Sexual Dimorphism in the Late Miocene Mihirung Dromornis stirtoni (Aves: Dromornithidae) from the Alcoota Local Fauna of Central Australia

ABSTRACT 
 The dromornithids were giant flightless birds endemic to Australia from the late Paleogene to the late Pleistocene. Dromornithids are generally considered to be divergent members of the Anseriformes, but they display many convergent features with extant ratites. In this study, we investigate Dromornis stirtoni from the Alcoota Local Fauna, a species for which little is known of its biology. We used traditional methods of comparative morphology, mass estimation, landmark-based morphometrics, and histological investigations to determine the presence of medullary bone, to assess the possible presence, form, and extent of sexual dimorphism in D. stirtoni. Two morphological groups were identified for each main leg element, differing primarily in relative robustness. Core samples from femora and tibiotarsi shafts revealed medullary bone in the less robust morph, indicating that these were females. Mass, as estimated by algorithms applied to our preferred measurement of least-shaft circumference of tibiotarsi, was significantly different between males (mean = 528 kg) and females (mean = 451 kg). Therefore, male D. stirtoni were more robust but not much taller than the females and challenge the elephant bird, Aepyornis maximus, for the title of the most massive bird to have existed. Sexual dimorphism in this largest of all dromornithids, therefore, was like that of extant Anseriformes. We infer long-term monogamy, mutual display, shared parental care, female incubation, and aggressive defense of nests in these birds. The techniques of geometric morphometrics applied in this study maximize the use of fragmentary material, helping to overcome the common paleontological challenge of limited sample sizes.


INTRODUCTION
Sexual dimorphism is the existence of distinct male and female morphs within a species. Understanding the nature of sexual dimorphism within birds can shed light upon several aspects of their evolutionary and behavioral biology. Appreciation of intraspecific variation in size and sex-specific behavior for extant taxa is challenging, and more so when attempting to make such deductions for extinct birds. This is especially applicable when taxa have fragmentary and incomplete fossil records and no close extant relatives with which to compare their morphology.
The development of modern geometric morphometric methods has facilitated a level of analysis that was inconceivable until recently. It is now possible to reconstruct fragmentary fossil specimens by estimating landmark coordinates for missing structures Mitteroecker and Gunz, 2009;Adams and Ot arola-Castillo, 2013). Inclusion of incomplete specimens through the application of effective estimators of missing landmark coordinates can better reflect patterns of shape and size variation than the use of fewer complete fossil specimens only (Arbour and Brown, 2014). These methods can add rigor to the comparison of morphologies and assist in the identification of intraspecific variation (Webster and Sheets, 2010). In this research, we investigate biological attributes such as sexual dimorphism for the giant extinct Dromornis stirtoni Rich, 1979 of Australia.
The dromornithids (Aves: Dromornithidae) were giant flightless birds endemic to Australia. They first appeared in the fossil record in the late Paleogene (Rich, 1979) and persisted through to the Late Pleistocene (Boles, 2006), when the last of their lineage, Genyornis newtoni Stirling and Zietz, 1896, became extinct around 50,000 years ago (Miller et al., 2005). The previous existence of giant flightless birds in Australia was first noted in the 1830s with the discovery of a large bird femur in the Wellington Caves, New South Wales (Mitchell, 1839:pl. 32, fig. 12). However, Richard Owen, to whom Major T. L. Mitchell forwarded the Wellington specimen, waited many years before naming the first giant bird from Australia Dromornis australis Owen, 1872 based on a femur recovered from a well in Queensland (Owen, 1872(Owen, , 1873. The subsequent discovery and description of dromornithid fossils over the last 184 years has been comprehensively reviewed by Rich (1979) and Murray and Vickers-Rich (2004).
The dromornithids were once considered to be ratites (see Rich, 1975Rich, , 1979, which include flightless ostriches (Struthionidae), emu and cassowaries (Casuariidae), moa (Dinornithiformes), kiwi (Apterygidae), elephant birds (Aepyornithidae), and rheas (Rheidae). These ratites together with volant tinamous (Tinamiformes) constitute the palaeognaths, the sister group of all other neornithes. Ratites lack a keel on the sternum, hence their name, literally 'raft-like'; they exhibit reduced wing morphology and are generally large terrestrial birds (Worthy and Holdaway, 2002;Phillips et al., 2010). All these features are shared with dromornithids, but in more recent times, phylogenetic analyses conducted by Murray and Megirian (1998) recognized that dromornithids displayed key anseriform cranial features, including the form of the palate, quadrate, and the postorbital process, and proposed that dromornithids were the sister group of the South American screamers (Anhimidae). Anhimids together with the Anseranatidae are the sister group to Anatidae (ducks and geese) within Anseriformes (Livezey and Zusi, 2007;Eo et al., 2009;Worthy, 2009). The conclusion that dromornithids were anseriforms was reinforced by Murray and Vickers-Rich (2004). Most recently, in a phylogenetic study of the affinities of Pelagornithidae (bony-toothed birds), Mayr (2011) concluded that the dromornithids were stem Galloanseres, e.g., a sister group to Galliformes and Anseriformes, but this phylogenetic relationship was poorly supported. Mayr (2011:453) himself posited that his analysis possibly reflected "inadequate character sampling rather than the true phylogeny." Four genera and eight species of dromornithids are now recognized: Dromornis australis, D. stirtoni, D. planei Rich, 1979, D. murrayi Worthy, Handley, Archer, andHand, 2016, Genyornis newtoni, Ilbandornis lawsoni Rich, 1979, I. woodburnei Rich, 1979, and Barawertornis tedfordi Rich, 1979(Rich, 1979Murray and Vickers-Rich, 2004;Nguyen et al., 2010;Worthy and Yates, 2015;Worthy et al., 2016). The greatest diversity of the Dromornithidae occurs during the Miocene, but the family had a much longer lineage stretching back into the Paleogene (Vickers- Rich, 1991;Murray and Megirian, 1998;Boles, 2006). They are among the best-represented fossil birds in Australia (Murray and Vickers-Rich, 2004;Nguyen et al., 2010), and their fossils form approximately 25% of the local faunas of Bullock Creek (middle Miocene) and Alcoota (late Miocene) in the Northern Territory (Murray and Megirian, 1998). The fossil localities at Alcoota have yielded two species of relatively gracile ostrich-like forms, Ilbandornis lawsoni and I. woodburnei, as well as Dromornis stirtoni with an estimated mass of 345-646 kg, making it possibly the heaviest bird known ever to have evolved (Murray and Megirian, 1998;Murray and Vickers-Rich, 2004). This dromornithid forms the focus of the present investigation.
Institutional Abbreviation-NTM P, Northern Territory Museum Paleontological collection, Alice Springs, Australia.

