Tickle 2002) Variations in limb form such as reductions, elongation ( e.g., bat wing), loss of limbs ( e.g., snakes and
39 dolphins), and proportions are all related to slight timing variations and expression or nonexpression of various Hox genes. Sears et al. (2007) recently investigated the evolutionary pattern of mammalian limb reduction in zeu gopod (forearm and lower leg) elements from a developmental and morphometric perspective. They have found that the most common pattern of reduction in a large sample of mamm als is a reduction in element widths. Using the development of bats and mice as a basis for developmental investigation into the mechanism of reduction they find both bat and mouse limb reduction (of the ulna and fibula of the bat and fibula of the mice) is achieved via a slower rate of growth relative to other skeletal elements embryologically (rather than decreased initial cellular condensations for example) Sears et al. (2007) posit that the reduction of mammalian zeugopods, an example of parallel evolution in a large number of mammalian families, could have occurred by the same developmental mechanism. Lovejoy et al. (1999) all suggest that using the knowledge gained from advances in embryology and evolutionary developmental biology regarding limb f ormation and positional information may advance formulation of hypotheses concerning human morphology. For instance they point out that suites of morphological characteristics selected for may in fact represent the change in only one field of development, creating a cascade of effects as a result of pleiotropy. A hy pothetical example is given to illustrate how the pelvis of a chimpanzee can through simple linear distortion, form the shape of an Australopithecus pelvis By a change in the increase or dec rease of slopes (concentrations and timing) of the molecular gradients in the limb bud, the effect is a distortion of the anlagen, consequently affect ing the adult morphology. Thus, by viewing all morphological changes as independently heritable adaptations cladists may
40 obscure functional and phyletic analyses, as many of the traits would be mere ly by products of the primary change. It follows that slight changes in timing of this initial anlagen patterning could be responsible for either elongation or shortening of sk eletal elements during development in modern humans Ecogeographical patterning of the major long bones is already observable in fetal remains, suggesting a strong genetic component rather than a strictly environmental or nutritional expl anation (W arren 1997; Warren et al. 2002). Warren (1997) conducted a study using radiographs of 252 fetuses and found that Blacks had significantly higher brachial and crural indices than their White counterparts. The pattern is under such strong devel opmental pathways that even teratogenic fetuses still display ecogeographical patterning ( W arren 2002). Thus if the pattern is already developed at the fetal stage for major limb bones, I posit that the limb bud anlagens prior to this are also similarly patterned, and are due to slight differences in the time spent in the progress zone, or as an interaction with the AER and prepositional information. Breadth and S caling Many studies investigating proportional issues tend to rely on long bone lengths al one However, Lazenby and Smashnuk (1999) and Ruff (1994) point out the need to include breadth in addition to lengths, of the long bones, as breadths should be stouter in colder climates Lazenby and Smashnuk (1999) investigated conformance to Allens r ule by looking at osteometric variation in second metacarpal s between Inuit populati ons and European settlers. They found that Inuit hands are better adapted to cold er climate s, with larger mass relative to surface area. One consideration not emphasized is that Laz enby and Smashnuk (1999) are looking at an already cold adapted/derived
41 European population versus a population that is currently living in an intensely cold environment. If the metacarpals of a tropically adapted population were also included they would undoubtedly exhibit even greater differences. Recently Holliday and Hilton (2010) found that that Inuit populations do not seem to be extremely coldadapted, in fact they display proportions similar to European and Europeanderived samples. H owever this entire point needs clarification regarding what broader means Is being broad merely a mechanical consequence of being shorter? Or are long and broad always coincident? In order to asc ertain if there is an ancestral based patterning diff erence or simply a scaling difference, one must examine whether broader elements regularly coincide with shorter lengths The extent that foot length, and subsequently individual bones of the foot, covaries with ecogeographical patterning is currently unknown. The current study seeks to understand the role of breadth and maximum length of various pedal elements to assess conformance to Allens r ule. The foot elements and overall foot shape of the Black sample is expected to be longer and more narrow tha n the White sample (lengt h and breadth). Foot S caling and S tature F oot length has been shown to be correlated with overall stature. For instance, Giles and Vallandigham (1991) studied the utility of estimating height from foot and shoeprint lengths in th e forensic context and found that with appropriate statistical caveats foot length as well as shoeprint length can inform investigators about stature. In a large anthropometric study of U.S. Army soldiers correlation coefficients for stature and foot len gth are 0.689 for males (n = 293) and 0 .731 (n = 491) for females (Parham et al., 1992) Ozden et al. (2005) report somewhat lower correlations between height
42 and foot length among a sample of adult patient s in a Turkish hospital (r = 0.579; males r = 0. 500; females). However, higher correlations have been documented for individual elements (or portions thereof) of the foot. F or instance, Holland (1995) found that the maximum length of the calcaneus, the length of the posterior calcaneus, and the maximu m length of the talus, were correlated with stature (r = 0.723, r = 0.817, and r = 0.731 respectively) in his sample of American White and Black males and females. Byers et al. (1989) report correlation coefficients ranging from 0 .58 to 0 .89 for various m etatarsals in a sample of 130 adults (male and female Euroand AfricanAmericans). In an investigation of prediction of foot length from individual elements of the foot Emanovsky (2009) reported correlations of between 0.64 to 0 .86 for a combined Black a nd White male only sample utilizing various elements of the foot Standard errors of the regression equations are on par with estimates of stature from tarsals which are useful in variety of forensic and archeological contexts (Holland 1995). Since the individual bones of the foot directly make up the total length of the foot it is not clear why these correlation coefficients are not higher. The medial longitudinal arch may be a confounding influence on t otal foot length, forcing the medial bones of th e foot (calcaneus, talus, navicular, medial cuneiform, and the first metatarsal) into a nonlinearly aligned arch Emanovsky (2009) noted that allometric scaling is another influenc ing factor on overall foot length, as the individual bones of the foot co nform to both biomechanical functions and ecogeographical patterning. This relationship was evident as there appeared to be a pattern to the residuals derived from the least squares regression (Figure 4 2 ) The combined sample shows an upward trend in the residuals from smaller foot lengths to longer foot lengths. When the sample is broken
43 out by ecogeographical ancestry it is clear the W hite sample tends to be overestimated and the black sample is underestimated by the equation. This is likely a result of positive allometry in the Black sample, and covariation with the long bones of the limb. Recently Gruss (2007) reinvestigated the e ffect of limb length on the biomechanics of gait of humans She demonstrated that individuals with longer legs consistently keep the center of pressure (the origin of the ground reaction force (GRF)) farther forward along the foot in absolute terms (not as a percentage of foot length). In other words, p eople with l onger limbs have larger GRF moment arms at the ankle and greater moments acting to dorsiflex the ankle during the last part of stance. A moment arm is the shortest perpendicular line between a force s line of action and its axis of rotation. A moment arm can also be a bending moment that bends or flexes the d iaphyses, such as depicted Figure 4.3 where for longer limbed individuals it can be seen that the bending moment arms are larger at analogous points along the limb, than smaller individuals. If the center of pressure changes relative to a lengthened limb (to reduce bending forces in the femur) how is it affecting the relative morphology of the foot? Is the length of the calcaneus increasing while the metatarsals stay the same; are both increasing isometrically or is it only the metatarsal region that inc reases (Figure 4 4 )? These questions are answered by comparing groups with differing body proportions after which the results can be used to test the hypothesis that the bones of the foot scale isometrically with the rest of the body (e.g ., with body mas s, stature or intrinsically with foot length) in these groups Figures 4 3 and 4 4 illustrate several isometric and allometric patterns and some of the biomechanical consequences thereof If the foot scales negatively in a group with longer limbs the ben ding moments will be
44 reduced (compare a with b in Figure 43) Isometric scaling of the foot in a longer limbed group results in larger bending moment arms (compare a and c in Figure 43). Positive allometry of the foot relative to limb leng th wo uld also result in larger bending moments (compare c and d in Figure 43). Scaling of the foot can be the result of several intrinsic factors such as elongation of every element isometrically, or elongation/shortening of only portions of the foot (e.g ., hindfoot stays the same while the forefoot increases/decreases). As with the limbs, longer elements would have increased bending moments during certain parts of gait (e.g., toeoff ). In intraspecific studies where sizerelated changes of adult indiv iduals of the same species (v ersu s ontogenetic and interspecific) are investigated, we can predict how various scaling scenarios affect the biomechanical environment. For instance positive allometry of the foot to overall stature (a proxy for lower limb l ength) indicates that the foot is longer than expected for a given height based on geometric similarity. Isometry relative to body mass indicates that while the foot scales as expected, in absolute terms larger individuals will experience more stress Lauge (2003) points out that a species with high body size dimorphism may demand structural changes in joint size to maintain similar levels of stress. If i sometric scaling is maintained in such individuals and their j oint surface area scales to twothird s body mass the result is greater compressive stresses in larger individuals. A highly dimorphic species sh ould then exhibit positive allometry. In instances where the calcaneus is positively isometric to the overall length of the foot, ( foot length inc reases and the calcaneus becomes disproportionally larger ) higher metabolic costs for modeling and remodeling the larger element is required. In such instances, more mass
45 and energy is required to move the limb during locomotion. The same is also true f or positive allometry relative to stature. However, positive allometry of the calcaneus (particularly positive allometry of the posterior calcaneus) relative to overall foot length or limb length (via stature) could actually enhance the effective mechani cal advantage (EMA; see below). Isometry of calcaneal breadth and length as it relates to body mass suggests geometric similarity. In other words, as body mass increases there is a proportional increase in all of the linear dimensi ons associated with the element. However, this also means that the forces exerted on the foot are higher in individuals with increased body mass. Sylvester et al. (2008) suggest that the upper and lower limbs of modern humans are, to a certain extent not isometric to a bod y mass surrogate. They looked at the allometric coefficients of the geometric means of sets of hum eri, radii, femorae, and tibiae in modern human populations. They tested isometry against a body mass surrogate based on size shape variables calculated f rom the elements under study. One striking result t hey found is a pattern of proximal to distal element allometry within each limb. T he distal element s were positive ly allometric (i.e., the radius more so than the humerus and the tibia more than the femu r ) T he general e ffect of this pattern is that the distal element should make up a larger proportion of the overall length of the limb in larger individuals. H owever, when size is controlled females have longer tibiae and shorter femora than males. Whe n sexes are segregated, the authors found deviations from isometry more often. Cost of Locomotion Aiello and Wells (2002) suggest that organisms are faced with tradeoffs and are constrained by the relationship of various systems and structural adaptations in order to
46 maintain homeostasis and reproductive fitness An increase in body mass can have a cascad ing eff ect on a multitude of biological functions ( Feagle, 19 84) ; e nergetic costs of locomotion are no exception. The advantage of bipedalism is the ene rgy sav ed at walking speeds and the potential for an increase in range (longer legs of Homo ). Recently Polk (2002, 2004) found that primates with relatively long limbs are able to move faster and more efficiently than shorter l imbed species with a similar mass. This is primarily the result of extended limb postures, which utilize less muscular force in the resistance of gravity. In a comparison of three species of monkeys with varying body proportions but similar body mass Polk (2002) found that the dis tal elements affected joint posture. These l onger segments distal to a joint increase the moment arm for the ground reaction force (GRF) about that joint (or any other point along the anatomical arm). Longer limbs also serve to increase the effective mec hanical advantage (EMA; the ratio of the anatomical moment arm to the GRF moment arm ). To maintain joint postures during locomotion then, larger animals requir e relatively less muscular output (Bei wener, 198 9). Pontzer ( 2005, 2007a,b ) recently compared theoretical models utilizing skeletal limb length (summed skeletal lengths) and effective limb lengths (those modeled as a strut rather than as individual skeletal components) to estimat e of the cost of transport (COT). He found that effective limb lengths, and not skeletal limb lengths, are better predictors of the COT. This principle illustrates a subtle, but potentially significant difference created from a slight leng thening of the foot rel ative to the length of the tibia and femur Figure 4 5 illus trates positive allometry of the foot. The effective limb length (Le) is increased and the position of the tibia relative to the ground reaction force is
47 shifted. Gruss (2007) measures the effects of bending moments between long legged a nd shorter legged individuals and found that in the second half of the stance phase a compensatory mechanism in long legged individuals acts to shorten the GRF moments along most of the limb (femur and tibia). That is, the center of pressure (COP) remains more distal along the foot, for longer limbed individuals. This in turn keeps the GRF moments closer to the limb, but increases the GRF moment at the ankle. Thus individuals with longer legs tend to have longer A P moment arms at the ankle in late stance and also greater dorsiflexion moments at the ankle. Gruss (2007) hypothesizes that the greater dorsiflexion forces could require greater musculo ligamentous stabilization of the ankle joint in people with longer limbs The variables measured by Gruss (2007) do not model bending strains of the foot and how they are affected by GRF. However, if other variables remain consistent individuals with longer feet ( e.g., longer metatarsals) will exhibit greater bending moments than the individuals with shorter feet. Effecti ve M echanical A dvantage The effective mechanical advantage ( EMA ) is the ratio of the extensor muscle moment arm (r) to the moment arm for the ground reaction force (R). This is also the ratio of the muscle force (Fm) to ground reaction force (GRF) in equil ibrium. In the current study PCAL refers to r and [ (CALMAX PCAL) + CUBMAX + 3RDMAX ] refers to R. Using t his configuration effectively captures the fulcrum point anterior to PCAL up to the metatarsophalangeal joint. The sum of CALMAX, CUBMAX and 3rdM AX is one of the best predictors of overall foot length (Emanovsky 2009) for Black and White males Figure 4 6 illustrates that an increase in R without an isometric (or positively allometric) relationship in r resul ts in a decrease in EMA. Addition ally, any increases in
48 R also result in greater bending moments of the metatarsal region for any two analogous sites. Stress F ractures Another area in which the foot has demonstrable disparities between males and females, and to some extent among races is susceptibility to stress fracture. One of the most common foot fractures is a fatigue or stress fracture of the metatarsals, so called boot camp fractures ( repetitive marching, and running that is typically undertaken by new recruits into the armed services ) Such stress fractures are also seen in athletes. These fractures occur from repetitive loading on bone so much so that the bone cannot remodel fast enough to prevent the propagation of microcracks (Martin et al. 1998). Muscular and soft tis sue buffers normally distribute the stress involved in loading the foot during walking and other activities. Various plantar flexors ( e.g., flexor hallu ci s longus, Flexor digitorum brevis and longus, tibialis posterior ) of the foot counteract the bending moments of the metatarsals due to body weight while increasing the forces across the metatarsophalangeal joints (Sharkey et al. 1995:1050) When muscle fatigue occurs the muscles are no longer able to act as a preventative buffer to any forces generat ed by locomotor activity and thus the geometry of the foot skeleton and the individual bones of the foot bear the total force. R elatively low impact exercises like walking and marching results in fractured metatarsal s. Sharkey et al. (1995) conducted a study of the strain involved in the loading of the second metatarsal during heel lift to investigate the role of muscular fatigue in the etiology of metatarsal stress fractures. They found that dorsal strain was significantly
49 reduced by the action of t he flexor hallicus longus and plantar dorsal bending was reduced by contraction of the flexor digitorum longus Microcracks are found in normal healthy bone ( typically between osteons in the interstitial matrix ) and are usually repaired during the remo deling process However, cumulative effects (initiation, benign accumulation, and then failure) and the properties of the bone result in the accumula tion of microdamage, hence stiffness rapidly declines and the bone fails If the load is lessened or alleviated during the benign accumulation phase, there is time for remodeling to repair the damage. A pattern in the susceptibility to stress fractures was observed in clinical settings and has been theoretically modeled. White females have an increased sus ceptibility to stress fractures of the lower limb ( Sharkey et al., 1995; Benell et al., 1996; Beck et al. 2000; Jones 2002; Shaffer et al. 2006; Queen 2009). For instance, in a review of the literature, Jones et al. ( 2002) identified sex as the most common intrinsic factor Military studies found that women incur stress fractures 210 times more often than men performing the same physical activities. Civilian studies ( e.g., long distance running track and field athletes ( Benell et al. 1996) ) also s eem to corroborate this however the findings may be misleading since the athletic training regimes are not always analogous between men and women The cumulative evidence suggests that females, in particular, White females incur stress fractures more of ten. This is likely due to a variety of reasons including : decreased bone mineral density, bone size, hormones, nutrition, training, anatomy and / or biomechanics (Queen et al. 2009:391) Jones (2002) su mmarizes four military studies examining race as a factor for intri nsic susceptibility for stress fractures. In a study by Brudvig (1983) the incidence of
50 fracture was higher among White trainees than the Black trainees. Also White females were higher than any group (11.8% compared to 1.4% for Black women and 4.3% for other nonW hite groups). Gardner et al. ( 1988 ) in a study of over 3,000 Marine recruits found that Whites were 2.5 times more likely to suffer from stress fractures. Shaffer et al. (1999) found no significant difference between Wh ite and n onWhite incidences in stress fracture. Friedl et al. (1992) found that incidences were 1.6 times higher for White or Asian females versus Black females. Stress fracture prevalence and incidence above primarily includes the tibia and fractures of the foot. Jones et al. (2002) reiterate that among runners the tibia is the most affected element and among earlier military studies march fractures of the foot were common, with an increase in the number of those affecting the tibia in more recent st udies. Queen et al. ( 2009) point out that metatarsal stress fractures account for 4.715.6% of all overuse injuries, with the second and third metatarsals the most common site for fracture. This follows the predictive models developed by Gross and Bunch (1989) who modeled the five metatarsals as rigid cantilevered elliptical bodies. Bending and shear strains were found to be highest in the second metatarsal and axial forces were greatest in the first metatarsal. One question to be examined in light of t his empirical evidence is: does the White female sample exhibit a difference in limb proportionality that might predispose that subgroup to fractures of the metatarsals?
51 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1400 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 3 4 BM W M PREDICTED LIMB LENGTH STATURE PREDICTED LIMB LENGTH STATURE 600 700 800 900 1000 1100 1200 1400 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 BF WF Figure 4 1 R elationship of predicted limb lengths calculated for hypothetical statures for Black and White males (top) and Black and White females ( bottom ).
52 Figure 4 2 Least squares regression of the sum of CUBMAX + CALMAX + 3MTMAX on Foot length for combined Black and White males (top) produces residuals that are clearly patterned. As foot lengths increase the model overestimates the length of the foot. When the variables are regressed using just a White male sample, these individuals tend to be overestimated by the model. When just a Black male sample is used, these individuals tend to be underestimated.
53 a b c d Figure 43. Theoretical scenarios for scaling of the foot and its relationship to the bending moment arms (red bars) of ground reaction force (GRF; blue arrows) at heel strike. (a) target (b) negative allometry; the foot stays the same length as leg length increases (GRF moments reduced); (c) isometry, (d) positive allometry; foot length increase is more than expected as leg length increases (GRF moments increased). Note that the consequence of isometric scaling (a to c) as well as positive allometry (c to d) results in greater bending moment arms.
54 a b c d Figure 4 4 Theoretical scenarios for scaling of the foot (a) target, (b) foot length is the same as the target but in order to maintain that foot length the calcaneus has elongated (positive allometry relative to foot) while the forefoot has been reduced; (c) the foot length has increased, ho wever, the calcaneus remains the same as the target (calcaneus exhibits negative allometry relative to foot), (d) foot length has increased relative to the target and all elements scale d isometrically (relative to foot length) to achieve this lengthening
55 L e b a Figure 4 5 Theoretical effect of positive allometry of foot length to stature; (a) is target, (b) represents increase in foot length without change in other limb proportions. Note that the slight change results in a significant shift in ground reaction force vector s (blue arrows) and results in a slight increase in effective limb length (Le; see text).
56 r = PCAL R = (CALMAX PCAL) + CUBMAX + 3RDMAX GRF GRF F m R r Figure 4 6 Schematic representation of foot and components for calculating effect ive mechanical advantage (EMA). For a lever the ratio of the force arm to the resistance arm is the mechanical advantage. Here, t he EMA is the ratio of the distance from the joint to the action of the muscle (Fm) or in lever (r) and from the joint to the pivot point during toeoff (the metatarsophalangeal joint) or the out lever (R) thus EMA = r/R. Here the in lever is the posterior calcaneus the fulcrum is the ankle joint and the out lever is the mid and fore foot up to the metatarsophalangeal joint.
57 CHAPTER 5 RELATIVE VARIATION Examining relative, or intrinsic, variation of a given trait is of interest to systematists, biologists, and anthropologists as such examinations eliminate confounding effects of size on the trait of interest (Lewontin, 1966; Franciscus and Long 1991; Holliday and Ruff 2001). As a dimension increases so too does the variance of t he measure, however this does not mean that a larger animal is inherently any more variable than a smaller one Coefficients of variation (V) are frequently used to measure variation in a population ( e.g., White males) h ow the character varies across several populations of the same species ( e.g., Homo sapiens from Germany, United States and Mexico) between species ( e.g., Homo sapiens versus Pan t r oglodytes ) or different characters within a population ( e.g., length and breadth measurements of nasal bones in Homo sapiens ) (Lewontin, 1966; Sokal and Braumann, 1980; Tague 1989; Franciscus and Long 1991; Cope and Lacy 1992 ; Holliday 1999; Scott and Stroik 2006). Coefficients of variation are calculated as the sample standard deviation divided by the sample mean (sometimes multiplied by 100). Examining the amount of variability of a character can provide information on the developmental control s for that trait. These developmental controls are used to make inferences regarding evolutionary processes For example, research involving the migration of modern humans into Europe from Africa was examined from the perspective of body type and body proport ions Ho l liday (1999) and Holiday and Ruff (2001) discuss however, issues of proportionality must first account for relative variation. I ndices like the crural index (tibial length X 100/femoral length) may obscure critical data with respect to the total limb length. In other words, i s t he crural index high
58 because a population has a long proximal region but short distal, or is it equal contributions from both segments leading to the results ? The re is conflicting data on the intrinsic variation of proxi mal and distal variability M eadows and Jantz (1995) and Jantz and Jantz (1999) found more variation in the distal segments while Jungers et al. (1988) found proximal limb segments more variable. Holliday and Ruff (2001) state that the best null hypothes is for within population variability between segments is that of equal variance. D ue to the lower limb s importance in bipedal locomotion, we might expect this region to display less variability in overall length between proximal and distal segm ents compar ed to the upper limb ; as the lower limbs must interface with the substrate (via the foot) However, Holliday and Ruff (2001) have found that the lower limb, especially the tibia is more variable. The fore and hind limb distal segments are last to be laid down during embryonic development, however, recent debate has emerged as to whether differentiation is due to le ngth of time in contact with a progress zone (Summerbell et al. 1973; Wolpert 2002) or if it is due to prespecification in early limb buds (Dudley et al. 2002). If the progress zone model is correct then it follows that the more distal segments have the potential to be influenced greatest by heterochrony, ambient environment, or generalized plasticity. Jantz and Jantz (1999) found that secular trends influence distal segments more than proximal segments and these trends affect males more so than f emales. This is an i ntriguing finding because it is indirect evidence of po tential microevolutionary ( i.e., changes in gene frequency) changes as observed from differing phenotypes.