Geological Setting and the Alcoota Local Fauna
Fossil dromornithids are part of the Alcoota Local Fauna (LF), found in a dense bonebed, or closely spaced complex of bonebeds, in the Waite Formation at Alcoota in the Northern Territory, Australia (22 52 0 S, 134 52 0 E). The Waite Formation includes a sequence of unconsolidated freshwater sediments between 29 and 42 m thick, which are dated to the late Neogene, with the bonebed dated to 7-8 Ma (Murray and Megirian, 1992;Megirian et al., 2010). Fossils in the bonebed vary from complete bones with fragile structures to very fragmented specimens (Woodburne 1967b;Murray and Megirian, 1992). They were concentrated in channel deposits following flood transport of bones that accumulated after drought-tethered animals had died around a waterhole (Murray and Megirian, 1992).
The condition of the fossilized material is distinctive in that it is cracked and fragmented in situ as a result of expansion and contraction of the siltstone substrate due to fluctuations of moisture content over the course of several million years (Fig. 1). The varying condition and fragility of specimens may also imply differing periods of surface exposure before fossilization (Murray and Megirian, 1992). This has led to nearly all specimens being damaged to some extent and exhibiting a range of completeness from minor damage, such as a condyle lost in some, to one or both ends of the bone being lost.

Sexual Dimorphism
Sexual dimorphism in body size is a widespread phenomenon in the animal kingdom and is quantifiable in the fossil record. In most birds and mammals, it is more common to observe sexual size dimorphism (SSD), with males as the larger sex; however, there are exceptions, e.g., in many species of raptors such as among eagles, females are larger than males, which has been termed reversed sexual size dimorphism (RSSD). Many Anseriformes display degrees of SSD (Livezey, 1996b), and all ratites (except ostriches and rheas) display remarkable RSSD, which is often associated with divergent roles in reproductive activities (Bunce et al., 2003), e.g., male casuariids alone tend the developing chicks and only male kiwi incubate (Davies, 2002).
The extinct moa (Dinornithiformes) from New Zealand, especially species of Dinornis, reveal considerable RSSD and is one of the best-understood examples among extinct birds (Bunce et al., 2003;Huynen et al., 2003;Worthy et al., 2005). Females of Dinornis (76-242 kg) were approximately 280% the weight and 150% the height of the males (34-85 kg) (Bunce et al., 2003;Worthy et al., 2005). These observations show that at least in large ratites, the sexes can be sexually dimorphic to the extent that the size ranges of each sex do not overlap and that values of coefficients of variation from ca. 10-12 for measurements reflect sexual dimorphism, even when ranges overlap.
Extremely sexually dimorphic anseriforms may develop elaborate mating systems where males compete for females, e.g., the lek mating system in musk ducks (McCracken et al., 2000). Because dromornithids are anseriforms, it could be predicted that if they had marked SSD, it would be associated with sophisticated mating behavior, including perhaps lifelong monogamy, ritual courtship and display, and extended investment in juvenile care. Therefore, determining the nature of sexual dimorphism within D. stirtoni would provide the basis for the reasonable inference of reproductive parameters and other biological attributes.