59 Experimental studies have shown that cold environments can lead to vasoconstriction of developing limbs (Weaver 1969). To test a hypothesis of adaptation versus epigenetic influences Higgins (2008) investigated modern human limb proportions from the Terry collection using a sample of European Americans and Afr ican Americans and found that the distal segments differed more between populations and that the European Americans exhibited relatively shorter distal se gments From this, Higgins concludes that ancestral climatic adaptation rather than adaptation to the North American environment is the cause. E cogeographical patterning is apparent even among fetal remains, suggesting a strong genetic component (Warren, 1997; Warren et al. 2002 ). Lovejoy et al. (1999) show from a morphological and developmental perspective, patterning of a limb is determined at the cellular level. Thus, selection is acting on positional and distributional information rather than solely on adult shape and size. In this study I hypothesize that there will be greater variability in the Black sample, due to increased genetic diversity (Jorde et al. 2000; Releth ford 2002 ) In order to answer questions regarding the relative variabilit y of the foot proximal to distal as well as length versus breadth variability was explored. T he proximal segment comprises the calcane us, while the distal segment comprises the first metatarsal 1) D oes the calcaneus have the same inherent variability as the first metatarsal, or is it perhaps more constrained due to the role this bone plays in bearing a majority of body weight dur ing locomotion? 2) D oes ancestr y result in different patterns of intrinsic variability between the proximal or distal segme nts? Moreover the calcaneus is a complex element in terms of overall geometry and biomechanical functions and since the lower leg tends to be more variable
60 (Holliday 1999; Jantz and Jantz 1999; Holliday and Ruff 2001 ; Sylvester et al. 2009) scaling o f the foot could theoretically be more easily attained by increasing/decreasing the length of the metatarsal region. Yet an increase in the forefoot without similar changes in the posterior elements could affect the center of pressure of the ground reacti on force (GRF) and hence GRF bending moments experienced by the other limbs. Proportional changes result in changes to the biomechanical environment Thus some analyses should model the human foot as a lever with a power arm and a load arm (in a lever m odel the calculations are more straightforward as the rigid body can be assumed to be in static equilibrium). If the overall lever is the heel to metatarsophalangeal joint then the power arm is the posterior calcaneus and the load arm includes the anterior calcaneus, other tarsals and the metatarsal region. The unique configuration of the human foot allows it to be modeled as a lever (type 1) ; however, one of the most important assumptions model ing the foot as single rigid body potentially ignori ng the atten uation of forces contributed by soft tissue arrangements ( e.g., fatty tissue, skin thickness, callus, plantar fascia and unique geometries). Again, one of the distinguishing characteristics of the human foot is the medial longitudinal arch fo rmed b y the medial row of foot bones and supported by numerous plantar ligaments and muscles. When not needed, such as during weight acceptance and quiet standing the arch loosens and lowers ; however, when needed the medial longitudinal arch acts as a rigid le ver during push off phase in gait (Zipfel et al. 2009). The joint configuration and soft tissue windlass effect essentially allows the several bones to act as one body. If one were to independently model each element instead as a beam, the situation bec ome s quite complex. Hsin Yi et al. (2008) recently modeled
61 the plantar fascia under stretch using finite element analysis, they found a stress concentration near the medial calcaneal tubercle and under the hallux which diminishes as one moves laterally. Gefen et al (2000) combined data from contact pressure measurements and digital radiographic fluoroscopy to model the stress distribution of the foot during locomotion. One of the more interesting results from that analysis is that at midstance nearly all regions of the foot are stressed evenly while the most dramatic stress distributions can be seen during pushoff in the dorsal third metatarsal. The heel bears a lot of the weight during a static plant as it is in line with the lower leg T he forefoot (an d distal midfoot) bears the weight dynamically during toeoff. As mentioned above the flexor tendons exert a force on the foot by pulling about the ankle joint. Fessler et al. ( 2005:49 ) state that t he longer the foot the more effective these muscles can be in stabilizing the forward motion of the body, because the leg acts as a lever, creating a countervailing moment at the ankle joint that diminishes the ability of the forefoot to stabilize forward motion, the greater the lever arm formed by the leg, the larger the force exerted by a given body mass on the forefoot. Aiello and Dean (1990) summariz ing a report by Bowden (1967) demonstrate that the forces to the foot during locomotion are considerable, over one times the body weight during walking two times body weight in running and up to five times when landing on ones feet from a height. F rom a deformation perspective, the longer the foot is the greater the potential to deform and change shape as the bending moments increase. The c alcaneus does n ot only bear the weight of the body during locomotion, but it must scale to accept the distal tibia (via the talus), and resist the action of the flexors. Thus, for the current analysis a major focus is on the first metatarsal and calcaneus because they s hould be under the
62 most constrained selective pressures, while arguably the first metatarsals should be less constrained and thus more variable. There was a tendency evolutionarily for a reduction in the length of the pedal elements, with perhaps the most drastic changes occurring in the phalangeal and forefoot region (Susman et al., 1984; White and Suwa 1987) The pedal bones of the Australopithecines for example were long relative to Homo A related question is whether the breadth of the calcaneus and first metatarsal is more variable than the length. Allens rule predicts that not only will extremities become shorter in cold adapted populations but they will also become broader so i t is useful to understand how inherently variable these elements ar e prior to making or interpreting selective and functional hypotheses. I ntrinsic variability in other elements of the foot and in foot leng th is also of interest particularly as it relates to sexual dimorphism. Tague (2002) suggests a tenet of evoluti onary theory is that, within a species, phenotypic (and genetic) variability is inversely related to the intensity of stabilizing selection (Tague, 2002:195) An increase in variability suggests less selectional constraints on that character. Tague (1989) tested the hypothesis that there are sexual differences in pelvic dimension variability to assess the validity of the above tenet He hypothesized that female pelvic morphology should be less variable than males given the demands between obstetric adeq uacy and efficient locomotion. In other words selecti ve pressures should be more intense on female pelves. Coefficients of variation were employed to assess the intrinsic variability of the male and female pelves. Tagu e (1989) found that the pelvis was not intrinsically more variable in either sex.
63 The above tenet of evolutionary theory can also be tested using the foot. B etween males and females variability of the foot is expected to be equal since the functional environment is the same. However, r esearchers have found that selective pressures affecting body size are different between sexes and observe increased plasticity in males ( Eveleth and Tanner 1990; Cole, 2000 ). S exual selection may increase variability in a particular trait F or instance Pawlowski et al. (2000) demonstrated that there is active selection for larger stature in men by women. Lovejoy et al. (1999, 2000) point out that variability of a trait and is not necessarily coupled to its selection due to the fact that selection may be acting far upstream of the adult morphological character. However, their argument is based on ramifications for assessing traits between taxa. Using relative variability can be of use then in distinguishing whether the foot morphology between groups o f the same species with differing proportions is epigenetic and plastic, in which case the adult morphology should be more variable given differing life histories, or whether the morphology is fixed by stabilizing selection. If the major elements of the f oot covary with the phenotypic changes in limb length due to a pleio t ro pic effect then they are expected to not be highly variable.
64 CHAPTER 6 MATERIALS AND METHOD S Samples The samples used in this study are from the HamannTodd Collection (HTH). The HTH consists of over 3000 skeletons originating from a cadaveric dissection collection that is now housed at the Cleveland Museum of Natural History (CMNH) Anthropometric data collected at the time of accession into the collection include: age, sex, ancestry, weight, stature, foot length, and foot breadth. HTH c adaver s ample A s ubset of the HTH collection database was utilized for comparison of fleshed foot dimensions (foot length and foot breadth) Table 6 1 provides the demographic makeup of the HT H cadaver sample used in this study. I n addition to the exclusion of individuals with missing data, all individuals less than 18 years old are removed. Eighteen years is considered a prudent cut off since the bones of the foot have ceased development pri or to this age, though stature may still be slightly increasing The head of the femur fuses between 1216 for females and 1419 for males and the distal femur fuses between 1418 and 1620 for females and males respectively (Scheuer and Black, 2000). Th e proximal tibia typically fuses at 1317 for females and 1519 for males while the distal tibia fuses between 1416 and 1518 for females and males respectively (Scheuer and Black, 2000). Thus there might be slight underrepresentation of true stature for some younger individuals in the HTH cadaver sample. Also, r ather than introduce correction factors following Giles (1991) used below for the skeletal sample individuals over 45 were simply excluded from the current analysis for the cadaver sample. The number of individuals available for the current study is still relatively large (n = 104 0 ).
65 HTH s keletal s ample Bony foot elements were measured for an initial sample of 185 individuals from the HTH. Data for an additional 18 individuals from the HTH were kindly provided by Drs. Byrd and Adams from their reference sample compiled for ostometric sorting of commingled remains (Byrd and Adams 2003 ; Adams and Byrd, 2006). For the purposes of this study the skeletal sample will be referred to as the HTH skeletal sample. The demographic information for the HTH skeletal sample is shown in Table 62 The entire ByrdAdams dataset was not incorporated into the HTH sample to avoid confounding influences of secular variation which will be explored in future work. C orrection factors for individuals of advanced age were utilized following Giles (1991). Giles (1991:900) provides a data table for corrections to stature that must be applied after estimation of stature from the long bones in individuals between the ages of 45 and 86. At this age stature declines but not due to the shortening of the long bones, thus one would overestimate the height of an individual of advanced age if the correction factor is not subtracted from the final estimate Here, the amount in millimeters was added to the cadaveric stature for individuals who were between 45 and 86 years. Thus the variable stature reflects an adjusted stature in this study. This correction factor is quite small in general but becomes more significant as one becomes very old. For instance, at age 50 males have a correction factor of 4.3 mm while females are corrected by only 0.4 mm, but at age 85 males need to be corrected by 43.2 mm and females by 49.0 mm. The age distribution of the HTH skeletal sample is shown in Figure 6 1
66 D escriptions of the 20 variables initially utilized for this study are presented in Table 63 Measurements taken by the author were taken with a Mit utoyo digital caliper s (all measurements were to the nearest 0.01 mm) Several measurements were novel to their original studies, for instance the breadths of the base of all metatarsals and the breadth of the first metatarsal head described by Robling and Ubelaker (1999). The maximum lengths of the cuboid, navicular, and the meta tarsals are also novel to the ByrdAdams (2003) commingling database. These were designed to be true maximum lengths in whatever orientation it can be found. The other measurements are commonly used in forensic and bioarchaeological investigations with t he exception of the maximum lengths of the proximal and distal phalanges, these were taken as the maximum leng ths in whatever orientation that was found. Error Measurement error. I dealt with length measurements as well as breadth measurements in this st udy and the absolute measurement error associated with the smaller measurements (breadths) may have a disproportionate effect on subsequent analyses. Thus intraobserver data was generated for length and breadth measurements of four elements, the calcaneus (CALMAX and CALMIDB), the first metatarsal (FSTMAX, 1MLH, and 1MLB) the fifth metatarsal (5MTMAX, and 5MLB) and the talus (TALMINB). These variables were measured three times, nonconsecutively ( ranging from 1 day to over one week between trials ). Data from the first two measurement trials was used to compute the technical error of measurement (TEM) following Dahlberg (1940) and Knapp (1992). The TEM is calculated as the square root of the sum of the squared differences between corresponding measurements divided by twice the sample size ( Knapp 1992:235). This then is the magnitude of
67 measurement error that can be expected for an infinite number of measurement trials. The TEM can further be examined as a relative measure of the magnitude by calculati ng the coefficient of variation of error (CVE) which takes the TEM and divides it by the mean of the first individuals first and second trial (Stephan et al., 2003) In order to further explore the amount of variability between the length and breadth meas urements that are attributable to measurement error all three measurement trials were used to calculate a percent measurement error (%ME) follow ing Bailey and Barnes (1990). This method uses A NOVA to partition the total variability into among group (sampl e variance) and withingroup variability (measurement error), such that the %ME evaluates the magnitude of the error relative to the among group variance rather than as an absolute measure. Other sources of error. Not every individual in the HTH skeletal sample and the HTH cadaver sample have all required variables for every test of interest in the current study. Efforts were m ade to maximize the sample sizes for each test (see below). Adams and Byrd (2002) found numerous errors arise during osteometri c data collection and thus all variables used in this study were examined for outliers that result from non biological factors such as data entry errors, transcription errors, or r ecording the wrong variable. When a variable was suspected of being erroneous due to one of the above factors it was removed from the analysis. Some erroneous data were identified after thorough reviews of various scatter plots of the variables. Only measurements or HTH sample record data that were notably out of line were rem oved from the analysis.
68 General S tatistical P rotocol Linear r egression and a nalysis of v ariance. For the specific hypotheses being tested (see below) the standard statistical tests used are linear regression (LR) and ANOVA. In general the protocols fol lowed are: Bivariate linear regression was utilized when comparing specific variables and specific ratios a s well as when testing variables for deviations from isometry. R egression plots were used to assess the structure of the data. Two way ANOVA was ut ilized to ascertain whether there are significant differences between the groups. Analysis of variance used the Levene statistic to test for the equality of variance within groups (also known as homoscedasticity). If this was not violated ANOVA proceeded. The n ull hypothesis for each test is that there is no difference between groups. Due to the number of statistical tests being made here there is an increased chance of making Type 1 errors (when the null hypothesis is incorrectly rejected, i.e., a fals e positive). In order to mitigate this, a Bonferroni correction w as applied for each grouping of tests. Ratios. Ratios used in various analyses were created to explore issues of relative size. They were not used to eliminate size from the investigation, this is appropriate when considering whether shape changes with size (Jungers et al., 1995); however the method has been criticized by others (Albrecht et al., 1993). Smith (1999) also supports the use of ratios and demonstrates that they do not lead t o invalid statistical results when used in bivariate regression, correlation and analysis of variance. Thus, ratios as used here are scalefree (dimensionless) variables used to assess relative size. Proportionality of the Foot Correlation. Correlation a nalysis was performed using the Pearsons product moment correlation coefficient, or Pearsons correlation, to assess how individual
69 elements of the foot and overall fleshed foot length covary (Tables 6 4 to 6 6 ) All 2 0 variables are significantly correl ated at the 0.01 level (two tailed) and t he majority of variables are strongly correlated ( i.e., 1988) Following this, the strongest relationships of individual elements of the foot were selected for further analysis. These were heuristically chosen, as mentioned above with a focus on the calcaneus and first metatarsal and various breadth and length measurements for specific tests of interest. ANOVA. It is hypothesized that significant differences will be found between groups. These differences should conform to expected ecogeographical patterns in that, B lack females and B lack males will have greater overall foot lengths, but more narrow feet both proportionate to stature and absolutely A nalysis of variance was utilized to t est for differences in: Foot length, Foot breadth, Foot Length /Stature, Foot Breadt h/Stature for both the HTH cadaver and HTH skeletal samples. Relative makeup of the foot. In addition to looking at the absolute values of the various pedal measurements t o identify patterns of proportional variation, and i n order to elucidate which portions of the foot (e.g., hindfoot, midfoot, forefoot) are contributing to the over all length of the foot the most the following r atios of FSTMAX, CALMAX, and PCAL to FOOT le ngth were explored during the above analyses. A new variable BIGTOE was calculated (1PP+1DP) in order to capture hallux proportions. Metatarsal ratios. In order to investigate the relative make up of the foot 10 ratios were created comparing the maximum lengths of the metatarsal to one another (all possible combinations were explored e.g., one:two, one:three two:three etc.) Such ratios were used to compare the contribution of the first ray to overall foot length
70 relative to the other rays. Given the biomechanical importance of the medial forefoot it is possible that proportional differences exist between the metatarsals among groups or between the sexes. Ratios of the lateral metatarsals (MT2MT5) to foot length as well as stature were created for each group as well. Two way ANOVA was used to compare groups. Metatarsal robusticity. Robusticity indices were created for the metatarsals using the basal measurements and their maximum lengths (e.g., 1MLB/FSTMAX, 2MLB/2MTMAX etc.). Box plots of these were examined and twoway ANOVA was performed to assess the variance between groups. Robusticity allows for the examination of proportional differences among groups from different perspective of shape rather than examining the length and breadths of the elements independently. Quick T est. One further test of the robusticity of the first metatarsal was conducted to explore differences between the ecogeographical ancestry and sexes. The expectation that the cold adapted group is shorter and broader leads to an additional question: Is being broad merely a mechanical consequence of being shorter? In order to asc ertain if there is an ancestral based patterning difference or simply a scaling difference, one must examine whether broader elements regularly coincide with shorter lengths This was explored using a Q uick T est for relative variation between the Black and White males and between Black and White females. The log transformed variable 1MLB was regressed against FSTMAX and the RMA regression line was used for the Quick Test following Tsutakawa and Hewett (1977). This method tests the null hypothesis that the distribution of measurements above and below the regression line for any two samples does not significantly differ.
71 Intrinsic v a riation within groups Coefficients of variation (V) were calculated for all males, all females, B lack males, W hite males, B lack females, and W hite females for 9 variables (stature, foot length, foot breadth, CALMAX, PCAL, CALMIDB FSTMAX, 1MLH and 1MLB) Because V are sensitive to deviations from normality, the absolute variables were tested using Kolmogorov Smirnov one sample test for goodness of fit, prior to utilizing the coefficients for additional analysis. For each grouping, relationships between V were explored testing proximal v ersus distal variability (CALMAX v ersus FSTMAX, PCAL v ersus CALMAX) and breadth v ersus length variability (via CALMIDB v ersus CALMAX and via FSTMLB v ersus FSTMAX). The Student t statistic ( tsSexual Dimorphism ratio compared to appropriate t distribution) used in the current study follows Sokal and Braumann (1980) and is designed to evaluate differences between correlated variables. Prior to calculating the t statistic, V was bias corrected (V* = (1+1/4n)V) and used in all subsequent analys es. This step is usually necessary for small sample sizes but given the current large sample siz e resu lted in rather small corrections Body mass dimorphism. Body mass dimorphism was computed for the HTH cadaver sample as well as th e HTH skeletal sample (combined samples, Black and White). Body mass dimorphism is the mean male body mass/mean female body mass. Cube root of body mass dimorphism. In order to assess overall sexual dimorphism of pedal elements the HTH skeletal sample was used to assess maleto female ratios of 12 l inear skeletal dimensions and compared to the expected ratio of the cube root of body mass dimorphism (of the appropriate sample). This was calculated for stature, the first proximal phalange, all metatarsal lengths, the first metatarsal
72 breadths, the maximum length of the cuboid, and the calcaneus as well as the breadth of the calcaneus. Indices of sexual dimorphism. For comparative purposes a dditionally, indices of sexual dimorphism (ISD) for the HTH sa mple were calculated for 12 variables. Following Kurki et al. (2009) ISD was calculated as : ISD = (male female)/((male+female)/2) (6 1) Allometry and Ecogeographical P attern ing Allometric a nalysis. A test of allometric relationships was conducted using logged variables. Log Log regressions were performed for the variable under scrutiny and the size element under consideration ( e.g., foot length, stature, body mass, or in some cases element length). Any deviation from isometry was tested for significance utilizing the reduced major axis (RMA) slope of the line which is considered a less biased estimate (Smith 2009, and see below ). For linear dimensions a RMA slope greater than 1.0 are positive ly allometr ic and slopes less than 1.0 are negatively al lometric. T he expected RMA slope for isometry when testing a linear dimension to body mass is 0.33. If the theoretical slope of isometry falls within the 95% confidence interval it is not significantly different than isometry Although allometric power functions and logarithmic transformations have been utilized ( and debated) in comparative biology for quite a long time ( Smith 1980; Jungers and German, 1981; Hills 1982; Corruccini 1983; Jolicoeur 1984; Jungers 1984; Jungers et al., 1995; Smith 199 3 ), t heir validity and tests of their efficacy continue to be the subject of much debate (Kaitaniemi 2004, Packard, 2008 ; Smith 2009; Kerkhoff and Enquist 2009) Kerkhoff and Enquist (2009: 520 ) reiterate that log transformation is entirely appropriat e, indeed necessary, for allometric analysis and many other
73 problems in biology. Recently anthropologists have also joined the debate against log transforming data (Haeusler and McHenry 2004) but many other researchers use log transformed data for allom etric analysis ( Holliday and Ruff 2001; Lemelin and Jungers 2007; Holliday and Franciscus 2009) Choices for regression line fitting techniques are plentiful ( e.g., Model I v ersus Model II regressions) however, for allometric comparisons reduced major axis (RMA) is most appropriate (Kaitaniemi 2004 ; Warton et al. 2006; Smith 2009). Smith (2009) recently reviewed differences between Ordinary l east squares ( OLS ) and RMA regression techniques W hile differ ent questions require different methods, allometric comparisons are more appropriate when the biological question at hand involves the partitioning of the variance of the natural biological variation between two traits (X and Y). For example, such as when the slope of the line will be used to interpr et the pattern in the change of shape ( i.e., proportions) with change in size. The question is whether X and Y maintain an isometric relationship, or whether Y exhibits positive or negative allometry (Smith, 2009:482). More recently, In applied anthropological allometric studies there seems to be more agreement that Model II regression (MA, RMA) is the most valid technique ( Gustafsson and Lindenfors, 2004; Lemelin and Jungers 2007). Predictive M odels and S caling Regression equations. The HTH skelet al sample d ata w as also used to create regression equations using least squares (LS) regression for the combined groups as well as individual groups for prediction of foot length and stature from individual elements of the foot These equations were generated using simple univariate regression models These equations were used, in part, to assess conformance to the ecogeographical pattern. For a given stature the Black sample should have longer feet
74 than the White sample (or put another way, for any gi ven foot length the Black sample equations should yield a smaller stature than would the same foot length using the White sample equation). Additionally, because of scaling differences, equations for predicting foot length from individual bony elements sh ould predict consistently longer foot lengths for Black males than White males with the same element length. Body mass was also subjected to least squares regression analysis in order to create predictive equations. F our variables, two from the calcaneus (CALMAX and CALMID B ) and two from the talus (TALMAX L and TALMIN B ), were entered into the regression analysis and stepwise selection was used choose the variable or combination of variables that best predict body mass. These elements were chosen as they both must directly transmit the weight of the body during locomotion are irregular bones comprised of much more trabecular bone than long bones, and given their functional relationship as articular joints, would also not be expected to vary in external dim ensions with levels of activity. Also rather than use the entire HTH skeletal sample for creation of body mass predictive equations, the sample was culled in that only individuals within the normal Body Mass Index (BMI = body mass (kg)/stature (m)2 Scaling for eco groups One further step was taken in the analysis of allometric scaling of the foot between ecogeographical populations. Ecogroups, groups that scale exactly as expected based on their ecogeographical pattern, were created. Ecogroups were created by using well studied and often utilized regression equations for the prediction of stature from long bone lengths ( i.e., using the Trotter and Gleser (1952, 1958) e quations as presented in Trotter 1970), and thus femora and ), o f 18.525 (WHO, 19 86) were used to generate these predictive equations.
75 tibiae could be generated for any hypothetical stature. For instance, us ing the regression equations for Black males: Stature = 2.11 (Femur) + 70.35 (6 2) Stature = 2.19 (Tibia) + 86.02 (6 3) and for White males: Stature = 2.38 (Femur) + 61.41 (6 4) Stature = 2.52 (Tibia) + 78.62 (6 5) by substituting 170 cm for stature, predicted femora lengths of 47.23 cm and 45.63 cm and tibiae lengths of 38.34 cm and 36.26 cm for Black and White males respectively, are derived. Hypothetical statures were used to generate ecoindividuals whose tibiae and femora, scale exactly as expected for their target statures for all four groups. Additionally, using the sex and group specific LS regression equations from the current study, target foot lengths were calculated for each ecoindividual. Scaling of the foot to the femur and to the tibia could then be analyzed for each ecogroup. T here is a noted discrepancy between how the tibia e w ere measured in the original stature estimation studies and how they were presented as having been measured (see Jantz et al., 1994). For the purposes of this analysis the difference is inconsequential Any correction factor, because it would be applied uniformly, woul d not change the scaling relationships between groups. Furthermore, using the original equations then predicts a more functional length of the tibia, from the lateral condyle of the proximal surface to the articular surface of the distal tibia rather than the medial malleolus (which contributes to maximum length of the tibia but not to stature). The
76 male data were originally generated from a large Korean War sample of Black and White m ales while the female data were generated from individuals from the Terry collection, an anatomical collection relatively contemporaneous with the HTH sample. Intrinsic V ariation B etween G roups Statistical methods for direct comparisons among groups ( e.g., WM vs WF or BM vs BF) utilizing V are not available (Sokal and Br aumann 1980). In order to compare relative variability among groups ( e.g., X and Y), the variance of log transformed variables (S2 lnX) is used and the ratio of S2 lnX/ S2 lnY is compared against the F distribution with Nx 1 and Ny 1 degrees of freedom (Lew ontin, 1966). The variance of the log transformed variables closely approximates the squared coefficient of variation ( V2) whe n the variation is less than 30% (Lewontin, 1966; Franciscus and Long 1991). Thus, V2B iomechanical E nvironment was utilized in this study. Comparisons between all females versus all males, B lack males versus B lack females, B lack males versus W hite males, W hite males versus W hite females and B lack females versus W hite females were conducted for 13 variables. Effective m echani cal a dvantage. The effective mechanical advantage was calculated by modeling the foot as a class 1 lever with the fulcrum at the ankle joint. In the current study PCAL refers to r the muscle moment arm, and the GRF moment arm is R and is calculated via [ (CALMAX PCAL) + CUBMAX + 3RDMAX ] Using t his configuration effectively captures the fulcrum point anterior to PCAL up to the metatarsophalangeal joint. Joint reaction forces (JRF). Calculations of ground reaction forces ( GRF ) during walking is based on body weight (GRF = 1.2 times body weight, following Keller et al.