Bone Histology
Extensive studies of modern and fossil bone histology have been useful for interpreting various aspects of the biology of extinct vertebrates such as the evolution of growth patterns and determining life history data such as the onset of sexual maturity and attainment of adult body size (e.g., Chinsamy-Turan, 2005, 2012Erickson, 2005).
Medullary-Medullary bone is a nonstructural type of woven bone that is found in various parts of the skeleton of female egglaying birds (Miller and Bowman, 1981;Chinsamy-Turan, 2005;Chinsamy et al., 2013). It is laid down as a store of calcium and to prevent hypercalcemia or osteoporosis during eggshell formation (Ascenzi et al., 1963;Whitehead and Fleming, 2000). Birds differ from other vertebrates in that during reproduction they do not resorb calcium directly from cortical bone, yet approximately 40% of the calcium within eggshell originates from the birds' skeleton (Schweitzer et al., 2007). This calcium is derived from endosteal deposits of medullary bone formed at the onset of ovulation (Miller and Bowman, 1981;Wilson and Thorpe, 1998), which may entirely fill the medullary cavity (Ascenzi et al., 1963;Dacke et al., 1993;Chinsamy-Turan, 2005;Chinsamy and Tumarkin-Deratzian, 2009). This tissue is highly vascularized, with a large surface area-to-volume ratio and has an extremely high turnover rate in comparison with both trabecular bone and cortical bone (Satterlee and Roberts, 1990;Schweitzer et al., 2005Schweitzer et al., , 2007. Medullary bone is distinctive and, due to its seasonal presence in domestic fowl, has long been used in archaeological studies to define the seasonal occupation of prehistoric settlements (see Rick, 1975;Eda et al., 2013). Schweitzer et al. (2005)  preserved within the medullary cavity of a femur of a theropod dinosaur, and Chinsamy et al. (2013) used the presence of medullary bone to identify a female specimen of the Mesozoic bird Confuciusornis sanctus, thereby confirming the sexual dimorphic nature of the taxon. Thus, medullary bone is useful in identifying females of extinct taxa and will be investigated among the dromornithids studied here.

Body Mass
As a result of our population-level sampling of the sizes of the bones of Dromornis stirtoni, we took the opportunity to estimate the mass of as many individuals as possible. An assessment of the body mass range of dromornithids would assist in the reasonable appreciation of their relative mobility and provide insight into their behavior, territory size, and paleoecology (Anderson et al., 1985;Worthy and Holdaway, 2002). Given this background, there were two aims to this research: (1) to develop a tool to enhance the amount of morphological data recoverable from fragile and fragmentary D. stirtoni fossils; and (2) to assess whether D. stirtoni was sexually dimorphic in size to enable inferences about reproduction and habitat use. Simultaneously, this investigation tests the current hypothesis that all large dromornithids in the Alcoota LF were representative of a single species.
Because dromornithids are considered to be anseriforms, wherein the form of sexual dimorphism most frequently observed is that males are predominantly larger than females, it was predicted that the males would be the larger morph. We searched for medullary bone in femora and tibiotarsi of D. stirtoni to assist in the identification of females and to possibly deduce the size range of the females.

MATERIALS AND METHODS
Measurements and comparisons were made of adult femora, tibiotarsi, and tarsometatarsi of Dromornis stirtoni in the collections of the Museum of Central Australia, Alice Springs, Australia. We made two classes of measurements: (1) physical measurements on actual fossils and (2) inferred measurements derived from landmarks, each described below.