77 (1996) ) Thus muscle force required to main static equilibrium can be calculated following the formula: R Fr = r* Fm (6 6) Where Fr is GRF and Fm is the force of the muscles pull ing on the Achilles tendon. The result s were examined for patterns related to joint forces at the ankle (calculated as the resultant force between Fr and FmTalar and calcaneal dimensions and JRF Least squares (LS) regression and RMA regressions on log log plots of the variables were used to explore scaling related to joi nt force reactions and maximu m lengths and breadths of the talus and calcaneus in equilibrium (Figure 6 2 ). Muscle force direction was estimated as the midstance/ mid support dir ection of the lower leg following Carrier et al. (1994).
78 Table 6 1 Mean age, mass, and stature of the HTH cadaver sample Sample Variable N Min Max Mean Std. Deviation BF Age (years) 163 18 45 32.42 7.56 Mass (kg) 163 27.22 136.08 49.44 13.6 8 Stature (mm) 163 1405 1841 1643.48 70.78 WF Age (years) 50 19 45 34.60 7.24 Mass (kg) 50 28.12 71.67 50.6 6 10.64 Stature (mm) 50 1436 1772 1620.90 77.63 BM Age (years) 479 18 45 33.84 7.64 Mass (kg) 479 29.94 99.79 55.5 5 11.05 Stature (mm) 479 1496 1985 1757.73 76.9 9 WM Age (years) 348 18 45 38.11 6.19 Mass (kg) 348 29.03 94.35 56.15 11.39 Stature (mm) 348 1515 1946 1711.72 68.3 2 Table 6 2 Mean age, mass, and stature of the HTH skeletal sample Sample Variable N Min Max Mean Std. Deviation BF Age (years) 35 17 72 38.69 15.92 Mass (kg) 34 25.40 89.81 49.60 13.7 5 Stature (mm) 35 1405.00 1800.00 1641.8 6 85.25 WF Age (years) 30 23 80 51.73 16.5 4 Mass (kg) 30 27.22 89 .81 51.3315 14.24 Stature (mm) 30 1411.00 1772.00 1606.10 83.6 2 BM Age (years) 68 18 58 33.78 10.2 7 Mass (kg) 67 37.65 99.79 61.6 2 10.9 3 Stature (mm) 68 1606.00 1985.00 1761.01 90.52 WM Age (years) 69 20 78 45.62 13 .57 Mass (kg) 67 37.42 89.81 63.57 11.47 Stature (mm) 69 1550.00 1928.00 1723.4 1 69. 20
79 Table 6 3 Skeletal measurements used in the current study Measurement Description Reference(s) CALMAX Maximum length of calcaneus Holland (1995) PCAL Posterior length of calcaneus Holland (1995) CALMIDB Middle breadth of calcaneus Buikstra and Ubelaker (1994) TALMINB Minimum breadth of talus Byrd and Adams (2003) TALMAXL Maximum length of talus Holland (1995) CUBMAX Maximum length of cuboid B yrd and Adams (2003) NAVMAX Maximum length of navicular Byrd and Adams (2003) FST MAX Maximum length of MT1 Byrd and Adams (2003) 1MTMLH Width of MT1 head Robling and Ubelaker (1997) 1MTMLB Width of MT1 base Robling and Ubelaker (1997) 1PP Maximum len gth of 1 st ray proximal phalanx 1DP Maximum length of 1 st ray distal phalanx 2MTMAX Maximum length of MT2 Byrd and Adams (2003) 2MTMLB Width of MT2 base Robling and Ubelaker (1997) 3MTMAX Maximum length of MT3 Byrd and Adams (2003) 3MTMLB Width of M T3 base Robling and Ubelaker (1997) 4MTMAX Maximum length of MT4 Byrd and Adams (2003) 4MTMLB Width of MT4 base Robling and Ubelaker (1997) 5MTMAX Maximum length of MT5 Byrd and Adams (2003) 5MTMLB Width of MT5 base Robling and Ubelaker (1997)
80 20 40 60 80age 2% 4% 6% 8% 10%Percent Figure 6 1 Histogram illustrating the age distribution of the HTH skeletal sample.
81 Table 6 4 Correlation coefficients for selected tarsals and phalanges and foot length Group Variable N R Sig Variable N R Sig All 194 0.77 < 0.00 1 197 0.70 <0.001 B F 32 0.77 <0.001 35 0.75 <0.001 WF CALMAX 30 0.82 <0.001 TALMAX L 30 0.69 <0.001 BM 67 0.64 <0.001 67 0.52 <0.001 WM 65 0.65 <0.001 65 0.56 <0.001 All 195 0.78 <0.001 199 0.60 <0.001 BF 33 0.80 <0.001 35 0.68 <0.001 WF PCAL 30 0. 81 <0.001 TALMIN B 30 0.48 0.007 BM 67 0.61 <0.001 68 0.36 0.003 WM 65 0.65 <0.001 66 0.52 <0.001 <0.001 All 196 0.69 <0.001 176 0.81 <0.001 BF 32 0.75 <0.001 33 0.83 <0.001 WF CALMIDB 30 0.62 <0.001 1PP 28 0.75 <0.001 BM 68 0.5 2 <0.001 58 0.79 <0.001 WM 66 0.44 <0.001 57 0.78 <0.001 All 190 0.73 <0.001 BF 32 0.66 <0.001 1DP 157 0.62 <0.001 WF NAVMAX 27 0.78 <0.001 28 0.74 <0.001 BM 66 0.66 <0.001 23 0.73 <0.001 WM 65 0.39 0.001 56 0.58 <0.001 50 0.53 <0.001 All 190 0.80 <0.001 BF 34 0.72 <0.001 WF CUBMAX 28 0.67 <0.001 BM 65 0.70 <0.001 WM 63 0.61 <0.001
82 Table 6 5 Correlation coefficients for metatarsal length and foot length Group Variable N R Sig Variabl e N R Sig All 190 0.85 <0.001 174 0.84 <0.001 BF 34 0.85 <0.001 31 0.82 <0.001 WF FSTMAX 27 0.75 <0.001 4MTMAX 25 0.70 <0.001 BM 66 0.79 <0.001 59 0.72 <0.001 WM 63 0.71 <0.001 59 0.74 <0.001 <0.001 <0.001 All 185 0.84 <0.001 168 0 .54 <0.001 BF 33 0.86 <0.001 30 0.51 0.004 WF 2MTMAX 28 0.56 0.002 5MTMAX 26 0.51 0.008 BM 64 0.77 <0.001 56 0.24 0.073 WM 60 0.70 <0.001 56 0.37 0.006 <0.001 All 177 0.85 <0.001 BF 32 0.84 <0.001 WF 3MTMAX 27 0. 72 <0.001 BM 60 0.76 <0.001 WM 58 0.73 <0.001 Table 6 6 Correlation coefficients for the metatarsal breadths vs. foot length Group Variable N R Sig Variable N R Sig All 169 0.66 <0.001 174 0.67 < 0.00 1 BF 31 0.69 <0.001 31 0.57 0.001 WF 1MLH 25 0.62 0.001 3MLB 26 0.64 <0.001 BM 58 0.57 <0.001 59 0.46 <0.001 WM 55 0.56 <0.001 58 0.48 <0.001 All 174 0.59 <0.001 168 0.54 < 0.00 1 BF 32 0.69 <0.001 30 0.51 0.004 WF 1MLB 25 0.41 0.041 4MLB 26 0.51 0.008 BM 58 0.48 < 0.00 1 56 0.24 0.073 WM 59 0.33 0.010 56 0.37 0.006 All 173 0.64 <0.001 172 0.56 < 0.00 1 BF 31 0.60 <0.001 31 0.53 0.002 WF 2MLB 26 0.42 0.031 5MLB 26 0.59 0.002 BM 59 0.48 0.000 57 0.26 0.047 WM 57 0 .46 0.000 58 0.52 < 0.00 1
83 20 160 C 2 = A 2 + B 2 2(A)(B) COS 160 Figure 6 2 Diagram of force vectors acting on the ankle joint. The green vector is the force of the muscle ( Fm) the blue vector is the ground reaction force ( Fr) and the red vector is the r esultant joint reaction force. During midstance the ground reaction force acts perpendicular to the ground surface, and the direction of the muscle force is 20 off vertical. Using the trigonometric function the length (and hence magnitude) of the result ant joint reaction force can be calculated.
84 CHAPTER 7 RESULTS Measurement E rror Technical e rror of m easurement (TEM). Data from two measurement trials was used to compute the technical error of measurement (TEM) following Dahlberg (1940) and Knapp ( 1992). The TEM was found to be rather small ranging from 0.216 mm to 0.453 mm (Table 71) The TEM examined as a relative measure of the magnitude of error is reflected in the coefficient of variation of error (CVE) Results of calculations of the CVE also show small relative magnitudes of error ranging from 0.4% to 2.6% (Table 7 1). Percent measurement error (%ME). To examine the amount of variability between the length and breadth measurements that are attributable to measurement error three measure ment trials were used to calculate a percent measurement error (%ME) following Bailey and Barnes (1990). This method of calculation uses a M odel II ANOVA to partition total variability among measurements into among group variance (sample variance) and wit hin group variance (measurement error). Rather than assessing an absolute measurement error, the %ME method evaluates the magnitude of the error relative to the among individual variation. Results indicate that breadth measurements are more variable than lengths however they are within tolerable limits for analysis of relative variability (Table 72) Proportionality of the HTH Cadaver S ample F oot F oot length and foot length to stature The Black sample has longer foot lengths and larger foot length to stature ratios than the White sample with males being larger than females, in the HTH cadaver sample (Table 7 3 ). Additionally, in absolute
85 terms the HTH skeletal Black sample has larger foot breadths than their White sample counterparts. ANOVA. A two way between groups ANOVA explores the impact of sex (M vs F) and race (B v s. W) on the length of the foot in the HTH cadaver sample. For foot length, the interaction effect between s ex and race was not significant ( F = 1.456, df = (1,1040) p = 0 .228 ) Therefore it is prudent to consider the main effects that is, the interaction between sex and race is not influencing the dependent variable (foot length). There was a statistically significant ( .001) main effect for sex and race for the length of the foot. In an analysis of size effects, Sex (25.1%) and Race (9.2%) account for over one third of the variability between groups. These are considered large and medium large size effects following Cohen (1988). The null hypothesis ( there is no diff erence between groups ) can be rejected for the main effects of sex and race. A two way between groups ANOVA explori ng the impact of sex (M vs F) and race (B vs W) on the variable foot length/stature was conducted. For foot length/stature the interaction effect between sex and race was not significant; F = 0.285, df = (1,1040 ) p = 0 .593. Therefore it is prudent to consider the main effects. There was a statistically significant ( .001 ) main effect for sex and race for the foot length/stature. E ffe ct size as inferred from the partial eta squared statistic shows that s ex accounts for 6.3% and r ace accounts for 5.8% of the variability found between the groups. These are considered small to medium effect sizes following Cohen (1988). That is, there is a real and significant difference between groups; however, it takes careful study to elucidate it. The null hypothesis that there is no difference between groups can be rejected for the main effects of sex and race.
86 Foot length and foot length relative to stature in the fleshed foot HTH cadaver sample do display statistically significant differences between the sexes and between races. The pattern is one that conforms to the expected in that females tend to have smaller feet than males and W hit e individuals are have smaller average foot lengths than B lack individuals. What is illuminating is that this pattern holds even for the relative measure. That is, relative to stature, females have shorter foot lengths than males. This result affirms Fe ssler et al.s (2005) finding that female feet are more dimorphic than males relative to stature. However, this alone does not address the issue of whether the female foot is scaling isometrically to stature or a n other body size variable, or if ancestral ecogeographical origin affects proportionality within the makeup of the foot itself (see below). Proportionality of the HTH Skeletal S ample F oot F oot length and foot length to stature The Black sample has longer foot lengths and larger foot length to stature ratios than the White sample with males being larger than females, in the HTH skeletal sample (Table 74 ). Additionally, in absolute terms the HTH skeletal Black sample has larger foot breadths than their White sample counterparts. ANOVA. The r esults of ANOVA for selected variables reveal several i nteresting patterns. First, several variables do not retain, statistically significant differences when scaled to stature or foot length (Table 75 ). For instance, PCAL, which is significant for both main effects of s ex and race shows no differences when examining PCAL/Stature. CALMAX is significant for sex as a standalone variable but not when examining it length relative to stature, and only for Race relative to foot length (while it is not signif icant as a standalone variable). The sum of the first ray phalanges is only significant for race as a
87 ratio to foot length, and is significant for sex as a standalone variable and relative to stature. Only the first metatarsal was found to differ between the White and Black samples relative to stature. This finding indicates that the metatarsal region is likely the region exhibiting the most influence on the ecogeographical proportional differences observed for the foot (see below). Metatarsals. White females tend to have the smallest metatarsals, while Black males are longest (Table 76 Figure 7 1). Males are generally larger than females; however Black females typically display very similar mean lengths to the White male sample (ANOVA results for s elected measurements (Table 75) ). Breadth measurements do not follow the same pattern (Table 77 Figures 72 and 73). Although Black females metatarsal length is similar to White males, they tend to be substantially smaller in their breadths. Black m ales tend to be largest in absolute terms, although it is clear that breadths are not as markedly different than White males. For instance breadth of the head taken as a ratio to maximum length (1MLH/ FSTMAX) shows that both the Black females and Black mal es have proportionally smaller first metatarsal heads than their White counterparts (Figure 74). Calcaneus. Three measurements of the calcaneus (Table 78 and Figure 75) exhibit the expected pattern of males larger than females and Black males larger t han White males; as do the other tarsal measurements (Table 79 and Figure 76). Between White and Black females the breadth measurement of the calcaneus is very similar with more variance in the Black sample. Additionally, the Black female sample is qui te close to the White male in the length of the posterior calcaneus. Consideration of these box plots suggests that the breadth measurement would be most useful for
88 distinguishing between groups, although there is considerable overlap between and among gr oups. Phalanges. The proximal phalanges are longer in the Black sample. The distal phalange is longer for Black females than White females but larger in White males than in Black males (Table 710, Figure 77). Relative makeup of foot. Ratios of BIGT OE (1PP+1DP), FSTMAX, CALMAX, and PCAL to Foot length were also explored. In all groups CALMAX typically accounts for over (or in the case of BM nearly) 1/3 of the total length of the foot (Table 7. 11 Figure 7.8) Notably CALMAX and PCAL are slightly s maller in the Black male group. Scaled to foot size White females, who in absolute terms represent the smallest dimensional group, are consistently greater than all other groups for the three main portions of the foot under scrutiny here. That is the fir st metatarsal the calcaneus and the hallux make up more of overall foot length for the White females than the other groups. Soft tissue thickness, scaling of the tarsals, height of the longitudinal arch differences might account for some of the differences observed. Metatarsal ratios. One striking pattern of the relative proportions of the metatarsals in relation to one another and between groups is that the first metatarsal is proportionally larger than the other metatarsals in the White samples (male and female) (Figure 7 9). Two way ANOVA (T able 7 12) confirms the graphical pattern in that statistically significant differences are present for the main effect race in three of the four first metatarsal ratios the exception being ONE / FIVE. Examinati on of F igure 7 9 shows that the Black sample has relatively longer third metatarsals than their fifth in comparison to their W hite counterparts. No ratios are statistically significant for the
89 main effect of sex. Although it should be pointed out that the Black female sample has the highest ratio for TWO / FIVE, THREE / FIVE and FOUR / FIVE, and it is the White female sample that has the highest ratios for the first metatarsal comparisons. Metata rsals 25 relative to stature and foot size To further test the pattern observed for the first metatarsal and the other two main regions of the foot tested above (the hindfoot via the calcaneus and the hallux via the phalanges), the additional metatarsals (relative to stature and foot size) were subjected to ANOVA These tests were conducted to establish whether it is scaling of the metatarsals in general, or simply the first metatarsal that contributes to the forefoot scaling observed thus far. The first metatarsal is unique compared to the other metatarsals in that it is homologous with phalanges and has a different load bearing role during locomotion. With respect to stature, all of the lateral metatarsals are statistically significant for the main effect of race (Table 71 3 ). The fifth metatarsal is also statistically significant for sex, while all other metatarsals did not show significant differences for sex. Relative to foot size there are no statistically significant differences for the main effect race for the lateral metatarsals (Table 714 ). There ar e significant differences for sex for all except the fifth metatarsal. Metatarsal robusticity. Robusticity indices were calculated from the metatarsal medial lateral base widths and their corresponding maximum lengths (ROB1 is robusticity for MT1; ROB2 is MT2 and so forth) (Table 71 5 Figure 710). Examination of the results of twoway ANOVA shows that for robusticity there is a significant difference for the main effect race for ROB1, and for race and sex for ROB2 (Table 71 6 ). There is an interacti on between the main effects of race and sex for
90 ROB2, the interaction plot (not shown) indicates that this is due to the Black female group. The ANOVA and box plots tend to show that the Black female group is well below the means for the other three groups (for instance ROB1, ROB2 and ROB3). The robusticity index for ROB4 however, shows a different pattern, in that White males are further from their Black counterparts and considerably lower than White females (although this is not significant). The index for ROB5 shows a significant difference for race but not for the interaction effect or sex. Thus, the Black females stand out as having particularly narrow bases of the first three metatarsals compared to all groups, and the White males have narrow MT4 bases scaled to metatarsal length. Quick Test Results of the Quick Test ( Table 7 17) indicate that among females there is a statistically significant difference between the relationship of the breadth and length of the first metatarsal. The Black femal es are significantly narrower for a given length than the White f emale sample. The same relationship is not apparent between Black and White males, who are equally variable in their robusticity. I ntrinsic variation within groups Results of calculations of bias corrected coefficients of variation (V*) are presented in T ables 7 1 8 and 7 1 9 Results of the tsSexual Dimorphism ratios tests of significance between correlated variables (within groups) show no significant differences in relative variability of any of the examined pairings (Table 720) Body mass d imorphism The ratio of mean body mass between males and females, in the combined group, Blacks and Whites in the HTH skeletal sample is equal to 1.24, meaning the males are 24% larger than the f emales in the study sample. This is larger than the overall sample from which they were drawn as t he HTH cadaver sample used in this study displays a body mass dimorphism ratio of 1.12. This
91 moderate dimorphism is typical, for instance u sing Parham et al s (1992) data M/F body mass dimorphism is 1.24 for that sample, and the current sample is also congruent with body size dimorphism calculated from Smith and Jungers (1997) which range from 1.061.23. Thus the skeletal sample selected is a good represent ation of typical human body size dimorphism. The ratio of the expected linear dimensions (based on cube root of body size dimorphism) is 1.07 for the combined and Black sample and 1.04 for the White sample (who have a body mass dimorphism of 1.12) Proportions based on cube root of body mass Examination of the observed minus expected proportions based on the cube root of body mass, shows that the White sample is more dimorphic than the Black sample (Table 721 ) The most notable dimorphic features for the Black sample are the breadth measurements of the first metatarsal as well as the breadth of the calcaneus and the maximum length of cuboid. The White sample tends to be more dimorphic for the length measurements, for instance the five metatarsal lengths range in differences of observedexpected from 4.3% to 5.9%, while for the Black sample the differences range from 0.1% to 0.8%. Indices of sexual dimorphism. Examination of the ISDs leads to a similar pattern of dimorphism Examination of the l engths of the metatarsals the White sample is more dimorphic (Table 722). For the maximum lengths of the tarsals (except CALMAX) the Black sample is more dimorphic. In terms of the breadth measurements associated with the tarsals and metatarsals, the Bl ack sample is more dimorphic. Allometry and Ecogeographical Patterning Allometric analysis. Individual tests for deviations from isometry were performed using bivariate regression of logarithmically transformed variables (Figure 7 11) Reduced m ajor a x is (RMA) line fitting technique was used to determine the slope of the
92 regression and deviations from isometry were noted if the 95% confidence interval contained the expected slope of isometry (1.0 for linear dimensions and 0.33 for body mass). Results o f RMA regressions for the HTH cadaver sample foot length versus stature and body mass are presented in Table 723. Results of RMA regressions against stature for six variables are presented in Table 72 4 Reduced m ajor a xis regressions against foot lengt h for five bony variables are presented in Table 72 5 Reduced m ajor a xis regressions against body mass for six variables are presented in Table 72 6 As can be seen from the summary of all RMA regressions for all groups (Table 72 7 ) when combining all gr oups into the analyses deviations from isometry are found more often than when broken out by sex and ecogeographical ancestry Black males appear to be the most isometric group as the only deviations from isometry detected in the HTH skeletal sample was n egative allometry of the first metatarsal relative to stature, and for the HTH cadaver sample, positive allometry of the foot relative to stature and body mass. White males are positively allometric for all variables relative to stature, and scale with is ometry by most measures of body mass and also intrinsically within the foot. The only exception was negative allometry in overall foot length with reference to body mass. White female feet scale with isometry relative to stature. However, the feet are sc aling negatively in relation to body mass in the HTH skeletal sample, as does the posterior calcaneus and the first metatarsal. Black females tend to scale positively by a number of measures including major elements of the foot to stature as well as intri nsically. Two variables indicate negative allometry the foot (in both the
93 HTH cadaver and HTH skeletal samples) and posterior calcaneus relative to body mass. Foot to stature and foot to body mass regressions show some differences depending on which sam ple is used (HTH cadaver sample versus HTH skeletal sample). The most significant difference in terms of interpretation is that for foot to stature Black males and females move from positively allometric to isometric. Also for Black males the HTH skeletal sample the foot is not significant with regard to body mass. The White male skeletal sample is isometric with regard to body mass versus negatively allometric for the cadaver sample. The larger HTH cadaver sample is likely the more accurate result in terms of how the foot scales to stature for these groups. Predictive M odels and S caling Regression equations. Least squares r egression equations generated using the HTH skeletal sample for the prediction of stature from foot length (Table 72 8 ) and from each metatarsal (Table 729) show relatively high correlations and reasonable standard errors Regression equations to predict foot length from the metatarsals, the calcaneus, and cuboid also show reasonable correlations and standard errors (Table 7 30). Least squares r egression using four measurements of the calcaneus and talus and stepwise selection results in two models (Table 7 31 ). Predictive models and scaling In terms of ecogeographical patterning there is a scaling difference among the groups i n foot size to stature. For instance, using population specific regression equations one can see that at any given stature the Black group will be predicted to have a longer foot than the White group ( Figure 714). There is also a scaling difference within the foot between the White and Black samples. For instance, using population specific regression equations one can see that at any given
94 length of the first metatarsal from the Black sample would be predicted to have a longer foot length ( Figure 7 15 ). The same is true of the calcaneus ( Figure 716). Thus intrinsically the foot is scaling differently among the groups. Scaling of eco groups This scaling was fur ther investigated by creating ecogroups groups who scale exactly as expected based on well studied and often utilized regression equations for the prediction of stature from long bone lengths. Relationships between scaling and isometry were carried out as before using RMA regressions ( T able 7 32). The foot scales positively with respect to the femur for all groups and negatively with respect to the tibia for Black males and females, but positively for White males and females. Intrinsic Variation A mong G roups Results of the F test comparisons of the between groups analysis show the largest number of significant differences can be found between Black males and Black females, with Black females tending to be more variable than Black males ( Table 7 33 ). There is no difference between Black and White males and females in terms of intri nsic variability. White females are more variable than White males in terms of the breadth of the base of the first metatarsal (1MLB). Biomechanical Environment E ffective mechanical a dvantage (EMA) The EMA based on an in lever of: PCAL and an out le ver using: (CALMAX PCAL)+CUBMAX+3RDMAX was shown to be very similar between all four samples (Figure 7 17; Table 7 3 4 ). The most variability is found in the Black male sample who range from 38% 48% ( t wo w ay ANOVA yields no significant differences between groups, results not presented). In a biv ariate regression
95 (LS) of log EMA (r/R) on log body mass (kg) in the HTH skeletal sample, t here is not a linear relationship between EMA and body size (Figure 7 18). L inear regression of the combined samples regres sing the in lever (r) on the out lever (R) (using the third metatarsal) yields a correlation coeficient of 0.778 (Figure 7 19). Breaking that regression down into the component subsamples yields correlations for WF, BF, BM, and WM are 0.861, 0.784, 0.617, and 0.646, respectively ). The coefficient of determination (R2Joint R eaction F orces (JRF). The relationship of the proportions of the EMA w as further explored using a free body diagram analysis of joint reaction forces. S tatic equilibrium calculation s of muscle force needed to counter the GR F are based on moment arms associated about the ankle, which are modeled here based on the in and out levers described above. This confi guration is appropriate for midstance of gait scenarios. Calculated muscle force reactions (with GRF = 1.2 (body mass) ) are presented in Table 7 3 5 and Figure 7 21 These calculated forces were then used to calculate resultant forces at the ankle. Descriptive statistics for the resultant magnitude of force at the ankle are presented in T able 7 3 6 Regression of body mass on joint reaction force (Figure 722) results in a high correlation for all groups (n = 189, r = 0.802, adj. r ) is decreased when the subsamples are analysed independently (Figure 7 19) With the exception of Black females PCAL alone is not a very good predictor of the out lever in these models, especially for the males. 2Talar and calcaneal dimensions and JRF The talus and the calcaneus together with the distal tibia and fibula make u p the ankle joint. The dimensions of the talus and calcaneus were tested for isometry to joint reaction forces for the HTH skeletal sample. = 0.641, SE = 11.91).