Physical Measurements for Dromornis stirtoni
Bone width measurements were taken for fossils of D. stirtoni using a 150 mm digital Vernier caliper and rounded to the nearest 1 mm. Shaft circumference measurements were made with a tailor's soft measuring tape and rounded to the nearest 1 mm. Length measurements greater than 150 mm were made with a retractable steel tape measure and rounded to the nearest 5 mm; greater precision was unjustified given wear, breakage, and adhering sediment, and that these bones were all longer than 360 mm. Specimens were placed with articular surfaces against a vertical surface perpendicular to the long axis of the bone, and measurements were made from that to the end of the relevant morphological structure. We use the anatomical nomenclature advocated by Baumel and Witmer (1993).
Descriptions of the specific measurements made from specimens of Dromornis stirtoni are indicated in Appendix 1.
Material-The specimens of Dromornis stirtoni that were measured and/or landmarked are indicated in Appendix 2.
Photography-Leg bones of Dromornis stirtoni were photographed using a Canon EOS 60D SLR camera fitted with a Canon EFS 17-55 mm f2.8 ultrasonic lens from a fixed tripod position in a standard orientation. Prior to all analyses, the photographs were processed in Photoshop (P4) using the geometric lens correction filter with respect to a tape measure, which traversed each image to alleviate any potential lens perspective error. To maximize the compared sample sizes, images were analyzed as if all were right elements. Therefore, all photographs of left elements were flipped horizontally using the flip tool function in Photoshop (P4) prior to being landmarked.
Landmark locations were selected to capture the shape of each element, with some chosen to facilitate comparisons of inferred measurements with selected physical measurement data. Landmarks located at least-shaft width points (e.g., femora and tibiotarsi, Lm1, Lm6; tarsometatarsi, Lm1, Lm5; Fig. 1A-C) were placed visually and formed no part of subsequent inferred measurement computations, because they were not precisely located on reliably identifiable morphological features (see Bookstein 1991:2, 58).
Missing landmarks were estimated using Geomorph v2.1.1 from templates of specimens preserving all landmarks in the data set (Adams and Ot arola-Castillo, 2013). Geomorph v2.1.1 requires a minimum of 10 specimens with complete landmark sets before estimation of the coordinates of missing landmarks can be done (E. Sherratt, pers. comm., August 2014, to W.D.H.). Because the data sets did not have 10 such complete elements in any group due to the fragmentary nature of the fossils, copies were made of the images of the complete specimens of femora, tibiotarsi, and tarsometatarsi so that each data set included more than 10 complete elements. Following estimation of missing landmarks (see below), these copies were then deleted from the data set.
Because femora, tibiotarsi, and tarsometatarsi of D. stirtoni had distinct bimodal size distributions for measurements with large sample sizes, best exhibited by least-shaft circumference (femora, tibiotarsi) and width of trochlea metatarsi III for tarsometatarsi ( Fig. 2A-D), we ensured that templates were made for each modal form. Therefore, we divided the sample of each element into robust and gracile groups based on the separation seen in Figure 2A-D. We then selected the complete elements in each group and duplicated them so that more than 10 complete specimens were present for each group in all elements. Thus, for the 'robust' femora group, three duplicates were made of each of the four complete specimens; for the 'gracile' femora group, three duplicates were made of each of the five complete specimens. Both 'robust' and 'gracile' tibiotarsi groups included three complete specimens, of which four duplicates were made of each. The 'robust' tarsometatarsi group included five complete specimens, of which three duplicates were made of each one. The 'gracile' tarsometatarsi group included four complete specimens, of which three duplicates were made of each one.
Landmarking was performed independently on each data set for each form in R v3.1.1, and estimation of the coordinates of missing landmarks was conducted using Geomorph v2.1.1 functions employing the TPS method of missing data estimation Adams and Ot arola-Castillo, 2013;Adams et al., 2014). From this, a data set composed of actual and estimated landmarks for all specimens in Appendix 2 was then written to CSV files and duplicate specimens were removed. The amended CSV files for the gracile and robust forms were then compiled into combined data sets for each element and became the basis for all subsequent analyses. Prior to any further analysis, all landmark coordinate data sets were subjected to a partial (least-squares) Procrustes fitting, standardizing orientation and position of all landmarks, leaving size and shape variation for further analyses (Rohlf, 1999;Slice, 2001).
In order to initially explore these multivariate data sets, pairedgroup cluster analyses based on Euclidean distance measures were conducted to identify possible grouping within the distribution of data, because it was expected that two groups relating to preliminary observations of relative robustness might be obtained. Resultant dendrograms identified two groups, which were arbitrarily assigned 'group 1' and 'group 2' (Fig. 3A-C). Hotelling's discriminant analyses, which compare the differences between the means of two multivariate samples (Davis, 2002:478, 481-482), were conducted on each data set in order to define the degree of separation of the groups found by the cluster analyses, shown as distribution plots ( Fig. 3D-F). Group discriminant statistics were computed. Principal component analyses (PCAs) were conducted that enabled visualizing in a two-dimensional plane the "allometric patterns" (Klingenberg, 1996:31) between the groups identified by the cluster analyses. Only PCA plots for the first two components are presented because these describe most of the variation. Convex hull polygons surround the distribution of specimens attributed to each group ( Fig. 3G-I).

Data Analyses
Summary statistics and distribution tests were conducted on all numerical data using the statistics program PAST v2.17c (Hammer et al., 2001). The Shapiro-Wilk test (Shapiro and Wilk, 1965) was used for all assessments of data distribution, because it is the best overall performer for small and large sample sizes (Royston, 1982;Hammer and Harper, 2006). The test statistic (W) is given, and the notation (P > 0.05) indicates a normal distribution. One-way analyses of variance (ANOVAs; see Davis, 2002:78-84) were conducted on normally distributed multivariate data, which included Tukey's pairwise comparisons where applicable. Non-parametric Kruskal-Wallis tests were conducted as an alternative to parametric one-way ANOVAs (Davis, 2002:105) to compare data that were not normally distributed. Student's t-tests were conducted for comparisons of means. Preliminary distribution plots of physical measurement data were made in Microsoft Excel. To assess the accuracy of inferred measurement data derived from landmark coordinates, comparisons were made between each individual physical measurement recorded from actual fossil specimens and the corresponding inferred measurement derived from landmark coordinate data using one-way ANOVAs and non-parametric Kruskal-Wallis tests in PAST v2.17c.
Computation of Inferred Measurement Data-Inferred measurement data sets were computed from the complete landmark coordinate data sets for each specimen in R v3.1.1 using the "ild" function described by Claude (2008:49): where (E, F) are the landmark coordinates.

Medullary Bone
To investigate whether medullary tissue was present, core samples were taken from selected femora at the point of leastshaft circumference and from tibiotarsi on either the caudal or anterior facies in the mid-shaft region. All cores were made using a 22-mm diamond-tipped core drill bit driven by a column drill press operated at slow speed. Lubrication was applied in the form of a drip water feed in order to cool the core bit and prevent bone swarf from clogging the cavity and binding the rotation of the core bit, which could possibly damage the fossils or the core sample being taken.

Body Mass Estimation
We estimated mass (kg) using algorithms based on femoral measurements as follows: least-shaft circumference (mm): Campbell and Marcus (1992;   comparisons showed that his other algorithm based on ratites including kiwi gave results 38% greater than the former and also greatly discordant to results from the algorithms of the abovementioned authors. Mass (kg) was also estimated using algorithms based on tibiotarsi least-shaft circumference proposed by Campbell and Marcus (1992; Log M D 2.424 log LCT C 0.076) and Dickison's (2007; incl. kiwi: M D 0.227TTC 2.7 ) algorithm, which was favored over Dickison's (2007) 'excluding kiwi' algorithm because it gave results insignificantly different from the algorithm developed by Campbell and Marcus (1992).
Summary statistics and distribution tests were conducted on estimated body mass data. Assessments were made of the similarity of the various body mass estimates for femora and tibiotarsi using one-way ANOVAs for parametric data and Kruskal-Wallis tests for non-parametric data. These tests included comparisons of mass estimation results derived from each method, with the cumulative average mass estimation results of all methods. We assessed the equality of the means of the estimated body masses for the gracile and robust groups derived from the cluster analysis of the landmark data sets for both femora and tibiotarsi using t-tests.