96 Reduced m ajor a xis regressions reveal several no n significant models (Table 73 7 ). It is probable that the non si gnificant models in this study result from inadequate sample sizes for the individual groups. Analysis of the combined samples indicates the talar and calcaneal dimensions tend to scale isometrically with joint reaction forces with the exception of CALMAX which is slightly negatively allometric.
97 Table 71. Technical error of measurement (TEM) and coefficient of variation of the error (CVE) for eight variables Variable N TEM (mm) CVE (%) CALMAX 19 0.402 0.5 CALMIDB 19 0.314 0.8 FSTMAX 21 0.248 0.4 1 MLH 20 0.273 1.4 1MLB 21 0. 355 2. 1 5MTMAX 18 0.216 0.3 5MLB 18 0.366 2.2 TALMINB 21 0.382 1.2 TEM is the sum of the square root of the sum of the squared differences between corresponding measurements divided by 2X sample size ( i 2/ 2n). CVE is the TEM divided by the mean of the test/retest for the first individual. Table 72. Percent measurement error (% ME) of eight variables Variable N (% ME ) CALMAX 19 0.87 CALMIDB 19 8.79 FSTMAX 21 1.22 1MLH 20 7.79 1MLB 21 8.85 5MTMAX 18 0.33 5MLB 18 9.65 TALMINB 21 7.66 %ME evaluates the magnitude of the measurement error relative to the sample variance for the variable
98 Table 7 3 HTH cadaver sample foot length, breadth and f oot length to stature descriptive statistics Sam ple Variable N Min Max Mean SD BF FOOT LENGTH 163 191 270 232.86 12.78 FOOT BREADTH 163 66 98 82.39 6.51 FOOT / STATURE 163 0 .12 0 .16 0 .1417 0 .00 6 WF FOOT LENGTH 50 199 249 222.08 11.97 FOOT BREADTH 50 71 96 82.84 6.17 FOOT / STATURE 50 0 .13 0 .15 0. 1371 0 .00 5 BM FOOT LENGTH 479 213 300 256.53 13.9 1 FOOT BREADTH 479 73 109 91.35 6.4 2 FOOT / STATURE 479 0 .13 0 .18 0 .1460 0 .006 WF FOOT LENGTH 348 198 274 242.87 13.56 FOOT BREADTH 348 69 105 88.98 5.91 FOOT / STATURE 348 0 .11 0 .16 0 .1419 0 .006 Table 7 4 HTH skeletal sample foot length, breadth and f oot length to stature descriptive statistics Sample Variable N Min Max Mean SD BF FOOT LENGTH 35 210 259 234.86 14.32 FOOT BREADTH 35 72 102 82.43 7.69 FOOT / STATURE 35 0 .1 3 0 .16 0 .1431 0 .006 WF FOOT LENGTH 30 192 258 218.80 15.62 FOOT BREADTH 30 73 94 81.90 6.2 4 FOOT / STATURE 30 0 .13 0 .15 0 .1362 0 .00 6 BM FOOT LENGTH 68 235 298 259.16 15.3 3 FOOT BREADTH 68 74 105 90.88 5.9 1 FOOT / STATURE 68 0 13 0 .16 0 .1473 0. 00 7 WF FOOT LENGTH 69 203 270 242.22 14.12 FOOT BREADTH 69 77 104 89.81 6.0 5 FOOT / STATURE 69 0 .12 0 .15 0 .1406 0. 006
99 Table 7 5. Two w ay ANOVA results for skeletal variables Variable N F Sig Partial Eta Squared CALMAX 1 95 sex race sex race 79.441 4.491 0.002 < 0.00 1 0.035 0.964 0 .294 0 .021 0 .000 CALMAX/stature 195 sex race sex race 4.648 0.635 0.212 0.032 0.426 0.646 0 .024 0 .003 0 .001 CALMAX/foot length 194 sex race sex race 2.656 46.691 0.598 0.105 < 0.001 0.440 0 .014 0 .197 0 .003 PCAL 196 sex race sex race 56.385 12.257 0.008 < 0.00 1 0.001* 0.931 0 .227 0 .060 0 .000 PCAL/ stature 196 sex race sex race 0.801 2.092 0.258 0.372 0.150 0.612 0 .005 0 .012 0 .008 PCAL/ foot length 195 sex race sex race 6.664 18.562 0.525 0.011* < 0.001 0.470 0 .034 0 .089 0 .005 FST MAX 191 sex race sex race 70.144 20.547 0.161 < 0.00 1 < 0.001 0.689 0 .995 0 .273 0 .001 FST MAX/ stature 191 sex race sex race 2.253 8.101 0.100 0.135 0.005* 0.752 0 .012 0 .042 0 .001 FST MAX/foot length 190 sex race sex race 10.150 18.071 0.002 0.002* < 0.001* 0.967 0 .052 0 .089 0 .000 1PP+1DP 157 sex race sex race 65.569 0.827 1.553 < 0.00 1 0.365 0.215 0 .300 0 .005 0 .010
100 Table 7 5 (cont) Two way ANOVA results for skeletal variables Variable N F Sign Partial E ta Squared 1PP+1DP/ stature 157 sex race sex race 10.209 0.511 0.795 0.002* 0.476 0.374 0 .063 0 .003 0 .005 1PP+1DP/ foot le ngth 156 sex race sex race 0.045 51.232 1.637 0.832 < 0.001 0.205 0 .000 0 .252 0 .011 *Bonferronis adjustment P Table 7 6 Descriptive statistics for the m aximum l engths of the metatarsals Sample Variable N Min Max Mean SD BF FSTMAX 34 55.22 72.54 64.2 6 4.6 7 2ndMAX 33 60.90 85.93 75.58 5.9 2 3rdMAX 32 63.38 82.48 71.04 4.98 4thMAX 31 59.35 78.82 69.5 5 5.1 9 5thMAX 32 59.2 80.8 70.10 5.34 WF FSTMAX 27 53.81 68.88 61.05 3.4 6 2ndMAX 28 60.33 83.02 70.68 4.9 4 3rdMAX 27 55.81 78.59 66.26 4.9 8 4thMAX 25 56.97 75.40 64.60 4.47 5thMAX 23 55.6 79.5 66.0 9 5.5 6 BM F STMAX 66 61.10 80.99 69.44 4.38 2ndMAX 64 70.40 93.51 81.22 4.97 3rdMAX 60 67.18 89.62 76.65 4.7 9 4thMAX 59 64.94 87.44 74.68 4.71 5thMAX 58 65.2 87.1 75.9 4 4.69 WM FSTMAX 64 58.62 75.67 66.7 6 3.9 3 2ndMAX 61 67.06 89.06 76.9 6 4 .03 3rdMAX 59 61.74 84.66 71.6 4 4.07 4thMAX 60 61.33 80.80 70.7 7 4.0 8 5thMAX 62 63.1 83.4 72.5 4 4.5 0
101 1.00 2.00 3.00 4.00racecode 60.00 70.00 80.001stMAX 1.00 2.00 3.00 4.00racecode 60.00 70.00 80.00 90.002ndMAX 1.00 2.00 3.00 4.00racecode 60.00 70.00 80.00 90.003rdMAX 1.00 2.00 3.00 4.00racecode 60.00 70.00 80.004thMAX 1.00 2.00 3.00 4.00racecode 60.0 70.0 80.05thMAX Figure 71. Box plots of the maximum lengths of the five metatarsals (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
102 Table 7 7 Descriptive statistics for b readth m easurements of the m etatarsals Sample Variable N Min Max Mean SD BF 1MLH 31 17.48 23.89 20.5 7 1.89 1MLB 32 14.39 22.32 19.1 7 1.80 2MLB 31 10.92 16.75 14. 10 1.28 3MLB 31 10.08 16.10 13.22 1.21 5MLB 31 16.19 23.73 19.24 1.87 WF 1MLH 25 16.94 25.87 20.6 8 1.79 1MLB 25 15.29 23.55 19.52 1.85 2MLB 26 11.47 17.20 14.3 6 1.3 6 3MLB 26 9.39 16.28 12.95 1.33 5MLB 26 16.02 22.58 19.21 1.75 BM 1MLH 58 20.06 26.86 23.07 1.28 1MLB 58 18.75 27.33 21.66 1.51 2MLB 59 13.88 18.49 16.36 0. 99 3MLB 59 12.25 18.83 14.92 1.20 5MLB 57 17.80 24.83 21.27 1.55 WM 1MLH 56 19.03 27.66 23.2 1 1.74 1MLB 60 17.48 24.34 21.3 4 1.3 5 2MLB 58 14.03 19.44 16.07 1.1 5 3MLB 59 11.30 18.17 14.0 1 1.1 7 5MLB 59 17.34 26.28 21.2 8 1.93
103 1.00 2.00 3.00 4.00 15.00 20.00 25.001MLB 1.00 2.00 3.00 4.00 17.50 20.00 22.50 25.00 27.501MLH Figure 72. Box plots of medial to later al breadths of the head (left) and base (right) of the first metatarsal (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
104 1.00 2.00 3.00 4.00racecode 10.00 12.00 14.004MLB 1.00 2.00 3.00 4.00racecode 10.00 12.00 14.00 16.00 18.003MLB 1.00 2.00 3.00 4.00racecode 12.00 14.00 16.00 18.002MLB 1.00 2.00 3.00 4.00racecode 17.50 20.00 22.50 25.005MLB Figure 73. Box plots of medial to lateral breadths of the base of metatarsals two through five (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
105 1.00 2.00 3.00 4.00 0.300 0.325 0.350 0.375 0.400ratioMLHvsfstmax Figure 74. Box plot of ratio of first metatarsal head width to length (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
106 Table 7 8 Descr iptive statistics for length and breadth measurements of the calcaneus Sample Variable N Min Max Mean SD BF CALMAX 32 64.62 87.81 76.83 5.7 9 PCAL 33 47.63 63.88 56.0 3 4.38 CALMIDB 32 34.38 45.12 39.40 2.9 6 WF CALMAX 30 66.30 87.94 75.24 5.24 PCAL 30 47.56 65.95 53.9 9 4.17 CALMIDB 30 32.79 47.85 39.31 2.84 BM CALMAX 67 73.70 94.00 83.6 9 4.59 PCAL 67 52.90 67.91 60.56 3.66 CALMIDB 68 36.90 52.08 44.1 9 2.67 WM CALMAX 66 70.40 95.57 82.03 4.80 PCAL 66 50.99 68.25 58.4 2 3.7 6 CALMIDB 67 37.24 50.94 42.68 2.7 1 Table 7 9 Descriptive statistics m inimum breadth of the talus and the maximum lengths of the talus, cuboid and navicular Sample Variable N Min Max Mean SD BF TALMINB 35 26.11 35.41 30.00 2 .3 5 TALMAXL 35 48.44 62.47 54.89 3.88 CUBMAX 34 30.91 44.17 38.58 3.04 NAVMAX 32 33.83 45.57 39.42 2.81 WF TALMINB 30 25.45 35.17 30.5 5 2.46 TALMAXL 30 44.93 61.81 55.1 7 4.0 5 CUBMAX 28 30.69 44.52 36.9 3 2.9 6 NAVMAX 27 30.63 47.18 38.27 3.7 2 BM TALMINB 68 29.55 37.70 33. 60 1.79 TALMAXL 67 54.71 73.29 62.44 3.63 CUBMAX 65 38.42 47.86 42.82 2.10 NAVMAX 66 38.71 51.09 44.08 2.74 WM TALMINB 67 29.47 37.87 33.72 1.82 TALMAXL 66 53.08 75.48 62.0 4 4.03 CUBMAX 64 35.7 3 46.56 40.69 2.44 NAVMAX 66 35.56 53.48 41.76 3.07
107 1.00 2.00 3.00 4.00 50.00 55.00 60.00 65.00pcal 1.00 2.00 3.00 4.00 35.00 40.00 45.00 50.00calmidb 1.00 2.00 3.00 4.00 70.00 80.00 90.00calmaxl Figure 75. Box plots of length and breadth measurements of the calcaneus (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
108 1.00 2.00 3.00 4.00racecode 50.00 60.00 70.00talmaxl 1.00 2.00 3.00 4.00racecode 30.00 35.00 40.00 45.00 50.00navmax 1.00 2.00 3.00 4.00racecode 32.00 36.00 40.00 44.00 48.00cubmax 1.00 2.00 3.00 4.00racecode 25.00 30.00 35.00talminb Figure 7 6 Box plots of m inimum breadth of the talus and the maximum lengths of the talus, cuboid and navicular (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes a nd whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
109 Table 7 10. Descriptive statistics of the l engths of the first pedal ray proximal and distal phalanges Sample Variable N Min Max Mean SD BF 1PP 33 29.16 43.45 35.84 3.20 1DP 28 20.95 28.29 24.90 1.6 4 WF 1PP 28 30.00 42.37 34.68 2.78 1DP 23 20.22 30.27 24.6 9 2.42 BM 1PP 58 34.16 47.39 38.82 2.7 4 1DP 56 21.58 36.70 27.40 2.79 WM 1PP 58 33.03 46.34 38.4 5 2.6 9 1DP 51 23.18 31.98 28.01 1.7 8 1.00 2.00 3.00 4.00racecode 30.00 35.00 40.00 45.001PP 1.00 2.00 3.00 4.00racecode 20.00 25.00 30.00 35.001DP Figure 77. Box plots of maximum lengths of the first pedal ray proximal (left) and distal phalanges(right) (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represen t 50% of the data sample each, the line represents the median value, circles depict outliers )
110 1.00 2.00 3.00 4.00racecode 0.30 0.32 0.34 0.36 0.38ratiocalmaxtofoot 1.00 2.00 3.00 4.00racecode 0.26 0.28 0.30ratiofstmaxtofoot 1.00 2.00 3.00 4.00racecode 0.24 0.26 0.28 0.30ratiobigtoetofoot 1.00 2.00 3.00 4.00racecode 0.22 0.24 0.26 0.28ratiopcaltofoot Figure 78. Box plot of ratios of the first toe, the first metatarsal, the calcaneus (maximum length, and the posterior calcaneus length) to foot length 1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
111 Table 7 11. Descriptive statistics for selected r atios (variable/ f oot length) Group Variable N Min Max Mean SD BF BIGTOE / FOOT 28 0.24 0.28 0.259 0.009 FSTMAX / FOOT 34 0.26 0.29 0.273 0.011 CALMAX / FOOT 32 0.29 0.36 0.326 0.016 PCAL / FOOT 33 0.22 0.26 0.238 0.011 WF BIGTOE / FOOT 23 0.25 0.30 0 .272 0.013 FSTMAX / FOOT 27 0.25 0.30 0.281 0.012 CALMAX / FOOT 30 0.31 0.37 0.344 0.014 PCAL / FOOT 30 0.23 0.27 0.247 0.011 BM BIGTOE / FOOT 55 0.24 0.29 0.257 0.013 FSTMAX / FOOT 66 0.25 0.30 0.268 0.011 CALMAX / FOOT 67 0.29 0.36 0.324 0.015 PCAL / FOOT 67 0.21 0.27 0.234 0.012 WM BIGTOE / FOOT 50 0.25 0.30 0.275 0.012 FSTMAX / FOOT 63 0.25 0.32 0.275 0.013 CALMAX / FOOT 65 0.30 0.39 0.338 0.017 PCAL / FOOT 65 0.22 0.28 0.241 0.013 Figure 79. Ratio values of metatarsals compared to one another.
112 Table 712. Two way ANOVA of metatarsal to metatarsal ratios Variable N F Significance Partial Eta Squared ONE / TWO 181 sex race sex race 0.002 11.018 0.004 0.961 0.001* 0.952 0.000 0.059 0.000 ONE / THREE 17 3 sex race sex race 0.013 20.521 0.073 0.909 0.000* 0.787 0.000 0.108 0.000 ONE / FOUR 172 sex race sex race 0.013 12.613 0.401 0.910 0.000* 0.527 0.000 0.070 0.002 ONE / FIVE 171 sex race sex race 1.527 3.336 0.005 0.218 0.070 0 .946 0.009 0.020 0.000 TWO / THREE 176 sex race sex race 0.011 7.483 1.172 0.916 0.007 0.280 0.000 0.042 0.007 TWO / FOUR 171 sex race sex race 0.028 0.796 0.007 0.866 0.374 0.935 0.000 0.005 0.000 TWO / FIVE 170 sex race sex race 1.753 0.564 0.132 0.187 0.454 0.717 0.010 0.003 0.001 THREE / FOUR 170 sex race sex race 0.103 2.164 1.159 0.749 0.143 0.283 0.001 0.013 0.007 THREE / FIVE 166 sex race sex race 2.403 4.952 0.093 0.123 0.027 0.761 0.015 0.030 0.001 FOUR / FIVE 167 sex race sex race 2.356 1.032 0.012 0.127 0.311 0.913 0.014 0.006 0.000 *Bonferronis adjustment P
113 Table 713. Twoway ANOVA results for metatarsal to stature ratios Variable N F Significance Partial Eta Squared TWO / STATURE 185 sex race sex race 1.300 28.878 0.177 0.256 < 0.001 0.674 0.007 0.138 0.001 THREE / STATURE 177 s ex race sex race 1.778 42.723 0.000 0.184 < 0.001 1.00 0.010 0.198 0.000 FOUR / STATURE 174 sex race sex race 2.908 32.306 0.543 0.090 < 0.001 0.462 0.017 0.160 0.003 FIVE / STATURE 174 sex race sex race 0.5.685 15.450 0.019 0.0 18 < 0.001 0.891 0.032 0.083 0.000 *Bonferronis adjustment P Table 714. Twoway ANOVA results for metatarsals to foot length ratios Variable N F Significance Partial Eta Squared TWO / FOOT 185 sex race sex race 13.073 2.581 0.001 < 0.00 1 0.110 0.918 0.067 0.014 0.000 THREE / FOOT 177 sex race sex race 12.003 0.008 0.008 0.001* 0.931 0.927 0.065 0.000 0.000 FOUR / FOOT 174 sex race sex race 7.995 0.144 1.762 0.005* 0.705 0.186 0.045 0.001 0.010 FIVE / FOOT 174 sex race sex race 2.207 2.170 0.143 0.139 0.143 0.706 0 013 0.013 0.001 *Bonferronis adjustment P
114 Table 7 1 5 Descriptive statistics for r obusticity indices by sample Sample Variable N Min Max Mean Std. Deviation BF ROB1 32 0.23 0.34 0.300 0.021 ROB2 31 0.15 0.21 0.187 0.011 ROB3 30 0.16 0.22 0.186 0.016 ROB4 28 0.13 0.19 0.162 0. 016 ROB5 30 0.25 0.34 0.275 0.022 WF ROB1 25 0.28 0.38 0.322 0.028 ROB2 25 0.18 0.24 0.207 0.016 ROB3 24 0.16 0.22 0.198 0.016 ROB4 23 0.14 0.20 0.171 0.017 ROB5 21 0.25 0.34 0.298 0.023 BM ROB1 58 0.27 0.38 0.315 0.021 ROB2 58 0.18 0.25 0.203 0.013 ROB3 54 0.16 0.23 0.195 0.015 ROB4 52 0.12 0.21 0.168 0.018 ROB5 53 0.23 0.33 0.281 0.023 WM ROB1 57 0.27 0.38 0.321 0.024 ROB2 54 0.18 0.25 0.209 0.013 ROB3 53 0.16 0.23 0.196 0.014 R OB4 53 0.14 0.20 0.164 0.015 ROB5 54 0.25 0.34 0.294 0.023
115 1.00 2.00 3.00 4.00racecode 0.25 0.30 0.35ROB1 1.00 2.00 3.00 4.00racecode 0.16 0.18 0.20 0.22 0.24ROB2 1.00 2.00 3.00 4.00racecode 0.16 0.18 0.20 0.22ROB3 1.00 2.00 3.00 4.00racecode 0.12 0.14 0.16 0.18 0.20ROB4 1.00 2.00 3.00 4.00racecode 0.250 0.275 0.300 0.325ROB5 Figure 71 1 Box plots of robusticity indices for metatarsals one through five (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
116 Table 71 6 Two w a y ANOVA of robusticity indices Variable N F Significance Partial Eta Squared ROB1 172 sex race sex race 3.757 14.224 4.614 0.054 0.000* 0.033 0 .022 0.078 0.027 ROB2 168 sex race sex race 17.796 35.014 10.168 < 0.00 1 < 0.001 0.002 0.098 0.176 0.058 ROB3 161 sex race sex race 1.865 6.252 5.204 0.174 0.013 0.024 0.012 0.038 0.032 ROB4 156 sex race sex race 0.011 0. 871 5.536 0.917 0.352 0.020. 0.000 0.006 0.035 ROB5 158 sex race sex race 0.052 20.490 1.428 0.819 < 0.001 0.234 0.000 0.117 0.009 *Bonferronis adjustment P Table 717. Results of the Quick T est analysis of metatarsal robusticity Sample Females Males 1MLB vs. FSTMAX White > Black ns (P=0.0005) (P= 0.1932) P = one tailed P value
117 Table 7 1 8 Bias corrected c oefficients of v ariation ( V*) f or pooled groups All Females All Males Variable N V* N V* S TATURE 65 7.45 138 4.79 FOOTL 65 8.56 137 6.78 FOOTB 65 5.51 138 6.61 CALMAX 62 7.32 133 5.75 PCAL 63 7.97 133 6.48 CALMIDB 62 7.34 135 6.42 FSTMAX 61 7.10 130 6.42 1MLH 56 8.93 114 6.58 1MLB 57 9.45 118 6.71 Table 7 1 9 Bias corrected c oefficients of v ariat ion (V*) for sub groups Black females White females Black males White males Variable N V* N V* N V* N V* STATURE 35 5.23 30 5.25 68 5.16 70 4.06 FOOTL 35 6.14 30 7.20 68 5.94 69 5 .85 FOOTB 35 9.39 30 7.68 68 6.52 70 6.71 FST MAX 34 7.31 27 5.72 66 6.34 64 5.91 2 MT MAX 33 7.89 28 7.04 64 6.14 61 5.26 3 MT MAX 32 7.07 27 7.58 60 6.27 59 5.71 4 MT MAX 31 7.52 25 6.99 59 6.32 60 5.79 5 MT MAX 32 7.68 23 8.50 58 6.21 62 6.23 CALMAX 32 7. 59 30 7.03 67 5.51 66 5.88 PCAL 33 7.88 30 7.80 67 6.07 66 6.46 CALMIDB 32 7.56 30 7.29 68 6.07 67 6.36 CU B MAX 34 7.94 28 8.08 65 4.93 64 6.02 1MLH 31 9.28 25 8.76 58 5.57 56 7.54 1MLB 32 9.50 25 9.58 58 7.04 60 6.35
118 T able 7 20. Results of ttests for coefficients of variation of correl ated variables (within groups) BF WF BM WM Variable T P T P T P T P FOOTL vs FOOTB 2.586 0.014 0.418 0.680 0.815 0.418 1.236 0.221 PCAL vs CALMAX 0.588 0.561 1.576 0.126 1.526 0.132 1.844 0.070 CALMAX vs F STMAX 0.378 0.708 2.787 0.010 1.437 0.156 0.059 0.953 CALMID B vs CALMAX 0.02 8 0.979 0.255 0.800 0.881 0.381 0.760 0.450 1MLH vs FST MAX 2.048 0.049 2.245 0.034 1.074 0.287 2.192 0.033 1MLB vs FST MAX 1.904 0.066 2.610 0.015 0.894 0.375 0.575 0.567 P = 2 tailed pvalues T = ts ratio, *Bonferronis adjustment P 0.008 Table 721. Observed ratios of dimorphism versus expected based on the cube root of body mass dimorphism Variable Combined obs exp Black obs exp White obs exp STAT URE 1.072 0.003 1 .073 0.002 1.074 0.035 FST MAX 1.084 0.009 1.081 0.006 1.093 0.055 1PP 1.094 0.019 1.083 0.008 1.109 0.070 2 MT MAX 1.079 0.004 1.075 0.000 1.089 0.050 3 MT MAX 1.077 0.002 1.079 0.004 1.081 0.043 4 MT MAX 1.080 0.004 1.074 0.001 1.095 0.057 5 MT MAX 1.084 0.009 1.083 0.008 1.098 0.059 CUBMAX 1.104 0.029 1.110 0.035 1.102 0.063 CALMAX 1.089 0.014 1.089 0.014 1.090 0.052 CALMIDB 1.104 0.028 1.121 0.046 1.086 0.047 1MLH 1.122 0.047 1.122 0.047 1.122 0.084 1MLB 1.113 0.037 1.130 0.055 1.093 0.055
119 Table 7 22. Indices of sexual dimorphism for selected variables of the HTH skeletal sample Variable Combined Black White STAT URE 0.070 0.070 0.071 FST MAX 0.081 0.078 0.089 2 MT MAX 0.076 0.072 0.085 3 MT MAX 0.074 0.076 0.078 4 MT MAX 0.077 0.071 0.091 5 MT MAX 0 .081 0.080 0.093 1PP 0.090 0.080 0.103 1DP 0.109 0.096 0.124 CALMAX 0.086 0.085 0.086 TALMAXL 0.122 0.129 0.113 CUBMAX 0.098 0.104 0.096 NAVMAX 0.098 0.112 0.085 CALMIDB 0.099 0.115 0.082 TALMINB 0.106 0.113 0.098 1MLH 0.115 0.115 0.115 1MLB 0.10 7 0.122 0.089 2MLB 0.130 0.148 0.109 3MLB 0.099 0.121 0.076 4MLB 0.080 0.105 0.053 5MLB 0.099 0.100 0.098
120 Table 72 3 HTH cadaver sample RMA regressions on foot length Variable Group N RMA Slope R 95% CI Allometric Pattern All 1040 1.39 0.738 1 .32 1.45 + BF 163 1.29 0.669 1.14 1.47 + STATURE WF 50 1.11 0.763 0.96 1.30 ISO BM 479 1.23 0.628 1.13 1.35 + WM 348 1.41 0.583 1.29 1.56 + All 1040 0 .31 0 .270 0 .2 6 0 .33 ISO BF 163 0 .2 2 0 .293 0 .1 9 0 .25 BODY MASS WF 50 0 .2 5 0 .079 0 .28 0.31 ns BM 479 0 .27 0 .245 0 .24 0 .29 + WM 348 0 26 0 168 0.24 0.29
121 Figure 711. Bivariate plot of HTH skeletal sample foot length to stature (All groups, n = 202, RMA slope = 1.42, r = 0 .773 95% CI = 1.301.55). 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 LOGMASS 5.22 5.28 5.34 5.4 5.46 5.52 5.58 5.64 5.7LOGFOOT Figure 712. Bivariate plot of HTH skeletal sample foot length to body mass (All groups, n = 198, RMA slope = 0 .332, r = 0 .410, 95% CI = 0.290.38).