Physical Measurement Data
Summary statistics of physical measurements taken from the fossils are presented in Table 1A, or in the following text when they are not common to all elements.
Femora of Dromornis stirtoni-All physical measurement data for femora (Table 1A) were normally distributed and had high coefficients of variation (CVs) for least-shaft circumference (CV D 8.7), proximal width (CV D 9.4), and depth of the condylus medialis (n D 11; mean D 131 mm; SD D 12.8; range D 112-154 mm; CV D 9.8). The CV for distal width was moderately high (7.8) and lowest for maximum length (5.1), which displayed the lowest variability. This variability reflected a bimodal distribution of the data in count distribution plots, seen most clearly for least-shaft circumference, obtainable in 50 of 54 femora ( Fig. 2A), and proximal width ( Fig. 2B; 38 of 54 femora).
Tibiotarsi of Dromornis stirtoni-All physical measurements (Table 1A) featured some variability, and a number were not normally distributed (Shapiro-Wilk [W], P [Norm > 0.05]), with moderate CVs of least-shaft circumference (CV D 6.9; W D 0.93, P D 0.01), mid-shaft circumference (n D 36; mean D 212 mm; SD D 14.4; range D 180-235 mm; CV D 6.8; W D 0.94, P D 0.05), condylus medialis depth (n D 15; mean D 138 mm; SD D 8.2; range D 120-150 mm; CV D 5.9; W D 0.78, P D 0.002), and condylus lateralis depth (n D 14; mean D 117 mm; SD D 7.7; range D 98-130 mm; CV D 6.5; W D 0.83, P D 0.01). The total specimen count was 59; however, because tibiotarsi are large elements, parts of which are not robust and derive from unconsolidated sediments, the majority of the specimens are fragmentary. For example, maximum length measurements were possible on only 10 (16%) of the specimens. Similar low frequency of preservation for proximal depth (15%) and proximal width (10%) measurements attest to the fragility of these elements. Preliminary count plots of the tibiotarsi produced a suggestion of bimodal distribution in the least-shaft circumference measurements (Fig. 2C); however, this bimodality was not distinct. Least-shaft circumference was the most frequently obtained measurement within the collection (46 of 59 tibiotarsi). Maximum length (CV D 4.9) and articular length (CV D 4.2) were the least variable tibiotarsal measurements. Proximal width (CV D 8.9) and proximal depth (n D 6; mean D 219 mm; SD D 26.7; range D 180-250 mm; CV D 11.9) were the least well-represented measurements, so although they had the highest CVs, these values must be considered cautiously.
Tarsometatarsi of Dromornis stirtoni-All physical measurement data (Table 1A) were found to be normally distributed with high CVs, particularly for least-shaft circumference (CV D 10.7) and trochlea metatarsi III width (CV D 8.7) measurements. Similarly, high CVs were recorded for maximum length (CV D 8.4) and proximal width (CV D 8.1). A high CV value for proximal depth (n D 3; mean D 95 mm; SD D 11.0; range D 85-107 mm; CV D 11.5) is not reliable on account of small sample size (n D 3). Preliminary distribution plots returned A, actual measurement data from fossil material, and inferred (unsexed) measurement data comprising linear measurements derived from coordinates for landmarks, some of which were estimated. B, inferred measurement data by sex for femora (including NTM P4879 as female) and tibiotarsi. Leastshaft circumference statistics use the physical measurements of those specimens included in each data set. Data are presented in the form: mean (range) standard deviation, where not expressly indicated. Physical measurement data include smaller values than inferred measurement data because these data included specimens too fragmented to landmark and predict missing values. Abbreviations: Art, articular; circ., circumference; Max., maximum; Prox., proximal; SD, standard deviation; Tib, tibiotarsi; Tmt, tarsometatarsi; Tr. M., trochlea metatarsi; ,, female; <, male.
a suggested bimodal distribution for trochlea metatarsi III width data (n D 30; Fig. 2D). Tarsometatarsi are robust elements and of the 48 specimens studied (Appendix 2), it was possible to obtain measurements of least-shaft circumference in 33. Distally, these elements were better preserved than proximally, with trochlea metatarsi III depth (n D 30; mean D 72 mm; SD D 5.6; range D 61-84 mm; CV D 7.7), trochlea metatarsi III width (CV D 8.6), and tarsometatarsus distal width (CV D 7.9) measurements best represented. Maximum length (n D 19) and proximal width (n D 17) measurements were not as well represented.