122 Table 72 4 HTH skel etal sample RMA regressions on stature Variable Group N RMA Slope R 95% CI Allometric Pattern All 202 1.42 0 .773 1.301.55 + BF 35 1.17 0.689 0.95 1.52 ISO FOOT WF 30 1.32 0.788 1.03 1.71 + BM 68 1.16 0.800 0.96 1.39 ISO WM 69 1.48 0.630 1.24 1.81 + All 195 1.28 0 .766 1.16 1.41 + BF 32 1.43 0 .835 1.14 1.85 + CALMAX WF 31 1.17 0 .665 0 .9 1 1.57 ISO BM 67 1.06 0 .559 0 .88 1.28 ISO WM 66 1.53 0 .670 1.30 1.81 + All 196 1.33 0 .753 1.22 1.45 + BF 33 1.51 0 .84 8 1.28 1.84 + PCAL WF 29 1.25 0 .656 0 .9 6 1.72 ISO BM 66 1.19 0 .632 1.00 1.45 ISO WM 66 1.58 0 .674 1.35 1.89 + All 191 1.30 0 .814 1.2 1.42 + BF 34 1.38 0 .856 1.18 1.68 + FSTMAX WF 27 0 .8 6 0 .742 0 .65 1.06 + BM 64 0 .81 0 .764 0 69 0 .95 WM 64 1.50 0 .699 1.29 1.76 + All 1 70 1. 70 0 .6 58 1.4 8 1.9 4 + BF 31 1.72 0.765 1.35 2.29 + 1MLH WF 25 2.03 0 .277 2.69 3.3 7 ns BM 58 1.39 0.330 1.05 1.78 ISO WM 55 1.93 0.494 1.51 2.48 + CALMIDB All 19 7 1.3 7 0 .6 59 1. 23 1.56 + BF 32 1.39 0.518 1.04 1.92 + WF 30 1.35 0.329 0.79 2.09 ISO BM 68 1.19 0.540 0.95 1.50 ISO WM 67 1.53 0. 520 1.20 1.96 +
123 Table 7 25. HTH skeletal sample RMA regressions on f oot length Variable Group N RMA Slope R 95% CI Allometric Pattern All 194 0 .88 0 .776 0 .80 0 .9 7 BF 31 1.24 0 .770 0 .9 8 1.53 ISO CALMAX WF 30 1.00 0 .817 0 .79 1.28 ISO BM 67 0 .92 0 .646 0 .7 8 1.10 ISO WM 65 0 .9 3 0 .634 0 .77 1.10 ISO All 191 0 .9 3 0 .784 0 .85 1.02 ISO BF 32 1.35 0 .819 1.12 1.64 + PCAL WF 30 1.09 0 .808 0 .84 1.36 ISO BM 66 1.02 0 .587 0 .8 4 1.25 ISO WM 65 1.02 0 .638 0 .86 1.22 ISO All 190 0 90 0 .846 0 .83 0 .9 8 BF 34 1.18 0 .852 0 .97 1.39 ISO FSTMAX WF 27 0.87 0 .742 0 .63 1.17 ISO BM 66 1.06 0 .779 0 .89 1.25 ISO WM 63 0 .96 0 .70 8 0 .83 1.13 ISO All 1 69 1.09 0 .653 0.96 1.2 4 ISO BF 31 1.48 0.698 1.20 1.70 + 1MLH WF 25 1.38 0.572 0.99 1.96 ISO BM 57 1.01 0.487 0.80 1.27 ISO WM 55 1.15 0.526 0.89 1.50 ISO CALMIDB All 196 0 .9 6 0 .694 0.86 1.0 7 ISO BF 32 1.21 0.754 0.98 1.47 + WF 30 1.02 0.603 0.63 1.48 ISO BM 68 1.03 0.504 0.82 1.26 ISO WM 65 1.07 0.446 0.84 1.30 ISO
124 Table 72 6 HTH skeletal sample RMA regressions on body mass Variable Group N RMA Slope R 95% CI Allometric Pattern All 198 0 .33 0.41 0 .29 0 .38 ISO BF 34 0.21 0.363 0.14 0.28 FOOT WF 30 0.22 0.468 0.16 0.32 BM 67 0 .3 3 0 .149 0 .3 7 0 .4 1 ns WM 67 0.32 0.286 0.24 0.40 ISO All 191 0 .29 0 .466 0 .26 0 .3 4 ISO BF 27 0 .2 2 0 .518 0 .15 0 .31 CALMAX WF 30 0.23 0 .353 0 .14 0 .33 ISO BM 66 0.30 0 .312 0 .24 0 .3 9 ISO WM 64 0.29 0 .347 0 .23 0 .3 7 ISO All 191 0 .3 1 0 440 0 .27 0 .35 ISO BF 32 0 .2 8 0 .325 0 .1 9 0 .40 ISO PCAL WF 29 0 .2 2 0 .391 0 .1 5 0 .2 9 BM 66 0.33 0 .359 0.27 0 .42 ISO WM 60 0 .3 6 0 .424 0 .29 0 .45 ISO All 190 0 .33 0 .399 0 30 0 .38 ISO BF 32 0 .26 0 .430 0 .18 0 .37 ISO FSTMAX WF 23 0.15 0 .461 0 .10 0 .2 3 BM 64 0.35 0 .329 0. 28 0 .45 ISO WM 62 0.31 0 .352 0 .24 0 .39 ISO All 167 0 .3 6 0 .40 7 0 .3 1 0 .41 ISO BF 30 0 .3 1 0 .466 0 .24 0 .41 ISO 1MLH WF 2 5 0 .29 0 .033 0 .4 2 0 .3 9 ns BM 57 0 .30 0 .06 3 0 .3 5 0 .3 7 ns WM 55 0 .3 8 0 .171 0 .4 2 0.51 ns CALMIDB All 19 2 0.31 0 .36 3 0.27 0 .3 7 ISO BF 31 0.25 0.413 0.18 0.34 ISO WF 30 0 .2 4 0 .159 0 .32 3.57 ns BM 67 0 .32 0 .028 0 .40 0 .42 ns WM 64 0 .31 0 .167 0 .34 0 .41 ns
125 Table 72 7 Summary of d eviations from i sometry after l og l og b ivariate RMA regressions RMA regression All groups Black females White females Black males White males FOOT to STATURE* (+) + (+) ISO (ISO) ISO (+) ISO (+) + FOOT to BODY MASS* (ISO) ISO ( ) ( ns ) (+) ISO ( ) ISO FST MAX to STATURE + + ISO + FSTMAX to FOOT ISO ISO ISO ISO FSTMAX to BODY MASS ISO ISO ISO ISO CALMAX to STATURE + + ISO ISO + CALMAX to FOOT ISO ISO ISO ISO CALMAX to BODY MASS ISO ISO ISO ISO PCAL to STATU RE + + ISO ISO + PCAL to FOOT ISO + ISO ISO ISO PCAL to BODY MASS ISO ISO ISO ISO CALMIDB to STATURE + + ISO ISO + CALMIDB to FOOT ISO + ISO ISO ISO CALMIDB to BODYMASS ISO ISO ns ns ns 1MLH to STATURE + + ns I SO + 1MLH to FOOT ISO + ISO ISO ISO 1MLH to BODY MASS ISO ISO ns ns ns *HTH cadaver sample results are in parentheses, all others HTH skeletal sample
126 1.00 2.00 3.00 4.00racecode 0.300 0.325 0.350 0.375 0.400ratioMLHvsfstmax Figure 7 13. Box plot of the ratio of the medial to lateral breadth of the head of the first metatarsal to the maximum length of the first metatarsal ( 1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
127 Table 7 2 8 LS regression equations for predicting stature from foot length Sample Equation N R Adj. R2 SE (mm) BF Stature = 678.72 + (4.10*FOOTLENGTH) 35 0.689 0.459 62.71 WF Stature = 678.00 + (4. 20 *FOOTLENGTH) 30 0.793 0.615 21.88 BM Stature = 771.30 + ( 3.82 *FOOTLENGTH) 68 0.647 0.4 09 69.57 WM Stature = 975.00 + ( 3.09 *FOOTLENGTH) 69 0.631 0.389 54.11 Table 72 9 LS regression equations for predicting stature from the metatarsals Sample Equation N R Adj. R2 SE (mm) BF Stature = 638.54 + (15.63*FSTMAX) 33 0.845 0.705 46.92 WF S tature = 575.74 + (16.82*FSTMAX) 26 0.759 0.559 50.88 BM Stature = 762.49 + (14.37*FSTMAX) 65 0.686 0.463 67.32 WM Stature = 921.41 + (12.02*FSTMAX) 62 0.702 0.485 47.88 BF Stature = 727.34 + (12.13 *2MTMAX) 32 0.820 0.663 50.81 WF Stature = 869 .06 + (10.42*2MTMAX) 27 0.664 0.420 58.97 BM Stature = 937.01 + (10.13*2MTMAX) 63 0.564 0.307 74.35 WM Stature = 852.13 + (11.36*2MTMAX) 59 0.679 0.452 48.45 BF Stature = 679.84 + (13.58*3MTMAX) 31 0.762 0.567 58.41 WF Stature = 967.09 + (9.75*3 MTMAX) 26 0.707 0.480 49.49 BM Stature = 954.93 + (10.48*3MTMAX) 59 0.554 0.295 75.94 WM Stature = 932.89 + (11.05*3MTMAX) 57 0.653 0.417 50.24 BF Stature = 759.08 + (12.73*4MTMAX) 30 0.732 0.520 62.53 WF Stature = 890.70 + (11.12*4MTMAX) 24 0.7 21 0.498 48.87 BM Stature = 989.89 + (10.24*4MTMAX) 58 0.523 0.261 79.05 WM Stature = 920.30 + (11.38*4MTMAX) 58 0.679 0.451 48.75 BF Stature = 753.84 + (12.71*5MTMAX) 31 0.764 0.570 58.20 WF Stature = 1024.73 + (8.86*5MTMAX) 22 0.685 0.444 53.6 5 BM Stature = 1204.53 + (7.16*5MTMAX) 57 0.382 0.131 81.94 WM Stature = 1151.18 + (7.92*5MTMAX) 60 0.547 0.288 54.85
128 Table 7 30. LS regression equations for predicting foot length from the metatarsal s, calcaneus and cuboid Sample Equation N R Adj. R2 SE (mm) BF Foot length = 64.43 + (2.65*FSTMAX) 33 0.853 0.719 7.69 WF Foot length = 29.33 + (3.08* FSTMAX) 26 0.746 0.538 9.71 BM Foot length = 66.21 + (2.78* FSTMAX) 65 0.790 0.618 9.56 WM Foot length = 67.30 + (2.63* FSTMAX) 62 0.706 0.490 10.35 BF Foot length = 74.08 + (2.13*2MTMAX) 32 0.855 0.722 7.77 WF Foot length = 104.47 + (1.60*2MTMAX) 27 0.559 0.287 11.94 BM Foot length = 64.83 + (2.39*2MTMAX) 63 0.770 0.587 9.94 WM Foot length = 44.63 + (2.58*2MTMAX) 59 0.695 0.475 15.51 BF Foot length = 58.88 + (2.47*3MTMAX) 31 0.837 0.691 8.18 WF Foot length = 89.28 + (1.95*3MTMAX) 26 0.723 0.503 9.48 BM Foot length = 64.43 + (2.54*3MTMAX) 59 0.763 0.575 13.40 WM Foot length = 51.50 + (2.66*3MTMAX) 57 0.728 0.522 9.83 BF Foot le ngth = 76.15 + (2.27*4MTMAX) 30 0.824 0.669 8.20 WF Foot length = 80.28 + (2.14*4MTMAX) 24 0.695 0.461 10.12 BM Foot length = 83.51 + (2.35*4MTMAX) 58 0.724 0.515 10.62 WM Foot length = 46.42 + (2.77*4MTMAX) 58 0.739 0.538 9.96 BF Foot length = 85.33 + (2.13*5MTMAX) 31 0.772 0.582 9.51 WF Foot length = 105.74 + (1.71*5MTMAX) 22 0.668 0.420 10.86 BM Foot length = 119.61 + (1.83*5MTMAX) 57 0.578 0.323 12.21 WM Foot length = 85.45 + (2.17*5MTMAX) 60 0.673 0.444 10.79 BF Foot length = 88.6 0 + (1.92*CALMAX) 31 0.773 0.585 9.25 WF Foot length = 35.19 + (2.44* CALMAX) 29 0.819 0.659 9.13 BM Foot length = 78.46 + (2.16* CALMAX) 66 0.643 0.405 11.89 WM Foot length = 74.07 + (2.06* CALMAX) 64 0.645 0.406 11.13 BF Foot length = 102.51 + (3 .43*CUBMAX) 33 0.719 0.502 10.24 WF Foot length = 93.24 + (3.44* CUBMAX) 27 0.668 0.425 11.53 BM Foot length = 38.04 + (5.16* CUBMAX) 64 0.703 0.486 11.06 WM Foot length = 24.24 + (3.60* CUBMAX) 62 0.612 0.364 11.44
129 Table 7 31. LS regression equations f or predicting b ody mass from calcaneus and talus Sample Equation N R Adj. R2 SE ( kg ) All groups Body Mass = ( CALMAX 0.813) 3.279 105 0.643 0.408 5.81 All groups Body Mass = (CALMAX 0.534) + ( TALMAXL 0.438) 7.142 105 0.670 0.438 5.66 150 170 190 210 230 250 270 1450 1500 1550 1600 1650 1700 1750 1650 BM 1650 WM 180 190 200 210 220 230 240 250 260 270 1450 1500 1550 1600 1650 1700 1750 1700 BF 1700 WF PREDICTED FOOT LENGTH PREDICTED FOOT LENGTH STATURE STATURE Figure 714. Relationship of predicted foot lengths calculated for hypothetical statures for Black and White males (top) and Black and White females (bottom).
130 190 210 230 250 270 290 310 330 50 55 60 65 70 75 80 85 BM WM PREDICTED FOOT LENGTH FSTMAX PREDICTED FOOT LENGTH FSTMAX 180 190 200 210 220 230 240 250 260 270 50 55 60 65 70 75 BF WF Figure 715. Relationship of predict ed foot lengths calculated for hypothetical first metatarsalsfor Black and White males (top) and Black and White females (bottom).
131 200 210 220 230 240 250 260 270 280 290 65 70 75 80 85 90 95 BM WM PREDICTED FOOT LENGTH CALMAX PREDICTED FOOT LENGTH CALMAX 190 200 210 220 230 240 250 260 270 65 70 75 80 85 90 BF WF Figure 716. Relationship of predicted foot lengths calculated for hypothetical maximum lengths of the calcaneus for Black and White males (top) and Black and White females (bottom).
132 Table 732. Eco groups RMA regressions of predicted foot length on predicted t i bia and predicted femur lengths Variable sample RM A Slope 95% CI Allometric Pattern All 1.07 0.99 1.14 ISO BF 0 94 0 92 0 97 ecoTIBIA WF 1.05 1.03 1.07 + BM 0 90 0.88 0.91 WM 1.30 1.27 1.32 + All 1.27 1.16 1.38 + BF 1.07 1.05 1.10 + ecoFEMUR WF 1.16 1.11 1.18 + BM 1.07 1.05 1.09 + WM 1.58 1.53 1.63 + T able 7 33. Results of F test comparisons of V2 between groups BF vs WF BM vs WM BF vs BM WF vs WM Variable F P F P F P F P Stature 0.992 0.51 1.615 0.02 1.027 0.45 1.672 0.04 FOOTL 0.727 0.81 1.031 0.45 1.068 0.4 0 1. 515 0.08 FOOTB 1.495 0.14 0.944 0.59 2.074 0.005 1.310 0.18 FSTMAX 1.633 0.10 1.151 0.29 1.329 0.16 0.937 0.56 2MTMAX 1.256 0.28 1.363 0.11 1.651 0.05 1.791 0.03 3MTMAX 0.870 0.65 1.206 0.24 1.271 0.21 1.762 0.04 4MTMAX 1.157 0.36 1.191 0.25 1.416 0. 14 1.457 0.12 5MTMAX 0.816 0.70 0.994 0.51 1.529 0.08 1.861 0.03 CALMAX 1.166 0.34 0.878 0.70 1.897 0.01 1.429 0.12 PCAL 1.021 0.48 0.883 0.69 1.685 0.04 1.458 0.11 CALMIDB 1.075 0.42 0.911 0.65 1.551 0.07 1.314 0.18 CU B MAX 0.966 0.54 0.671 0.94 2.59 4 0.000 1.801 0.03 1MLH 1.122 0.39 0.546 0.99 2.776 0.000 1.350 0.18 1MLB 0.983 0.52 1.229 0.22 1.821 0.02 2.276 0.005 P = 2 tailed pvalues ; F = f statistic, significant at Bonferronis adjustment P
133 1.00 2.00 3.00 4.00 0.36 0.40 0.44 0.48EMAthrd Figure 7 17. Box plot of EMA calculated using the third metatarsal (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers).
134 Table 7 3 4 Descriptive statistics for the e ffective m echanical a d vantage Sample Variable N Min Max Mean SD BF EMAthrd 30 0.38 0.47 0.429 0.018 WF EMAthrd 26 0.40 0.48 0.436 0.022 BM EMAthrd 57 0.36 0.48 0.422 0.020 WM EMAthrd 56 0.38 0.47 0.429 0.021 25.00 50.00 75.00 100.00masskg 0.36 0.40 0.44 0.48EMAthrd EMAthrd = 0.43 + 0.00 masskg R-Square = 0.00 Figure 718. LS regr ession of the effective mechanical advantage (calculated using the thrid metatarsal as a component of the out lever) versus body mass (in kg).
135 110.00 120.00 130.00 140.00 150.00 160.00Rthrdmax 50.00 55.00 60.00 65.00pcal pcal = 10.99 + 0.35 Rthrdmax R-Square = 0.61 Figure 7 19. Combined sample LS r egression of PCAL on Rthrdmax (CALMAX PCAL) + CUBMAX + 3RDMAX
136 50.00 60.00 70.00pcal pcal = -3.72 + 0.46 Rthrdmax R-Square = 0.74 1.00 2.00 3.00 4.00 pcal = 8.50 + 0.37 Rthrdmax R-Square = 0.56 110.00 120.00 130.00 140.00 150.00 160.00Rthrdmax 50.00 60.00 70.00pcal pcal = 18.24 + 0.29 Rthrdmax R-Square = 0.38 110.00 120.00 130.00 140.00 150.00 160.00Rthrdmax pcal = 10.85 + 0.35 Rthrdmax R-Square = 0.42 Figure 7 20. Sub sample LS r egressions of PCAL on Rthrdmax = (CALMAX PCAL) + CUBMAX + 3RDMAX (1 = BF, 2 = WF, 3 = BM, 4 = WM)
137 Table 7 3 5 Results of calculated muscle force (in N) to counter ground reaction force Sample Variable N Min Max Mean SD BF Muscle 29 69.61 248.97 141.239 40.730 WF Muscle 26 77.02 201.86 139.141 36.286 BM Muscle 56 120.55 261.84 173.797 31.970 WM Muscle 54 104.34 253 177.235 34.355 1.00 2.00 3.00 4.00 100.00 150.00 200.00 250.00Muscle Figure 7 21. M uscle force (in N) required to counter GRF (estimated as1.2 times body mass; 1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers).
138 Table 7 3 6 Descriptive statistics for the calculated ankle joint force Sample Variable N Min Max Mean SD BF JOINTFmid 29 98.80 352.18 199.208 57.360 WF JOINTFmid 26 108.74 284.20 197.044 50.796 BM JOINTFmid 56 170.06 376.60 243.859 44.836 WM JOINTFmid 54 147.34 345.63 249.8 14 47.631 100.00 200.00 300.00JOINTFmid 25.00 50.00 75.00 100.00masskg masskg = 1.03 + 0.25 JOINTFmid Figure 7 22. LS regression of body mass (in kg) and calculated ankle joint forces ( HTH skeletal sample, all groups; n = 164 )
139 Table 73 7 RMA r egressions of talar and calcaneal dimensions and joint reaction force Variable Group N RMA Slope R 95% CI Allometric Pattern All 163 0.30 0.427 0.260.36 ISO BF 29 0.27 0.423 0.19 0.38 ISO TALMINB WF 26 0 .28 0 .111 0.40 0 .3 8 ns BM 56 0.29 0.131 0.38 0.35 ns WM 52 0.26 0.222 0.26 0.34 ns All 162 0.32 0.495 0.28 0.37 ISO BF 29 0.24 0.424 0.17 0.34 ISO TALMAXL WF 26 0 .23 0 .188 0 .31 0 .3 2 ns BM 56 0 .32 0 .156 0 .3 4 0 .40 ns WM 51 0 30 0 .444 0 .2 3 0 .3 9 ISO All 162 0 .28 0.448 0.24 0.33 BF 29 0 .26 0 .274 0 .28 0 .3 9 ns CALMAX WF 26 0 .2 3 0 .270 0 .3 1 0 .3 2 ns BM 56 0 .29 0 .260 0 .29 0 .31 ns WM 51 0 .2 7 0 .361 0.21 0 .34 ISO All 162 0.30 0.385 0.25 0.35 ISO BF 29 0.23 0.366 0.25 0 .32 ns CALMIDB WF 26 0 .24 0 .101 0 .37 0 .35 ns BM 56 0 .3 3 0 .012 0 .39 0 .42 ns WM 51 0.26 0.325 0.18 0.37 ISO All 162 0.29 0.379 0.25 0.34 ISO BF 29 0.28 0.283 0 .26 0 .40 ns PCAL WF 26 0 .25 0 .237 0 .3 4 0 .3 5 ns BM 56 0 .3 1 0 .234 0 .34 0 .39 ns WM 51 0.29 0.239 0.30 0.371 ns
140 CHAPTER 8 SYNTHESIS AND APPLIC ATIONS Measurement Error The measurements used in this study are either commonly used in skeletal biology (e.g., CALMAX, PCAL, CALMID B TALMAXL following Buikstra and Ubelaker (1994), and Holland (1995)) or they are novel measurements from an original study (e.g., breadths of the bases of the met atarsals following Robling and Ubelaker (1997 ); maximum lengths of the additional tarsals and metatarsals following Byrd and Adams (2003)). These measurements were selected for the current study because of high reliability and low error. For example, Ada ms and Byrds (2002) interobserver error study found that measurements defined by maximum and minimum dimensions were more reliable than measurements defined by element orientation (e.g., anterior to posterior). In the current study, the maximum lengths o f the metatarsals and tarsals and the minimum breadth of the talus are such measurements. Measurements from Robling and Ubelaker (199 7 :1065) used herein also demonstrated low inter and intraobserver error rates (e.g., for the medial lateral metatarsal base widths they report 1.37% 3.00% differences for inter and 1.02% 2.10% for intraobserver error rates). I use both length and breadth measurements in this study. Since the absolute measurement error associated with smaller measurements (e.g., breadths) may have a disproportionate effect on subsequent analyses, intraobserver data was generated for eight length and breadth measurements of four elements: the calcaneus (CALMAX and CALMIDB), the first metatarsal (FSTMAX, 1MLH, and 1MLB) the fifth metatar sal (5MTMAX, and 5MLB) and the talus (TALMINB). These variables were measured three times, non consecutively (ranging from 1 day to over one week between trials). Data
141 from the first two measurement trials was used to compute the technical error of measurement (TEM) following Dahlberg (1940) and Knapp (1992). The TEM is calculated as the square root of the sum of the squared differences between corresponding measurements divided by twice the sample size Knapp (1992:235). This then is the magnitude of measurement error. An increase in TEM magnitude was observed among the breadth measures; however, these errors are negligible (Table 71) and do not appear to affect the results. A relative measure of the magnitude of TEM, the coefficient of variation of error (CVE) takes the TEM and divides it by the mean of the first individuals first and second trial. The CVE also shows that some breadth measurements are more variable than lengths; however, as the CVE are low the measurements are reliable. To furthe r test the effects of measurement error, and to more thoroughly compare variability between length and breadth measurements, the percent measurement error (%ME) was calculated for the eight variables using three measurement trials, following Bailey and Bar nes (1990). This method of calculation uses a model II ANOVA to partition total variability among measurements into among group variance (sample variance) and withingroup variance (measurement error). Rather than assessing an absolute measurement error, the %ME method evaluates the magnitude of the error relative to the among individual variation. Bailey and Barnes (1990) recommend the %ME method for all morphometric studies needing to assess the measurement reliability of the variables under scrutiny. If %ME for a variable is high, the authors recommend deleting that measurement from the study. If the variable needs to remain in the study, the authors recommend remeasuring all individuals a number of times.
142 I elected to use the coefficients of variation (V) to assess the relative variability of certain traits within and among groups. Polly (1998) found that if the variables being compared have a large range of means or if they are within an order of magnitude of their measurement error, then coeffic ients of variation will be misleading. However, if the percent measurement error, as calculated by Bailey and Barnes (1990), is less than 10% or all variables are of similar size then the coefficient of variation may be used with impunity (Polly 1998:89) Of the eight variables, which represent length and breadth measurements of the calcaneus, the first and fifth metatarsals, and the breadth of the talus, measurement errors are greater among breadth measurements (Table 72) However, these errors were below the 10% threshold championed by Polly (1989) and are therefore still useful for this analysis. Relative Variability To Tague (2002) within a species, phenotypic (and genetic) variability is inversely related to the intensity of stabilizing selection (Tague, 2002:195) An y increase in variability suggests less constraints on selection for that character S ince the functional environment is the same for males and females, foot and elements of the foot should be equally variable between men and wom en. However, as I mentioned earlier, males are more plastic in their responses to environmental stimuli (Eveleth and Tanner, 1990; Cole, 2000) a nd therefore might be expected to display higher variability than their female counterparts. For example, Cole (2000) points out that females are not making gains in total height proportional to males, which he suggests is evidence of sexual dimorphism and increasing height. T his could result from increased plasticity among males during periods of better health occurring in childhood when they grow relatively faster.
143 Measures of relative variability can distinguish whether foot morphology between groups of the same species with differing proportions is to the result of epigenetics and plasticity of phenotype. If that is the case, the adult morphology should be more variable given differing life histories. However, i f the major elements of the foot covary with the phenotypic changes in limb length due to a pleiotropic effects, then high variability would not be expected. In general the variables I studied display nearly equal levels of variability, which tend to be low. Intrinsically, the lengths of the five metatarsals are not more variable among any one group. T he r esults of the F test comparisons ( Table 733) in the between groups analysis show no difference between Black and White males and females in terms of intrinsic variability. T he largest number of significant differences is found between Black males and Black females ; Black females tend to be more variable than Black males. On the other hand, White females are more variable than White males but only in terms of the breadth of the base of the first metatarsal (1MLB). This is counter to the expectation that males are more variable due to longer periods of growth and a more generalized plasticity ( Eveleth and Tanner, 1990; Cole, 2000). Overall the length and breadths of foot elements appear to be highly conserved; this is consistent with a pleiotropic effect of covariation with limb long bones elem ents. Proportions of the Foot: Dimorphism and Patterning Although the human foot has interest to numerous researchers from a biomechanical point of view, this region of the skeleton is still one of the least understood structures in the human body (DA out et al. 2009). The current study examines the variability of foot dimensions and foot elements from an allometric perspective utilizing differences in size between the sexes and proportional differences
144 among modern humans from disti nct ecogeographical backgrounds to examine intrinsic variability and withinfoot scaling. The sample of American Blacks has on average, longer feet ( and longer feet proportional to stature) than the American White s. Both the cadaver sample and skeletal sample appear to be congruent with other investigations of foot size, wherein foot size is roughly 14% of total stature (Tables 73 and 74). For example, Fessler et al. ( 2005:46) compile published data for 32 populations of varying ancestries from various time periods and report that foot length as a percent of stature falls between 13.5% and 15.9%. However, tests of isometry show that when examining individual subgroups, the maximum lengths of the calcaneus and the first metatarsal scale isometrically with foot length. Yet when the four subgroups were combined, deviations from isometry were detected and shown to be negatively allometric (Table 727). In other words, there are proportional differences between the relationships of these two elements to overall foot leng th among groups. The four ratios generated from the summed proximal and distal first phalanges, the first metatarsal, calcaneus length and posterior calcaneal length produced even more information on this relationship. These four ratios provide insight i nto the relative contributions of the hallux, midfoot, and heel length to foot length (Figure 7 8). Analysis of variance (ANOVA) demonstrates that the hallux and calcaneus to foot length are not significantly influenced by sex but ancestry was a contribut ing factor. The other two ratios differed significantly for both sex and ancestry. Where ancestry is significant, the differences are all linked to the White sample, whose
145 elements contribute proportionally more to total foot length than is seen among th e Black sample. The relationship of the length of the first metatarsal to the lateral metatarsals also demonstrates proportional differences (Figure 79). In the White sample, t he first metatarsal is longer relative to the other metatarsals. Statisticall y significant differences in proportionality were also observed for several metatarsal ratios, including the ratios MT1 to MT2, MT3 to MT4 (Table 712). Sexual Dimorphism Functional implications for locomotor stresses are evidenced by the White sample wh ich tends to have longer first metatarsals relative to foot size, and relative to the lateral tarsals (see below). Levels of s exual dimorphism of the foot were assessed in terms of relative size via the cube root of body mass dimorphism and indices of sex ual dimorphism (ISDs). The latter is a ratio with several desirable properties. First, the measure is proportional and has numerical symmetry. Also, the ratio can be intuitively understood, as it is not in log form (where magnitude and direction of the difference between males and females may not be easily comprehensible). The log of the male and female means (ln (M/F)) is the ratio recommended by Smith (1999) for statistical examination of size sexual dimorphism. However, the ISD: (male (female)/((ma le+female)/2) yields almost identical numerical values to ln (M/F) when the range of dimorphism is narrow ( i.e., near equally sized males and females) (Smith 1999, Fairbairn, 2006). Therefore, I used the ISD in this study. As a function of the cube root o f body mass dimorphism the linear dimensions of the foot skeleton scale as expected based on Gingerichs (1981) model. Observed differences between expected dimensions for 12 variables for the combined group are
146 often less than 1% (6/12 variables) and all are less than 5% (Table 7 21). Interestingly the breadth measurement for the head of the first metatarsal displays nearly equal dimorphism between the White and Black samples (ISD = ~12% and the difference between expected and observed based on cube root of body mass is = ~4.7% for both groups ). The maximum lengths are not as dimorphic as the breadths. As I mentioned earlier, t his result is potentially a compensatory mechanisms for the increased stresses of absolute size differences. The most notable discrepancy between samples is the breadth of the base of the first metatarsal. This measurement displays much broader dimensions than expected for Black males (Table 721). The White sample has more robust first metatarsal than the Black sample, evidenc ed by the near equal breadth measurements of the head and base of the first metatarsal between the samples, although the maximum lengths are markedly different. This overall shape of the first metatarsal is best illustrated by the robusticity index for th e MT1. White females are markedly more robust than Black females and are surprisingly robust even compared to Black males. To put my sample into a comparative context, several ISDs from other groups were calculated from data culled from the literature, or provided by colleagues (Table 81). In some instances measurement definitions are not the same, so direct comparison of absolute values is not possible; however, because the ISDs are calculated as ratios, measurements only need to be broadly comparable t o be informative (e.g., maximum lengths or breadths). The Late Stone Age (LSA) South African sample represents burials in Cape Province is included here as they are considered broadly ancestral to historical San populations of the same region (Rightmire et al., 2006). Late Stone Age
147 South African samples are characterized small bodied individuals throughout the past 20,0002,000 years BP (Kurki et al., 2008 2009). The LSA sample was drawn as a comparative sample because length and breadth data is available for both the first, second, and fifth metatarsals. Recent South African Blacks were included to draw comparisons with the LSA sample and the HTH Black sample as well as Blacks from the Terry collection. Terry collection data from Robling and Ubelaker (1997) were also used to draw comparisons to the HTH White sample. Data for the maximum lengths of Japanese male and female first metatarsals and calcanei were provided by Ms. Atsuko Hayashi and Mr. Hugh Tuller, and while limited, provides insight into levels of dimorphism of an Asian population. The LSA i ndices are lower than the modern South African B lack sample which is in turn less dimorphic than the US based anatomical collections the HTH sample and the Terry collection sample. Comparing the calcaneal measurements of the HTH black sample and the South African sample reveals less dimorphism in the SA sample for both variables I nterestingly the CALMIDB is considerably less dimorphic. The ISD of the metatarsals is congruent with ISD for stature found by Kurki et al. (2009) for a n LSA population. The statures were reconstructed using the Revised Fully Technique (Raxter e t al., 2006) as well as other stature estimation methods ; and depending on the method of estimation used yields ISDs for stature bet ween 0.033 and 0.050. The breadth measurements are generally more dimorphic in the Terry collection Black sample. Special attention should be given to the similarity in the pattern of dimorphism based on the head of the first metatarsal. In both the cur rent study and the data collected by Robling and Ubelaker (199 7 ) the heads display nearly the same level of dimorphism,
148 while the base of the first metatarsal is considerably more dimorphic in the Black HTH sample. This is not found in the LSA sample where the MT1 base width is less dimorphic than the head. The relatively low dimorphism noted in the LSA stature and metatarsals coincides with Carlson et al.s (2007) finding that sexual dimorphism of the lower limb robusticity is absent in the sample of m odern Hunter Gatherers from Australia. The degree of mobility is equitable between the sexes and thus robusticity differences are not always characteristic of these populations. This might also be reflected in the foot, but has yet to be examined. Robus ticity of the metatarsals is markedly different between the Black males and females but less so in the White sample. I doubt this finding is a result of differences in mobility, but is likely linked to allometric scaling between long limbed individuals and shorter limbed individuals. In other words, although the Black male sample is longer and might be expected to be narrower following the pattern of linearity observed in other elements, it might be up against a critical threshold for scaling and thus mus t maintain a more robust structure due to absolute differences in body mass. The Black females, who tend weigh less, can afford reduced robusticity (which may have the benefit of less energetic demands for locomotion and maintenance of tissue). Breadt hs and Scaling Being broad could be nothing more than a mechanical consequence of scaling. In order to determine if this is an ecogeographical based patterning versus differences in mechanical scaling, first metatarsal lengths and breadths of female s were compared to males. I f stouter breadth i s ecogeographically linked and not a purely functional phenomenon, t he shorter female elements should only be short and broad in the cold adapted populations (White females). The first metatarsal base breadths were
149 very similar among Black and White females (Figure 72); however, their lengths differ markedly (Figure 71). The robusticity index for the first metatarsal further illustrates this difference the first metatarsals of White females are broader than B lack females (Figure 7 10). An additional test to ensure that the metatarsal robusticity is related to ancestry versus a functional mechanism is to break down the entire sample of first metatarsals into two groups, short and long, irrespective of their ancestry. Each group is then reclassified according to ancestry and box plots of 1MLB to FSTMAX examined. Box plots reveal again that the short group patterns according to ancestry White females are broader than Black females and White males are broader than Black males (Figure 8 5) The long group does not display the same pattern. A Quick Test was used to test for relative variation between the Black and White males and between Black and White females. The log transformed variable,1MLB, was regressed against FSTMAX and the RMA regression line was used for the Quick Test following Tsutakawa and Hewett (1977). This method tests the null hypothesis that the distribution of measurements above and below the regression line for any two samples d oes not significantly differ. It was found that the White females have s ignificantly broader first meta tarsals for a given length while males do not display significant differences (Table 717) Relative proportional differences of the lengths and brea dths of the first metatarsal between the sexes and between the ancestral groups have functional implications for the distribution of locomotor stresses and implications for interpreting robusticity in metatarsals. During locomotion, the center of pressure at heel strike is lateral to the
150 midpoint of the heel. By midstance, the center of pressure has shifted laterally. Finally, at toe off the center of pressure moves medially from the metatarsal phalangeal joints through the hallux. The relative elongat ion of the medial line observed in the White sample would create increased bending moments for the first metatarsal during the later phases of gait. Likewise, the Black sample, which has less significant proportional differences between the first metatars al and the lateral metatarsals, would have less bending moments at toe off, even with proportionally longer feet. Assuming relatively equal cortical bone thickness between the Black and White samples and that they share the same biological and mechanical properties for resistance to compression and tension, fracture repair, and cortical remodeling, then an increase in robusticity would reduce stresses on a relatively longer metatarsal. Allometry To examine allometry of the foot I used bivariate plots to investigate scaling of various foot elements with stature, body mass and foot length as well as foot length to stature (Figure 81) and foot length to body mass (Figure 82) Results indicate that detections of deviations from isometry (geometric similarity), depend on the choice of the size measure and sample composition. Smith (1993) points out that in addition to categories of allometric analyses, such as ontogenetic and intraspecific, there are also two broad categories of allometry : body size allometry and biomechanical allometry. S tature and body mass plots relate to exploratory questions investigating changes in shape as size increases. Plotting individual elements versus foot length is a more functionally oriented approach. This allows for in dividual relationships of the makeup of the foot to be discerned. Figure 83 illustrates how an increase in foot length relative
151 to stature results in longer moment arms relative to the ankle but shorter moment arms (bending moments) at the knee. Detecti ng deviations from isometry are only meaningful in a biological context. For instance, CALMAX is positively allometric in Black females relative to stature, but negatively allometric to body mass and isometric for foot length. Drawing from only one of these analyses a researcher might not detect scaling of biological interest. For instance, many allometric studies use body mass, or a highly correlated proxy for body mass, as the size measure for comparison. That the calcaneus is scaling negatively to body mass but positively to stature has implications for the interpretation of the biomechanical consequences. Lemelin and Jungers (2007:828) point out that body size is one of the most fundamental variables influencing diversity of design in primates ; how ever the choice of appropriate body size measures varies Body mass is a n excellent choice and much research focuses on identifying appropriate skeletal estimators of body mass C urrent research has focused on using geometric means of the long bone variables as a proxy Holliday and Franciscus (2009) recently reiterated that allometric comparisons are best made with reference to body mass. Body mass is considered the standard from which to evaluate deviations from geometric similarity (West et al., 1997; Darveau et al., 2002; Garcia and da Silva, 2006). Deviations from Isometry That deviations from isometry are so often found in the pooled sample is not surprising, since the pooled sample combines individuals from groups that vary in dimorphism and ec ogeographical backgrounds. Sylvester et al. (2008) report a similar phenomenon when combining their world wide samples.
152 Additionally, when males and females are combined, deviations from isometry are increased. The authors note that the meaning of their population level comparisons is unclear because of uneven contribution of ancestry across the populations (Sylvester et al. (2008:373) Their Forensic sample (n = 800), in particular, is quite a heterogeneous sample. Sylvester and colleagues consid er this to be the sample which best represents overall human variation. However, I feel a combined sample of individuals who scale differently with respect to stature obscures isometry; that is, to look for differences that can be useful for understanding underlying biological phenomena. It would have been more informative if they had pooled the Forensic sample by racial affiliation and thus account for differing levels of dimorphism and ecogeographical patterning. Scaling differences between ecogeographically distinct populations has been well documented for the elements in their study (humerus, radius, femur, tibia). Nevertheless, the analysis produced notable findings of withinlimb patterning, where the distal limb is more positively allometric than the proximal. The authors suggest this is potentially a universal human trait as it was documented in numerous studies (Jantz and Jantz, 1999; Holliday and Ruff, 2001). Temple et al. (2008) contend that lower limb variation in proportions are more prono unced in their comparative sample (while focusing on proportions of Japanese foragers [Jomon] and agriculturalists [Yayoi]) and theorized that the lower limb may be more susceptible to changes in climate. Stock (2006) points out that there are theoretical and experimental evidence for greater selective pressures found on distal elements. The balance is that an element must be strong enough to resist fracture and light enough to not hinder energetic requirements.
153 Observed ecogeographical patterning is a se parate issue from secular changes. S ecular trends of increasing stature in Europe (Cole, 2000) and the United States (Jantz and Jantz 1999) have been well documented, and are largely due to nutritional benefits and issues relating to affluence and matern al care. Cole (2000) suggests that sexual dimorphism as increasing height among females is related to gains in total height proportional to males. This could be increased plasticity among males during childhood periods of better health, when they grow re latively faster. Most of the differences in the increased height are due to increases in leg length (Tanner et al., 1982; Cole, 2000). Jantz and Jantz (1999) found stronger secular change in the long bones of males versus females and more in White versus Black samples. Further scrutiny of the relative variability and patterning of the foot is necessary. First, in terms of proximodistal variability, the most distal element, the metatarsal, is no more variable than the most proximal. Second, in terms o f deviations from isometry, the distal element is no more positively allometric than the calcaneus in all groups. In fact the first metatarsal was negatively allometric relative to body mass for the White female sample. Compared relative to stature, the calcaneus is positively allometric in the White male and Black female samples. The calcaneus scaled isometrically for foot length in all samples and is negatively allometric with respect to body mass in the Black female sample. Within the foot, the invest igated elements scale isometrically with total length of the foot. The finding that the foot is positively allometric with respect to stature for all groups except White females (isometric) highlights the biomechanical environment thusly created. First, larger White females will experience absolutely larger locomotor
154 stresses (e.g. bending moments) than smaller White females, unless another compensatory mechanism is in play (e.g., limb posture). Positive allometry in the other groups suggests that the foot is longer than expected for a given stature. Aside from increased energetic requirements (metabolic) that positive allometry suggests, biomechanical consequences are also possible. During the initial heel strike phase of locomotion, positive allometry of the foot would produce larger moment arms to ground reaction force and hence increased anterioposterior bending of the femur (Figure 43c). During the latter phases of gait (e.g., at toe off), this would have the effect of increasing the moment arms about the ankle but decreasing them at the knee ( Figure 83). This finding is congruent with the finding that longer limbed individuals tend to walk with more extended joint postures which would serve to attenuate such bending moments (Gruss, 2007). Walki ng with more extended limb postures would likely then incur large joint reaction forces as the center of gravity and body mass are shifted more anteriorly or in line with the limb. Polk (2004) found that in patas monkeys, longer limbed individuals move more efficiently as their limb angular excursions are and contact and stride frequencies are smaller, while maintaining. This is achieved through more extended limb postures, a configuration that requires less energetic expenditure. Longer foot lengths ho wever, would require greater expenditure of energy from increased distal mass. P ositive allometry suggests that additional metabolic requirements are required to sustain such growth and to maintain locomotion. Although the foot was not modeled into the o riginal equations Ponzer (2005) found that effective limb length ( i.e., hip height) was a better predictor of cost of locomotion (COL) and cost
155 of transport (COT) than other models and variables such as the Frounde number and contact time. Ponzer (2005; 2007a ,b ) posits that limb length drives betweenspecies differences in locomotor cost and finds evidence that body mass is not independently a ffecting cost Furthermore, Ponzer finds that across a large spectra of animals the effective limb length explains 98% of the observed variance in locomotor costs. When the foot is taken into account (Ponzer 2007), the added length of the limb (calculated trigonometrically from foot length and excursion angle) allows the model to more accurately predict GRFs and i ncreases the effective limb length. Thus this positive allometry of the foot found in the current study may be beneficial from a mechanical point of view since it would add to the effective limb length. Biomechanical Environment Effective Mechanical Adv antage ( EMA ). The EMA based on an inlever of PCAL and an out lever using (CALMAX PCAL) + CUBMAX + 3RDMAX was shown to be very similar between all four samples (Figure 7 17; Table 734 ). The most variability in EMA is found among Black male s who rang e from 38% to 48% ( a t wo w ay ANOVA yields no significant differences between groups, results not presented). Wang and Compton (2004) modeled the forces acting on the foot during standing and suggest that an optimal range of the ratio of power arm to load arm is 35% 45% depending on attachment of the Tibialis Anterior. All groups in the current study have a mean value higher than the 40% optimum calculated by Wang and Compton (2004), but all are within the range. Note that the Wang and Compton (2004) stud y utilized the measurements of one human skeletal foot and compared theoretical models based on allowing various variables in their model range ( e.g., the range of the load arm length was allowed to vary between 2% 10%). Thus, here calculation of observed ratios
156 provides more empirical support for the proportions theorized by Wang and Compton (2004). Joint R eaction F orces Examination of the LS regression of body mass on ankle joint force demonstrates a high correlation coefficient (0.988) and a high coef ficient of determination (0.976). This is not surprising since body mass is a factor in calculating the forces of the muscles as well as the GRF. However, it is important to remember that the Fm and Fr were free to vary based on the inand out lever lengths (measured). Thus, while many of the tests of isometry above indicate isometric scaling with respect to body mass, this independent finding affirms that joint forces scale with body size and that the proportions of the calcaneus (PCAL and CALMAX), as well as CUBMAX and THRDMAX, scale isometrically for body mass. Testing the breadth measurements of the talus and calcaneus in relation to the joint reaction force is also necessary. The width of the talus (TALMINB) should scale in relation to the distal tibia, and the CALMIDB is theoretically a good approximation of the articular surface between the talus and calcaneus. Results of tests of i sometry with respect to this joint reaction force do scale with body mass, and have a slope of isometr y equal to 0 .33. For the most part the variables scale isometrically however many of the variables are not significant results, as the slope of the 95% confidence interval pass through zero. CALMAX appears to be negatively allometric in relation to joint force but P CAL and CALMIDB are isometric. Even for significant relationships, the best model (all groups, LOG TALMAXL versus LOG joint reaction force) only has approximately 25% of the variance explained by the relationship. In general, only the all groups results can be considered, which precludes
157 me from inferring relationships regarding ecogeographical pattern. Future work with larger sample sizes may yield an array of variation sufficient to explore scaling with joint forces relative to ecogeographical patterning. The high hind limb joint size dimorphism in humans identified by Lague (2003) reflects size related increases in joint stress. In the current study this is reflected in the measurements that essentially capture joint surface areas as a single linear measurement (e.g., middle breadth of calcaneus, minimum breadth of the talus, base breadths of the metatarsals); however, additional work is necessary to accurately model joint surfaces for the foot relative to stress. Body M ass Body mass is often not recorded for museum specimens making comparative analyses difficult (Smith and Jungers 1997). In the case of the HTH specimens used in the current study, body mass may have been confounded by the low socioeconomic class of the sample and the chronic illnesses ( and hence wasting ) the individuals comprising the sample suffered. Add to this the manner of death (B lack males tended to die from violent deaths while the other three groups typically suffered chronic illness ) ( Todd and Lindala, 19 28) ) it is clea r that estimations of body mass are difficult, at best However, m ean body mass in this sample is greater than that of the Todd and Lindala (19 28) sample in every category suggesting this might not be a problem for the HTH skeletal subsample in the curre nt study. Furthermore, the White male subsample is greater than the Black male subsample indicating they were not likely systematically underweight. Reviewing the collection records, Todd and Lindala (1928) discovered that there were inconsistencies in how weight was recorded for some the weight of some individuals (estimates rather than measurements). While this is at first
158 problematic, examination of the Body Mass Indices (BMI = body mass (kg)/stature (m)2 ) of the HTH skeletal sample reveals that the individuals were, on average, within the normal range of 18.5 to 25 (WHO, 19 86 ). Only the Black female sample is underweight (BMI = 18.43), but the average is very close to the normal range cut off. All groups contain individuals who are severely underweight, and all groups contain individuals who are considered overweight or obese. Examination of the box plots for BMI (Figure 8 4) does not suggest a skewed dataset, and thus these measures are likely a good representation of variance in the overall popul ation from which the sample was drawn. N umerous tests of isometry relative to body mass in this study were not significant Consider the foot on body mass test for the all groups cadaver sample, which shows a low correlation (n = 1040, RMA slope = 0.3 13, r = 0.270, r2 = 0.073). Body mass covaries weakly with foot length (only 7% of the variance in foot length is explained by mass). Nonsignificant results were also found in the cadaver sample W hite females for the foot l ength to body mass regression, and middle breadth of the calcaneus and medial lateral head of the first metatarsal for White females, Black males, and White males. The all groups analyses for these measurements performed well and have relatively narrow RMA 95% confidence interval (CI) slopes. H owever correlations for all comparisons involving body mass were relatively low. The highest significant correlation for any comparison with body mass was only 0.518 (Black females for the variable CALMAX). Predication of b ody m ass. The skeletal dimensions best performing in tests of isometry (as inferred from correlations and range of 95% CI) are comparable to the
159 correlations that Ruff et al., (1991) report for human femoral head (FH) diameter and body weight (all groups r = 0.486 (raw data) r = 0.491(logged data)). Femoral head diameter is a commonly used surrogate for body mass in morphometric studies (see Auerbach and Ruff, 2004). Likewise, articular surfaces do not change appreciably with changes in activity (Lieberman et al., 2001, Auerbach and Ruff 2004), an d are therefore better for estimations of body size than diaphyseal measurements. However, diaphyseal dimensions are commonly used in allometric studies, usually incorporated into an overall surrogate for body size such as the geometric mean. Thus such estimates may be influenced by levels of activity. Aside from the potential problems encountered when using the recorded measurements of body mass mentioned above, elements of the foot can serve as a proxy for the estimation of body mass. Good candidates for prediction of body mass from the skeleton are the calcaneus and talus, which directly bear the weight of the body during locomotion. The calcaneus and talus are irregular bones comprised of much more trabecular bone than long bones, and given the functional relationship of their articular joints, should not vary in external dimensions with varying levels of activity. Instead use and disuse changes are more likely displayed by density differences and remodeling of the internal trabecular architecture. Further, the calcaneus is fully developed prior to full attainment of stature in both males and females, and thus is not remodeling (externally) or increasing in length in response to body mass loads and ground reaction for ces, but instead is canalized toward an individuals expected body size range.