Landmark Coordinate Data
Summary and comparative statistics of physical measurements and the corresponding inferred measurements derived from landmark coordinate data are presented in Supplemental Data, Table S1A-C. Summary statistics of the complete inferred measurement data sets are presented in Table 1A and Table S2A-C.
Femora of Dromornis stirtoni-The values of the inferred measurements for femora were not significantly different to the corresponding physical measurements (P > 0.05; Table S1A), except for femur maximum length where inferred length approached being significantly different (P D 0.048; Table S1A). Therefore, the data set derived from landmark coordinates (actual and estimated) for femora (n D 34) was used in subsequent analyses. Cluster analysis of the partial Procrustes-fitted landmark coordinate data produced two defined groups of D. stirtoni femora, group 1 with 16 specimens and group 2 with 18 specimens (Fig. 3A). Subsequent Hotelling's discriminant analysis showed that there are two significantly distinct groups (Hotelling's T 2 D 377.55; F D 9.83; P D 2.58E-05). The degree of separation of these cluster analysis-defined groups is shown by the discriminant axis of Figure 3D. Principal component analysis of the landmark coordinate data revealed the same two distinct groups identified by cluster analysis, with the first two principal components (Fig. 3G) accounting for 75.5% of total variance. Summary statistics and distribution tests indicated that inferred measurement data derived from landmark coordinate data of D. stirtoni femora were normally distributed (Table S2A).
Tibiotarsi of Dromornis stirtoni-The values of the inferred measurements derived from the landmark coordinate data differed significantly from the corresponding physical measurement data for maximum length (P D 6.67E-03; Table S1B) and articular length (P D 4.42E-05; Table S1B) measurements. Proximal width results were also significantly different, but less so (P D 0.033; Table S1B). In contrast, distal width measurements were not significantly different (P D 0.510; Table S1B). The significant differences found between the inferred measurements and the physical measurements of maximum length, articular length, and proximal width were most likely due to the fact that the physical measurements were made on some incomplete specimens. This was especially so in the areas of the crista cnemialis cranialis and the crista cnemialis lateralis, which form an integral part of the maximum length and proximal width measurements respectively, and whose missing extent was not appreciated. In retrospect, several of the maximum length and proximal width physical measurements should not have been recorded. After careful consideration and comparison of existing or preserved structures, it is reasonable to argue that the positioning of the landmarks was more informed, reflected a more sensible representation of the original morphology of the tibiotarsi than the physical measurement data and allowed larger comparative samples of data.
In the case of articular length, physical measurements were made from the posterior aspect, based on articular surfaces, which were masked by the crista cnemialis cranialis in anterior aspect. The distance between landmark 4 and landmark 11 (Lm4-Lm11; Fig. 1A) placed on images of tibiotarsi in anterior aspect appears to give comparable length values taken between the articular surfaces on a few complete specimens, but because they are not the same, this likely explains some of the difference between the two methods of estimating length. The data set of tibiotarsi landmarked and for which missing landmarks were estimated (n D 19) was used in subsequent analyses. Cluster analysis of the partial Procrustes-fitted landmark coordinate data set produced two defined groups of tibiotarsi: group 1 with 10 specimens and group 2 with 9 specimens (Fig. 3B). Subsequent Hotelling's discriminant analysis of the results of the cluster analysis did not find a significant t-test difference between the two groups because the number of specimens in the data set was less than the number of data points: 19 tibiotarsi specimens vs. 24 landmark coordinates (12 landmarks: x1, y1, x2, y2, etc.). These results do not mean that there was no significant separation between the groups, but that the t-tests defining the degree of separation were unsuccessful. However, the Hotelling's discriminant analysis plot returned from this analysis demonstrates the clear separation between cluster analysis specified groups across the discriminant axis (Fig. 3E).
Principal component analysis of the landmark coordinate data found the same distinct groups identified by cluster analysis, with PC1 and PC2 (Fig. 3H) accounting for 76.9% of the total variance. Summary statistics and distribution tests indicated that inferred measurement data derived from landmark coordinate data for tibiotarsi were normally distributed (Table S2B).
Tarsometatarsi of Dromornis stirtoni-The inferred measurements derived from the landmark coordinate data were not significantly different from physical measurement data for the corresponding tarsometatarsi, except for maximum length, where significance was weak (P D 0.034: Table S1C). Therefore, the tarsometatarsi landmark coordinate data set (n D 29) was used in subsequent analyses. Cluster analysis of the partial Procrustes-fitted landmark coordinate data set (actual and estimated) produced two defined groups of tarsometatarsi: group 1 with 22 specimens and group 2 with 7 specimens (Fig. 3C). Subsequent Hotelling's discriminant analysis of this data set did not identify any significant separation of the two groups (Hotelling's T 2 D 157.32; F D 2.33; P D 0.11), which is demonstrated by the discriminant axis of Figure 3F. This is probably due to the few specimens in the second group. Principal component analysis of the landmark coordinate data retrieved the same distinct groups identified by cluster analysis, with PC1 vs. PC2 (Fig. 3I) accounting for 91.2% of the variance. Summary statistics and distribution tests indicated that inferred measurement data derived from landmark coordinate data of D. stirtoni tarsometatarsi were normally distributed (Table S2C).

Femora
Specimen NTM P4879-In the perimedullary region, there are several enlarged erosion spaces. The bone tissue in this region is distinct from the cortical bone and is endosteally formed, woven textured, and penetrated by a large number of vascular channels and is identified as medullary bone. Some of the erosion spaces are lined with lamellar bone deposits.
Specimen NTM P5037-In cross-section, the perimedullary region shows large cancellous spaces that are lined with lamellar bone tissue. The tissue in between the cancellous spaces appears to be compacted coarse cancellous bone tissue, which, although endosteally formed, does not appear to be medullary bone.
Specimen NTM P5163-The section for this specimen appears to be slightly more tangential in nature. Towards the medullary cavity region, a large number of erosion spaces are visible. The endosteally formed bone tissue in between the cancellous spaces is woven textured and richly vascularized, suggesting that it is medullary bone. The margins of the spaces have an irregular appearance and are not lined with lamellar bone.
Specimen NTM P5076-This specimen shows medullary bone within the medullary cavity. The tissue in between the large cancellous spaces tends to be a mix of woven bone and lamellar bone, with the latter lining the cancellous spaces and so reducing the spaces. This femur was not landmarked due to severe proximal and distal taphonomic damage and so was not included in the cluster analysis. However, the shaft for NTM P5076 is well preserved and its least-shaft circumference (LSC) is 215 mm, from which the estimated body mass value (EBM) is 352.8 kg, or 84.9 kg (19.4%) lighter than the smallest male femur NTM P5104 (LSC D 235 mm; EBM D 437.7 kg), and therefore well within the size range for females.