160 In each sample subgroup the calcaneus scales isometrically to foot length (Table 7 27), and the ratio CALMAX / stature is not statistically significant for ancestry (Table 75 ). This and several other tests indicate that proportional differences in foot length are not driven by the calcaneus but rather the metatarsal and distal tarsal region, so the calcaneus can be used to estimate body mass for individuals from different eco geographical backgrounds. Finally, although there are absolute size differences in the calcanei between males and females, ISDs and dimorphic expectations based on cube root of body mass dimorphism demonstrate that the maximum length of the calcaneus is o nly as dimorphic as stature. Ruff et al., (1991) discuss how the increased body weight exhibited by modern Americans would necessitate decreasing body mass es estimated of earlier populations by 10%. The current sample represents individuals born between 1850 and 1900 (Ousley, 1998), and as such, represent populations that would not have suffered from increased in adiposity as much as the Ruff et al. (1991) sample. Only all groups were considered for LS regression g iven the poor performance of the RMA regression models (tests of isometr y) when subgroups are split out. The LS regression models for body mass were generated incorporating only those individuals in the reference data who are within the normal range for BMI (18.525). This was done in an eff ort to construct a normal population, by segregating the underweight individuals and thus decreasing bias from individuals whose low body mass is due to chronic illness. Obese individuals were likewise excluded so that the resultant equations might be m ore applicable to researchers interested in using the data to make inferences about past populations, when obesity was not typical.
161 Results of stepwise LS regression for the four calcaneal and talar variables indicate that CALMAX and CALMAX and TALMAXL produce the best models. Using only the maximum length of the calcaneus provides a good model to estimate body mass. However, slightly better is the inclusion of both maximum lengths of the calcaneus and the talus (Table 729). Thus stepwise select ion eliminates the breadth measurements of these elements in favor of utilizing only the maximum lengths in the models. These measures highly correlate to body mass and the standard errors of the estimate are comparable to those reported by Ruff et al., ( 1991). Tests of efficacy of the LS regression equations were used on a separate HTH sample for which maximum lengths of the calcaneus and talus were made available (by T. Holland). Tests of efficacy were also limited to individuals who fell in the range of a normal BMI (n = 41) Three measures were used to evaluate the performance of these predictive models percent prediction errors (%PE), accuracy and bias. Percent prediction errors were calculated as [(observedpredicted)/predicted] *100 following R uff et al. (1991) in order to make direct comparisons to their published tests of efficacy. Using this calculation positive numbers indicate underestimates. A ccuracy is the absolute value of the difference between observed and predicted values ( observed mass estimated mass | / n) while bias is the signed difference. Using the CALMAX only equation, results in %PE ranges from 2 7 12 to 19.46 (mean = 3.03 SD = 11. 28), a ccuracy is 5.96 kg, and bias is 1. 94 kg While using the model that incorpora tes both CALMAX and TALMAXL results in %PE ranges of 26.21 to 19.57 (mean = 2.64, SD = 11.24) inaccuracy is 5.74 kg, and bias is 1.70 kg.
162 Ruff et al. (1991) report a test of efficacy for their FH diameter models using eight individuals not included in the dataset from which their regression equation was generated. They report %PEs ranging from 22 to 57 (or a maximum of 28 if one obese individual is dropped from their test), using their general equation (combined sample). While the current study pr oduces overestimates comparable to the FH method, it does not produce underestimates of the magnitude originally reported by Ruff et al. (1991). However, the negative bias observed in the current study indicates t hat the models do tend to under estimate the mass of the individuals. Furthermore, the Ruff et al. (1991) FH equations have recently been tested on a large sample of adults (n = 1173) using a worldwide sample (Auerbach and Ruff, 2004). Auerbach and Ruff (2004) report that the mechanical method of body mass estimation using FH diameters is congruent with morphometric methods which incorporate body size estimates using stature and body shape (e.g., pelvic dimensions). Note that these tests were comparisons of models a gainst one an other ; not tests of efficacy utilizing individuals with measured body mass. Given the theoretically improved performance of the CALMAX and TALMAXL equations, tests of efficacy should be performed across a wider array of populations. These two elements have already proven useful for prediction of stature (Holland, 1995) and indices such as weight/stature highly correlate to weight, independent of stature (Micozzi et al., 1986). Stature Stature is a linear measurement of body size and is an often used variable for the assessment of health in populations (Wood et al., 1992). Components of stature are also often used to study migration, climatic adaptation, secular change, epigenetic influence, dimorphism and a multitude of other evolutionary and biological processes
163 ( Jantz and Jantz 1999 ; Holliday and Ruff, 2001; Gustafsson and Lindenfors 2004). The biological processes affecting the growth and development of such proportions must also contend with the primary biomechanical functions of the limb during locomotion. Statur e and subsequently limb length scaling has significant influences on energetics, cost of transport, and locomotor stresses. Therefore, stature is an important contrast to body mass for allometric studies. When all groups are considered together the gen eral pattern is that the foot is positively allometric relative to stature (Table 727). There is some discrepancy between tests of isometry for the HTH cadaver and HTH skeletal sample regarding overall foot length to stature. In the HTH cadaver sample, Black males and females are positively allometric, while the HTH skeletal sample indicates isometry for the same groups. The HTH cadaver sample is probably a better representation of the true biological condition (larger sample sizes). In fact, deviation s from isometry are often detected when sample sizes are large (Sylvester 2008). Closer examination of the HTH skeletal subsample reveals that while the White samples are both positively allometric, the White females are only positive because of rounding (the 95% CI range is 1.031.71); for all intents and purposes they too are isometric (see Table 724). White males are positively allometric for foot length to stature in both samples. The discrepancy noted between the two samples (HTH cadaver and HTH skeletal) makes interpretation of the scaling of the individual elements of the foot more difficult. It is possible that the HTH skeletal sample is not a good representation of the overall populations from which they were drawn. However, the sample sizes are not small (the smallest sample size in these tests of isometry is 25, for White females, while
164 most range from 3069 individuals) and the variables do not significant ly deviate from normality. Both of these factors suggest that the HTH skeletal resul ts can be interpreted independently from the cadaver sample. Moreover, the 95% CI for the RMA regressions were bootstrapped using 2000 replicates ( Hammer et al 2001). One of the more interesting findings from the tests of isometry of foot elements rel ative to stature is that the Black male group is isometric for calcaneus length, but negatively allometric for the first metatarsal, while White males are positive for both variables. In the other variables tested, including two breadth measurements the g eneral pattern is that the Black males are isometric and White males are positively allometric. In other words, in a study examining, or predicting, body size relative to ecogeographical expectations one would incorrectly assume that all elements scale positively for stature in tropically adapted populations. Although isometric for foot length, the first metatarsal scales differently for both tropically adapted and cold adapted groups relative to stature, at least among males. This element scales contra the expectation that it would be longer relative to stature in the tropically adapted group for males. Interestingly this pattern is not the same for Black females, who scale more similarly to the pattern seen among White males. Least squares regressions of foot elements and foot lengths to stature also prove enlightening, conforming to the expected ecogeographical pattern. Using my equations, at any given stature the Black males and females have longer feet. This is not all together unexpected since the re are known differences in long bone to stature ratios for the two groups. More interesting is that when using the same data to generate equations to predict foot length from any of the selected tarsals or metatarsals, the
165 same pattern emerges, indicating the foot is scaling differently (intrinsically) among groups. This scaling was further investigated by creating ecogroups who scale exactly as expected based on well studied and often utilized regression equations that predict stature from long bone lengths. Hypothetical statures were used to generate ecoindividuals whose long bones (tibia and femur) scale exactly as expected for their target statures. Least squares regression equations for each group were used to create expected foot lengths f or these ecoindividuals based on the same stature. Relationships between elements were tested for isometry using RMA regressions. Results indicate that the foot scales positively to the femur in all groups, although the Black sample is nearly isometric. The tibia yields more varied results with the foot negatively allometric with respect to tibia length in the Black sample, positively allometric in the White sample. White males are positively allometric in almost every case, while the White female patt ern is nearly isometric. Prediction of stature from the metatarsals. Scaling differences in the groups pointed out above requires population and sex specific equations to predict stature from long bones of the foot. Holland (1995) provides regression equations for prediction of stature from the talus and the calcaneus using adequate sample sizes (n = 25 for each group, BF, WF, WM, BM). Hollands (1995) regression equations were created using a sample from the HTH, and thus equations for the calcaneus a nd talus are not presented here. Byers et al. (1989) developed stature estimation regression equations for the five metatarsals. They present regression equations for White (EuroAmericans) and Black
166 (Afro Americans) males and females. The White sample is composed of 57 males for each metatarsal and ranges from 47 to 49 individuals for females. However, their Black sample is only 9 to 11 males (depending on the metatarsal) and only 7 females. While these models performed relatively well with high corr elation coefficients (which range from 0.70 through 0.89) and moderate standard errors (39.9 mm to 68.0 mm), their regression equations should be used with caution as the sample sizes are too small to have captured the true variability of these elements and their covariation with stature. The current sample provides large sample sizes for the Black and White males and females (Table 729). Correlation coefficients range from 0.523 to 0.845, and standard errors of the predictive models are on par with est imation of stature from tarsals and fragmentary long bones. Compared to the Byers et al. (1989) formulae, the standard errors presented here have increased for the Black male and female formulae. This is most likely due to the increased sample sizes pres ent, which capture more covariation between metatarsals and stature for these groups. These equations should be used when comparing past populations believed to fit a tropically adapted phenotype. The effect that secular trends in increased stature and l ower limb long bones have for the scaling of the foot is currently not known. These regression equations could be used for studies with relatively contemporaneous populations; however, they may not be as accurate or precise for modern forensic investigati ons. Prediction of stature from foot length. While the predicti ve equations generated here for estimating stature from foot length designed to investigate scaling there may be instances in which researchers are interested in using the equations in arch eological, paleontological or forensic contexts. For instance Giles and
167 Vallandigham (1991) studied the utility of estimating height from foot and shoeprint lengths in the forensic context and found that, with appropriate statistical caveats, foot length as well as shoeprint length can inform investigators about stature. However that analysis combined individuals of differing ancestral groups. Gordon and Buikstra (1992) improved this line of analysis, offering sex and ancestry specific linear regression equations. Both of these studies used U.S. military populations and were thus slightly biased for younger individuals, who may have not attained full stature at the time the anthropometric data was collected. However, foot growth for these individuals was likely complete. The equations presented here (Table 728) may be useful in some contexts, such as stature estimation from foot length data from comparable populations, or as a comparative basis for secular trend investigations or within the context of investigation of footprints
168 Table 8 1 Indices of sexual dimorphism for selected variables from various populations. Variable HTH (B lack ) HTH (W hite ) LSA 1 SA 1,2 Terry 3 Terry 4 Chiba 5 AdjSTAT 0 .07 0.07 0.033 0.050 6 0 .06 FSTMAX 0.07 0.09 0.04 1 0.05 1 0.08 0.07 0 .06 2ndMAX 0.07 0.09 0.03 1 0.04 1 0.09 0.08 3rdMAX 0.08 0.08 0.09 0.08 4thMAX 0.07 0.09 0.08 0.08 5thMAX 0.08 0.09 0.05 1 0.08 0.08 CALMAX 0.09 0.09 0.08 2 0 .08 CALMIDB 0.11 0.08 0.08 2 1MLH 0.11 0.12 0.12 1 0.13 0.13 1MLB 0.12 0.09 0.10 1 0.16 0.15 2MLB 0.15 0.11 0.04 1 0.14 0.10 3MLB 0.12 0.08 0.12 0.12 4MLB 0.11 0.05 0.09 0.10 5MLB 0.10 0.09 0.12 0.10 1. Late Stone Age (Holocene) South African data from Rightmire et al. (2006) 2. South African Blacks (rec ent) data from Rightmire et al. (2006) and Bidmos ( 2006 ) 3. Terry Collection (Black, recent, SMNH) Robling and Ubelaker (1997) 4. Terry Collection (White, recent, SMNH) data from Robling and Ubelaker (1997) 5. Japanese (Chiba University data provided by Atsuko Hay ashi and Hugh Tuller (unpublished) 6. Late Stone Age (Holocene) South African data from Kurki et al. (2009)
169 7.25 7.3 7.35 7.4 7.45 7.5 7.55 7.6 LOGSTAT 5.22 5.28 5.34 5.4 5.46 5.52 5.58 5.64 5.7LOGFOOT F igure 8 1 LogLog plot of foot length to stature for the HTH cadaver sample (all groups, n = 1040; RMA slope = 1.385, r = 0 .738). The foot scal es positively with regard to stature.
170 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 LOGmass 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6LOGfoot Figure 8 2 LogLog plot of foot length to body mass for the HTH cadaver sample (all groups, n = 1040, RMA slope = 0 .313, r = 0 .270). The foot scales isometricly with regard to body mass. b a Figure 8 3 Illustration of the consequence of positive allometry relative to stature. In a an individual experiences a shorter moment arm to GRF (arrows) than b at the ankle, but greater at the knee; and the scenario in b there is a decrease in the GRF moment arm at the knee but greater at the ankle.
171 1.00 2.00 3.00 4.00 10.00 20.00 30.00BMI Figure 84. Box plots of the Body Mass Index (BMI) for the HTH skeletal sample. (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents t he median value, circles depict outliers ) 1.00 2.00 3.00 4.00 0.275 0.300 0.325 0.350 0.375mlbtofstmax 1.00 2.00 1.00 2.00 3.00 4.00 Figure 85 Box plots o f the r obusticity index for short (left) and long (right) first metatarsals HTH skeletal sample (1 = BF, 2 = WF, 3 = BM, 4 = WM ; Boxes and whiskers represent 50% of the data sample each, the line represents the median value, circles depict outliers )
172 Table 82. Demographics for HTH test of efficacy sample for body mass predictive equations Variable N Min Max Mean Std. Deviation Age (years) 41 17 83 45.20 16.72 Mass (kg) 41 44.45 75.30 59.10 7.82 STATURE (mm) 41 1436 1847 1675 85.01
173 CHAPTER 9 CONCLUSIONS The current study examined the variability of foot dimensions and foot elements from an allometric perspective utilizing differences in size between the sexes and proportiona l differences among modern humans from disti nct ecogeographical backgrounds to examine intrinsic variability and withinfoot scaling. In terms of sexual dimorphism, the female foot is dimorphic in both absolute terms and proportionally to stature. Result s of ANOVA indicate statistically significant differences between Black males and females and White males and females for foot length to stature ratios in the HTH cadaver sample. Further inquiry into the proportionality of the foot via allometric analysis reveals that only the White female group scales with isometry with respect to stature. All other groups scale positively, that is, they have larger feet than expected based on the principle of geometric similarity. Overall, the White female and Black male samples tend to be isometric in most of the relationships under examination. Scaling with isometry means that the absolute stresses are increased for larger individuals. The foot conforms to the expected ecogeographical pattern among both males and f emales as the ancestrally tropically adapted group have longer feet for a given stature. Results of ANOVA indicate statistically significant differences between Black males and females vice White males and females for foot length to stature ratios in the HTH cadaver sample. Results of ANOVA for the HTH skeletal sample show that the calcaneus/stature, and sum of the first ray proximal and distal phalanges/stature variables are not significant for race and hence are not conforming to the ecogeographical pattern, however, the metatarsal s are Thus it appears that the meta tarsal region is driving most of the variation in the foots conformance to the
174 ecogeographical pattern. Results of least squares regression for prediction of foot length, based on the HT H skeletal sample, show that for a given tarsal or metatarsal measurement, the Black sample would be estimated to have a longer foot than the White sample. Conformance to the ecogeographical pattern is also examined via breadths of the tarsals and metatarsals. As the length of the foot elements increase or decrease in proportion to stature they should too be increasing or decreasing in breadths. Focusing on the first metatarsal, and calcaneus, tests for deviations from isometry indicate that the head of the first metatarsal and the middle breadth of the calcaneus are positively allometric for Black females relative to overall foot length. Other groups are isometric indicating that the breadths are scaling appropriately to foot length for maintenance of geometric similarity. Examination of robusticity indices also informs the proportional differences between groups. In general the Black sample is narrower than the W hite sample, however, Black females have very narrow metatarsal bases relative to lengths especially in MT1MT3. Proximo distal variability was explored using coefficients of variation and their derivatives. It was found that the more distal element, the first metatarsal, was not more variable. Secondly, in terms of deviations from isometr y, the distal element, the first metatarsal was not more positively allometric than the calcaneus in all groups by the three measures (stature, body mass and foot length) with which they were compared. In fact the first metatarsal was negatively allometri c for the White female sample. Compared to stature the calcaneus was positively allometric in the White males and Black females samples. The calcaneus scaled isometrically for foot length in all
175 samples and was negatively allometric with respect to body mass in the Black female sample. Effective mechanical advantage at the ankle was found to be similar for all groups. Modeling of the joint force reactions at the ankle indicate that t he joint surfaces (as inferred by middle breadth of the calcaneus and minimum breadth of the talus) scale isometrically for body mass. Linear regression models were presented for estimation of body mass, stature, and foot length from various pedal elements. E quations for predicting body mass from the calcaneus and talus w ere found to be an improvement upon existing methods for estimation of body mass in human populations based on femoral head dimensions. Furthermore, equations presented here for estimating stature from metatarsals provide an important tool for forensic an d bioarchaeological analyses, as previously published methods are based on inadequate sample sizes for Black males and females.
176 LIST OF REFERENCES Adams BJ, Byrd JE. 2002. Interobserver variation of selected postcranial measurements. J Forensic Sc i 47:11931202. Adams BJ, Byrd JE. 2006. Resolution of small scale commingling: a case report from the Vietnam War. Forensic Sci Int 156:6369. Aiello LC, Dean C. 1990. An Introduction to Human Evolutionary Anatomy. London, UK: Academic Press. Aiello LC, Wells JCK. 2002. Energetics and the evolution of the genus Homo Annu Rev Anthropol 31:323338. Albrecht GH, Gelvin BR, Hartma SE. 1993. Ratios as a size adjustment in morphometr ics. Am J Phys Anthropol 91:441 468. Allen JA. 1877. The influence of phys ical conditions on the genesis of species. Rad Rev 1:108140. Anderson M, Blais M. Green WT. 1956. Growth of the normal foot during childhood and adolescence: length of foot and interrelations of foot, stature, and lower extremity as seen in serial records of children 118 years of age. Am J Phys Anthropol 14:287308. Anil A, Peker T, Turgut HB, Ulukent SC. 1997. An examination of the relationship between foot length, foot breath, ball girth, height and weight of Turkish university students aged between 17 and 25. Anthropol Anz 55:7987. Auerbach BM, Ruff CB. 2004. Human body mass estimation: a comparison of morphometric and mechanical methods. Am J Phys Anthropol: 125:331342. Ashton KG, Tracy MC, de Queiroz A. 2000. Is Bergmanns rule valid for m ammals? Am Nat 156:390415. Baba K. 1975. Foot measurement for shoe construction with reference to the relationship between foot length, foot breadth, and ball girth. J Human Ergol 3:149156. Bailey RC, Byrnes J. 1990. A new, old method for assessing m easurement error in both univariate and multivariate morphometric studies. Syst Zool 39:124130. Barber N. 1995. The evolutionary psychology of physical attractiveness: s exual selection and human morphology. Ethol Sociobiol 16:395424. Beck TJ, Ruff CB, Shaffer RA, Betsinger K, Trone DW, Brodine SK. 2000. Stress fracture in military recruits: gender differences in muscle and bone susceptibility factors. Bone 27:437444.
177 Bennell KL, Malcolm SA, Thomas SA, Reid SJ, Brunker PD, Ebeling PR, Wark JD. 1996. Ris k factors for stress fractures in track and field athletes: a twelvemonth prospective study. Am J Sport Med 24:810818. Bergmann C. 1847. Uber die Verhaltnisse der Warmeokonomie deThiere zu ihrer Grosse. Gottingen Studien 1:595708. Bidmos MA. 2006. Met rical and nonmetrical assessment of population affinity from the calcaneus. Forensic Sci Int 159:613. Bidmos MA, Asala S. 2003. Discriminant function sexing of the calcaneus of South African whites. J Forensic Sci 48:12131218. Bidmos MA, Asala S. 2004. Sexual dimorphism of the calcaneus of South African blacks. J Forensic Sci 49:446450. Biew e ner AA. 1989. Scaling body support in mammals: l imb posture and muscle mechanics. Science 250:10971103. Biewener AA. 1990. Biomechanics of mammalian terrestrial locomotion. Science 104:10971103. Bindon JR, Baker PT. 1997. Bergmanns rule and the thrifty genotype. Am J Phys Anthropol 104:201210. Blackburn TM, Gaston KJ, Loder N. 1999. Geographic gradients in body size: a clarification of Bergmanns rule. Dive rs Distrib 5:165174. Bowden REM. 1967. The f unctional a natomy of the f oot. Physiotherapy 53: 120 126 Brudvig TJ, Gudger TD, Obermeyer L. 1983. Stress fractures in 295 trainees: a oneyear study of incidence as related to age, sex, and race. Mil Med 148: 666667. Byers S, Akoshima K, Curran B. 1989. Determination of adult stature from metatarsal length. Am J Phys Anthropol 79:275279. Byrd JE, and Adams BJ. 2003. Osteometric sorting of commingled human remains. J Forensic Sci 48:717724. Cameron N. 2002. Human growth curve, canalization, and catchup growth. In: Cameron N, editior, Human growth and development. New York: Academic Press. P 1 20. Carlson KJ, Grine FE, Pearson OM. 2007. Robusticity and sexual dimorphism in the postcranium of modern hunter gatherers from Australia. Am J Phys Anthropol 134:923.
178 Carrier DR, Heglund NC, Earls KD. 1994. Variable gearing during locomotion in the human musculos keletal system. Science 265:651653. Case DT, Ross AH. 2007. Sex determination from hand and foot bone lengths. J Forensic Sci 52:264270. Cohen J. 1988. Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum. Cole TJ. 20 00. Secular trends in growth. P Nutr Soc 59:317 324. Cope DA, Lacy MG. 1992. Falsification of a single species hypothesis using the coefficient of variation: a simulation approach. Am J Phys Anthropol 89:359378. Corruccini R. 1983. Principal components for a llometric analysis. Am J Phys Anthropol 60:451453. DAout K, Pataky TC, De Clercq D, Aerts P. 2009. The effects of habitual footwear use: foot shape and function in native barefoot walkers. Footwear Science 1:8194. Davenport CB. 1932. The growth of the human foot. Am J Phys Anthropol 17:167211. Davis KT. 1990. The Foot Length to Stature Ratio: A Study of Racial Variance. Masters thesis, Lubbock TX : Texas Tech University. Droessler J. 1981. Craniometry and biological distance. Evanston IL: C enter for American A rcheology at Northwestern University. Duboule D 1994. How to m ake a l imb? Science 266: 5 75 5 76 Dudley AT, Ros MA, Tabin CT. 2002. A reexamination of proximodistal patterning during vertebrate limb development. Nature 418:539544. Emanovsky PD. 2009. Prediction of shoe size from tarsals and metatarsals. Proc Amer Acad For Sci 15:344. Evel eth P, Tanner J. 1990. Worldwide Variation in Human Growth. Cambridge, UK: Cambridge University Press. Fairbairn DJ. 2007. Introduction: the enigma of sexual size dimorphism. In: Fairbairn DJ, Blanckenhorn WU, and Szekely T, editors. Sex, Size and Gender Roles: Evolutionary Studies of Sexual Size Dimorphism. New York: Oxford University Press. p 110. Fessler DT, Haley KJ, Lal RD. 2005. Sexual dimorphism in foot length proportionate to stature. Ann Hum Biol 32:4459.
179 Fransiscus RG, Long JC. 1991. Variation in human nasal height and breath. Am J Phys Anthropol 85:419427. Friedl KE, Nuovo JA, Patience TH, Dettori J. 1992. Factors associated with fracture in young Army women: indications for further research. Mil Med 157:334338. Gardner LI, Dziados JE, Jones BH, Brundage J, Harris J, Sullivan R, Gill P. 1988. Prevention of lower extremity fractures: a controlled trial of a shock absorbent insole. Am J Public Health 78:1563 1567. Gefen A, Megido Ravid M, Itzchak Y, Arcan M. 2000. Biomechanical analysi s of the threedimensional foot structure duing gait: a basic tool for clinical applications. J Biomed Eng 122:630639. Giles E. 1991. Corrections for age in estimating older adults' stature from long bones. J Forensic Sci 36:898901. Giles E, Vallandig ham PH. 1991. Height estimation from foot and shoeprint length. J Forensic Sci 36:11341151. Gingerich PD. 1981. Cranial m orphology and a daptations in Eocene Adapidae. 1. sexual d imorphism in Adapis magnus and Adapis parisiensis Am J Phys Anthropol 56:217 234. Gordon CC, Buikstra JE. 1992. Linear models for the prediction of stature from foot and boot dimensions. J Forensic Sci 37:771782. Gross TS, Bunch RP. 1989. A mechanical model of metatarsal stress fracture during distance running. Am J Sport Med 17:669 674. Gruss LT. 2007. Limb l ength and l ocomotor b iomechanics in the g enus Homo : a n e xperimental study. Am J Phys Anthropol 134:106116. Gustafsson A, Lindenfors P. 2004. Human size evolution: no evolutionary allometric relationship between male and female stature. J Hum Evol 47:2 53266. Haeusler M, McHenry HM. 2004. Body proportions of Homo habilis reviewed. J Hum Evol 46:433446. Hammer O, Harper DAT, Ryan PD. 2001. PAST: paleontological statistics software package for education and data analy sis. Palaeontol Electron 4:19. Hanna JM, Brown DE. 1983. Human heat tolerance: an anthropological perspective. Ann Rev Anthropol 12:259289.
180 Hefner JT. 2007. The statistical determination of ancestry using cranial nonmetric traits. Ph.D. dissertat ion. Gainesville, FL: University of Florida. Higgins RW. 2008. Modern human limb proportions follow Allen's rule predictions and reflect long term climate adaptations rather than short term epigenetic influences. Am J Phys Anthropol S 135:117. Hills M. 1982. Bivariate versus m ultivariate a llometry: a note on a paper by Jungers and German. Am J Phys Anthropol 59:321322. Hoerr NL, Pyle SI, Francis CC. 1962. Radiographic atlas of skeletal development of the foot and ankle: a standard of reference. Spring field, IL: Charles C Thomas. Holden C, Mace R. 1999. Sexual dimorphism in stature and women's work: a phylogenetic cross cultural analysis. Am J Phys Anthropol 110:2745. Holland TD. 1995. Estimation of adult stature from the calcaneus and talus. Am J Phys Anthropol 96:315320. Holliday TW. 1997a. Body proportions in Late Pleistocene Europe and modern human origins. J Hum Evol 32:423447. Holliday TW. 1997b. Postcranial evidence of cold adaptation in European Neandertals. Am J Phys Anthropol 104:245258 Holliday TW. 1999. Brachial and crural indices of European Late Upper Paleolithic and Mesolithic humans. J Hum Evol 36:549566. Holliday TW, Falsetti AB. 1995. Lower limb length of European early modern humans in relation to mobility and climate J Hum Evol 29:141153. Holliday TW, Franciscus R. 2009. Body size and its consequences: a llometry and the lower limb length of Liang Bua 1 ( Homo floresiensis ). J Hum Evol 57:223228. Holliday TW, Hilton C. 2010. Body proportions of circumpolar people as evidenced from skeletal data: Ipiutak and Tigara (Point Hope) versus Kodiak Island Inuit. Am J Phys Anthropol 142:287302 Holliday T W Ruff CB. 2001. Relative variation in the human proximal and distal limb segments. Am J Phys Anthropol 116:2634. 1925. The Old Americans. Baltimore, MD: Williams and Wilkins Co. blood American negro. Am J Phys Anthropol 12:1533. 460.
181 Hsin Yi KC, Chun Li L, Hsien Wen WB, Shih Wei CC. 2008. Finite element analysis of plantar fascia under stretch The relative contribution of windlass mechanism and Achilles tendon force. J Biomech 41:19371944. Jantz RL, Hunt DR, Meadow LJ. 1994. Maximum length of the tibia: how did trotter measure it? Am J Phys Anthropol 93: 525528. Jantz LM, Jantz RL. 1999. Secular change in long bone length and proportion in the United States, 18001970. Am J Phys Anthropol 110:5767. Jolicoeur P. 1984. Principal components, f actor analysis, and m ultivariate allometry: a smallsample direction test. Biometrics 40:685 690. Jones BH, Thacker SB, Gilchrist J, Kimsey CD, Sosin DM. 2002. Prevention of lower extremity stress fractures in athletes and soldiers: a systematic review. Epidemiol Rev 24:228247. Jorde LB Watkins WS Bashad MJ Dixon ME Ricker CE Seielstad MT 2000. The d istribution of h uman g enetic d iversity: a comparison of m itochondrial, a utosomal, and Y chromosome d ata Am J Hum Genet 66:979 98. Jungers WL, Cole TI, Owsley DW. 1988. Multivariate analysis of relative growth in the limb bones of Arikara Indians. Growth Develop Aging 52:103107. Jungers WL Falsetti AB Wall C. 1995. Shape, r elative size, and size a djustments in m orphometrics. Yearb Phys Anthropol 38:137 161. Jungers WL, German RZ. 1981. Ontogenetic and interspecific skeletal allometry in nonhuman primates: bivariate versus multivariate analysis. Am J Phys Anthropol 55:195202. Jungers WL, Larson SG, Harcourt Smith WEH, Morwood MJ, Sutikna T, Awe RD, Djubiantono T. 2008. Descriptions of the lower limb skeleton of Homo floresiensis J Hum Evol 57:538554. Kaitaniemi P. 2004. Testing the allometric scaling laws. J Theor Biol 228:149153. Keller T Weisberger A. Ray J Hasan S Shiavi R, Spengler D. 1996. Relationship between vertical ground reaction force and speed during walking, slow jogging, and running. Clin Biomech 11:253259 Kerkhoff AJ, and Enquist BJ. 2009. Multiplicative by nature: w hy logarithmic transformation is necessary in allometry. J Theor Biol 257:519521. Kidd RS, Oxnard CE. 2002. Patterns of m orphological d iscrimination in selected h uman t arsal e lements Am J Phys Anthropol 117:169181.
182 Kurki HK, Ginter JK, Stock JT, Pfeiffer S. 2008. Adult proportionality in small bodied foragers: a test of ecogeographic expectations. Am J Phys Anthropol 136:2838. Kurki HK, Ginter JK, Stock JT, Pfeiffer S. 2009. Body size estimation of small bodied humans: applicability of current methods. Am J Phys Anthropol 141:169180. Lague MR. 2003. Patterns of joint size dimorphism in th e elbow and knee of catarrhine primates. Am J Phys Anthropol 120:278297. Lague MR, Jungers WL. 1999. Patterns of sexual dimorphism in the hominoid distal humerus. J Hum Evol 36:379399. Lazenby R, Smashnuk A. 1999. Osteometric variation in the Inuit sec ond metacarpal: a test of Allen's r ule. Int J Osteoarchaeol 9:182 188. Lemelin P, Jungers WL. 2007. Body size and scaling of the hands and feet of prosimian primates. Am J Phys Anthropol 133:828840. Lewontin RC. 1966. On the m easurement of r elative v ari ability. Syst Zool 15:141142. Lieberman DE, Devlin MJ, Pearson OM. 2001. Articular area responses to mechanical loading: effects of exercise, age, and skeletal location. Am J Phys Anthropol 116:266277. Lovejoy CO Cohn MJ White TD 1999. Morphologi cal analysis of the mammalian postcranium: A developmental perspective. P roc Natl Acad Sci USA 96: 1324813252 Mann RW Sledzik PS Owsley DW Droulette MR. 1990. Radiographic examination of Chinese foot binding. J Am Podiat Med Ass 80:405409. Martin R. 1914. Lehrbuch der anthropolgie. Geneva: Gustav Fischer. Martin RB, Burr DB, Sharkey NA. 1998. Skeletal Tissue Mechanics. New York, NY: Springer Verlag. Meadows L, Jantz R. 1995. Allometric secular change i n the long bones from the 1800s to the pres ent. J Forensic Sci 40:762767. Micozzi MS Albanes D Jones Y Chumlea WC 1986. Correlations of body mass indices with weight stature, and body composition in men and women in NHANES Am J Clin Nutr 44: 725 731 Morton DJ. 1922. Evolution of the human f oot, Part 1. Am J Phys Anthropol 5:305336. Morton DJ. 1924. Evolution of the human foot, Part 2. Am J Phys Anthropol 7:152.
183 Niswander LA 2003. P attern f ormation: o ld m odels out on a l imb Nat Rev Genet 4: 131141. Nudds RL, Oswald SA. 2007. An inters pecific test of Allens rule: evolutionary implications for endothermic species. Evolution 61:28392848. Ousley SD, and Jantz RL. 1998. The forensic data bank: documenting skeletal trends in the United States. In: Reichs KJ, editor, Forensic Osteology : Advances in the Identification of Human Remains. Springfield, IL: Charles C Thomas. p 441 458. Ozden H, Balci Y, Demirustu C, Turgut A, Ertugrul M. 2005. Stature and sex estimate using foot and shoe dimensions. Forensic Sci Int 147:181184. Packard GC 2008. On the use of logarithmic transformations in allometric analyses. J Theor Biol 257:515519. Parham KR, Gordon CC, Bensel CK. 1992. Anthropometry of the foot and lower leg of U.S. Army soldiers: Fort Jackson, SC 1985. Natick, MA: U.S Army Natick Re search, Development, and Engineering Center. Pawlowski B, Dunbar RIM, Lipowicz A. 2000. Evolutionary fitness t all men have more reproductive success. Nature 403:156156. Plavcan JM. 2001. Sexual dimorphism in primate evolution. Yearb Phys Anthropol 44:2553. Plavcan JM, Van Schaik C. 1992. Intrasexual competition and body weight dimorphism in anthropoid primates. Am J Phys Anthropol 87:461477. Plavcan JM, VanSchaik C. 1997. Intrasexual competition and body weight dimorphism in anthropoid primates. Am J Phys Anthropol 103:3767. Polk JD. 2002. Adaptive and phylogenetic influences on musculoskeletal design in cercopithecine primates. J Exp Biol 205:3399 3412. Polk JD. 2004. The influence of body size and limb proportions on joint posture in terrestrial monkeys and fossil hominins. J Hum Evol 47:237252. Pontzer H. 2005. A new model predicting locomotor cost from limb length via force production. J Exp Biol 208:15131524. Pontzer H. 2007 a Effective limb length and the scaling of locomotor cost in terrestrial animals. J Exp Biol 210:17521761. Pontzer H. 2007 b Predicting the cost of locomotion in terrestrial animals: a test of the L IMB model in humans and quadrupeds. J Exp Biol 210:484494.
184 Queen RM, Abbey AN, Chuck B, Wong P, Nunley JA. 2009. Plantar l oading comparisons between w omen w ith a h istory of s econd m etatarsal s tress f ractures and n ormal controls. Am J Sport Med 37:390395. Raxter MH, Auerbach BM, Ruff CB. 2006. Revision of the Fully technique for estimating statures. Am J Phys Anthropol. p 374 384. Relethford JH. 2002. Apportionment of global human genetic diversity based on craniometri cs and skin color. Am J Phys Anthropol 118:393398. Richardson MK Jeffery JE Tabin CJ 2004. Proximal patterning of the limb: insights from evolutionary m orphology Evol Dev 6: 1 5 Robling AG, Ubelaker DH. 1997. Sex estimation from the metatarsals. J Forensic Sci 42:10621069. Ruff CB. 1991. Climate and body shape in hominid evolution. J Hum Evol 21:81105. Ruff CB. 1994. Morphological adaptation to cli mate in modern and fossil hominids. Yearb Phys Anthropol 37:65107. Ruff CB. 2000. Body size, body shape, and long bone strength in modern humans. J Hum Evol 38 :269 290. Ruff CB, Scott W, Liu AC. 1991. Articular and diaphyseal remodeling of the proximal femur with changes in body mass in adults. Am J Phys Anthropol 86:397413. Sears KE Behringer RR Rasweiler JJ Niswander LA 2007. The e volutionary and d evelopmental b asis of p arallel r eduction in mammalian z eugopod e lements Am Nat 69: 106 117 Scheuer L, Black S. 2000. D evelopmental Juvenile Osteology San Diego, CA: Academic Press. Schultz AH. 1963. The relative lengths of the foot skeleton and its main parts in primates. Sym Zool S 1:199206. Shaffer RA, Rauh MJ, Brodine SK, Trone DW, Macera CA. 20 06. Predictors of stress f racture s usceptibility in y oung f emale r ecruits. Am J Sports Med 34:108115. Sharkey NA, Ferris L, Smith TS, and Matthew DK. 1995. Strain and loading of the second metatarsal during heel lift. J Bone Joint Surg 77:10501105. Smi th RJ. 1980. Rethinking a llometry. J Theor Biol 87:97111. Smith RJ. 1993. Logarithmic transformation b ias in allometry. Am J Phys Anthropol 90:215228.
185 Smith RJ. 1996. Biology and body size in human evolution: statistical inference misapplied. Curr Anthr opol 37:451481. Smith RJ. 1999. Statistics of sexual size dimorphism J Hum Evol 36:423459. Smith RJ. 2005. R elative size versus controlling for size: i nterpretation of r atios in r esearch on sexual d imorphism in the h uman corpus callosum. Curr Anthropol 46:249 273. Smith RJ. 2009. Use and misuse of the reduced major axis for linefitting. Am J Phys Anthropol 140:476486. Smith RJ, Jungers WL. 1997. Body mass in comparative primatology. J Hum Evol 32:523559. Smith SL. 1997. Attribution of foot bones t o sex and population groups. J Forensic Sci 42:186195. Sokal RR, Braumann CA. 1980. Significance tests for coefficient of variation and variability profiles. Syst Zool 29:5063. Steele D. 1976. The estimation of sex on the basis of the talus and calcane us. Am J Phys Anthropol 45:581 588. Stephan CN, Henneberg M, Sampson, W. Predicting nose projection and pronasale position in facial approximation: a test of published methods and proposal of new guidelines. Am J Phys Anthropol 122:240250. Stevenson R D. 1986. Allens rule in North American rabbits ( Sylvilagus ) and hares ( Lepus ) is an exception, not a rule. J Mammal 67:312316. Stock JT. 2006. Hunter gatherer postcranial robusticity relative to patterns of mobility, climatic adaptation, and selection f or tissue economy. Am J Phys Anthropol 131:194204. Summerbell D, Lewis J, Wolpert L. 1973. Positional information in chick limb morphogenesis. Nature 244:492496. Susman RL, Stern JT, Jungers WL. 1984. Arboreality and Bipedality in the Hadar hominids. Folia Primatol 43: 113156. Sylvester A, Kramer P, Jungers W. 2008. Modern h umans are n ot ( q uite) i sometric. Am J Phys Anthropol 137 :371383. Tague RG. 1989. Variation in pelvic size between males and females. Am J Phys Anthropol 80:5971.
186 Tague RG. 2002. Variability of m etapodials in p rimates w ith r udimentary d igits: Ateles geoffroyi, Colobus guereza, and Perodicticus potto. Am J Phys Anthropol 117:195208. Tanner JM, Hayashi T, Preece MA, Cameron N. 1982. Increase in length of leg relative to trunk in Japanese children and adults from 1957 to 1977: comparison with British and with Japanese Americans Ann Hum Biol 9:411423. Temple DH Auerbach BM Nakatsukasa M Sciulli PW. Larsen CS. 2008. Variation in limb proportions between Joman foragers and Yayoi agriculturalists form prehistoric Japan. Am J Phys Anthropol 137:164174 Tic kle C 2002. V ertebrate l imb d evelopment and p ossible clues to diversity in limb form. J Morph 252: 2937. Tilkens MJ, WallScheffler C, Weaver TD, Steudel Numbers K. 2007. The effects of body proportions on thermoregulation: an experimental assessment of Allen's rule. J Hum Evol 53:286291. Todd TW, Lindala A. 1928. Dimensions of the body : w hites and American negroes of both sexes. Am J Phys Anthropol 12:35119. Trotter M. 1970. Estimation of stature from intact long limb bones. In: Stewart T, editor. Personal Identification in Mass Disasters. Washington, DC: Smithsonian Institution Press p 7183. Topinard, P. 1876. LAnthropologie. Paris: C. Reinwald. Trotter M Gleser GC. 1952. Estimation of stature from long bones of American whites and negroes. Am J Phys Anthropol 10:463514. Trotter M Gleser GC. 1958. A re evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. Am J Phys Anthropol 16:79 123. Tsutakawa RK, Hewett JE. 1977. Quick test for comparing two populations with bivariate data. Biometrics 33:215219. Waldro n T. 1987. The relative survival of human skeleton: implications for palaeopathology. In: Boddington A Garland A and Janaway R, editors. Death Decay and Reconstruction. Approaches to Archeology and Forensic Science. Manchester, UK: Manchester University Press. p 5564. Wang WJ, Crompton RH. 2004 Analysis of the human and ape foot during bipedal standing with implications for the evolution of the foot. J Biomech 204:18311836.
187 Warren MW. 1997. Prenatal limb growth in h umans: linear growth, a llometry, l o comotion and skeletal age. Ph.D. dissertation. Gainesville, FL: University of Florida. Warren MW, Holliday T W and Cole T 2002. Ecogeographical patterning in fetal limb proportions. Am J Phys Anthropol S34:161162. Warton DI, Wright IJ, Falster DS, West oby M. 2006. Bivariate linefitting methods for allometry. Biol Rev 81:259291. Weaver ME, Ingram DL. 1969. Morphological changes in swine associated with environmental temperature. Ecology 50:710713. Wells JCK. 2000. Environmental temperature and human growth in early life. J Theor Biol 204:299305. Wells JCK. 2002. Thermal environment and human birth weight. J Theor Biol 214:413425. White TD, Suwa G. 1987. Hominid footprints at Laetoli: facts and interpretations. Am J Phys Anthropol 72: 485 514. W hittow GC. 1973. Evolution of thermoregulation. In: Whittow GC, editor. Comparative Physiology of Thermoregulation. New York: Academic. p 202258. WHO. 1986. U se and interpretation of anthropometric indicators of nutritional status. B World Health Organ 64:929941. W olpert L. 2002. The p rogress z one m odel for specifying p ositional i nformation. Int J Dev Biol 46:869870. Wood JW, Milner GR, Harpending HC, Weiss KM. 1992. The osteological paradox. Curr Anthropol 33:343370. Wunderlich RE, Cavanagh PR. 1999. External foot shape differences between males and females and among races. American Society of Biomechanics. Wunderlich RE, Cavanagh PR. 2001. Gender differences in adult foot shape: implications for shoe design. Med Sci Sport Exer 33:605611. Zip fel B, DeSilva J, Kidd RS. 2009. Earliest complete h ominin f ifth metatarsal i mplications for the e volution of the l ateral column of the f oot. Am J Phys Anthropol 140:532545.
188 BIOGRAPHICAL SKETCH Paul D. Emanovsky grew up in Bohemia, Long Island, N ew Y ork and received his bachelors degree in human biology at the S tate University of New York at Albany in 1998. H e subsequently attended the University of Indianapolis receiving a masters in h uman b iology in 2002. H e then went to work at the Department of D efenses Central Identification Laboratory (CIL), in Hawaii. At the CIL Paul is responsible for conducting forensic anthropological l aboratory analyses and leading humanitarian search and recovery missions around the world; all toward the ultimate goal of identifying unaccountedfor Service m embers from the n ations past conflicts Beginning in 2004, while concurrently working at the CIL, he pursued his doctorate in Anthropology at the University of Florida (UF). While at UF, in addition to concentrating on his study of biological anthropology and anatomy, Paul was also able to assist various medicolegal agencies throughout the country with forensic analyses and services via his affiliation with the C.A. Pound Human I dentification Laboratory (CAPHIL).