Tibiotarsi
Specimen NTM P5533-This sample was initially selected to test the coring procedure for histological analysis, as the fossil was visually gracile and uncrushed. Thin sections of this specimen show a well-preserved cortex with a large amount of endosteally formed medullary bone that extends into the medullary cavity. This tissue has a distinctive spongy texture, and the interstitial tissue has a distinctive woven-textured nature and is richly vascularized (Fig. 4A, B). The shaft circumference of NTM P5533 (190 mm) allows calculation of an EBM of 395.7 kg, which is 55.6 kg (12.3%) lighter than the smallest tibiotarsi designated as group 1 (NTM P3057 and NTM P3072; LSC D 200 mm; EBM D 451.3 kg) and is the same size as the group 2 tibiotarsus NTM P3061, so NTM P5533 falls comfortably within the female group.
Specimen NTM P3053-The sample is quite diagenetically altered, which obscures the histological structure. However, even with this limitation, it is evident that no medullary bone is present (Fig. 4C).
Specimen NTM P5124-This sample is also quite diagenetically altered, and histological details in and around the medullary cavity are not clearly visible. Although large cancellous spaces are visible from the mid-cortex to the inner cortex, these appear to be erosion cavities formed as a result of secondary remodeling and therefore unrelated to medullary bone. Its LSC D 185 mm enables a calculated AEBM of 369.6 kg, showing that it is a member of group 2, and therefore female.

Identifying the Size Range of Each Sex
Summary statistics of inferred measurement data by sex are presented in Table 1B. Except for one specimen, NTM P4879, medullary bone was only observed among specimens assigned to group 2 (i.e., the more gracile individuals), for both femora and tibiotarsi, by cluster analyses of the landmarked data set (actual and estimated landmarks), thus permitting the identification of individuals in group 2 as females. Conversely, the individuals assigned to group 1 are male. The exception is NTM P4879, whose well-preserved histology clearly reveals medullary bone. The shaft circumference for this specimen is the smallest among those clustering in group 1. It appears that NTM P4879 was misassigned to group 1 (male) by the cluster analysis because of its maximum length of 426 mm (group 1 specimens had a mean of 439.1 mm; Table 1B), despite it being less robust than all others assigned to group 1. We therefore think that NTM P4879 is just a slightly long and large female femur.
The femoral metrics (Table 1B) are based on the enhanced data set of actual and estimated landmarks and thus present a more complete approximation of the two morphs than is available solely from the fossils. The femora of the females, with a mean length of 390.5 mm, were 11.1% smaller than the male femora, with a mean length of 439.1 mm, indicating that femur length alone is a poor discriminator of the sexes. For femora of D. stirtoni, most variation occurred in the distal and proximal ends. The female femora had a mean proximal width of 158.3 mm, 13.8% smaller than that of the male femora (mean D 183.7 mm). Mean distal width of the female femora was 187.5 mm, 10.1% smaller than that of the male femora (208.5 mm).
The females (group 2) had a mean femur least-shaft circumference of 234.7 mm, 11.1% smaller than the mean of the males (264 mm). The measurement proximal width varied most between the morphs, with the absolute range for male femora 29.5% wider than that of the female, a value much higher than for the distal width of the male femora, which were 19.6% larger than the female femora, perhaps reflecting increased robustness in the proximal femur in larger individuals.
The tibiotarsi (Table 1B) of the females had a mean length of 836.2 mm, or 11.7% smaller than the males, with a mean of 947.4 mm. The mean proximal width for the females was 241.4 mm, only 1.1% smaller than that of the males (244.1 mm). The mean tibiotarsi distal width for the females was 155 mm, 0.9% smaller than that of the males (153.6 mm). The mean shaft circumference of tibiotarsi for females was 199.4 mm, or 6.2% smaller than that of the males (212.5 mm). The variation between the morphs for tibiotarsi is most strongly expressed by maximum length, where tibiotarsi of the males were 11.7% longer than the females, followed by a difference of 6.2% in leastshaft circumference between the females and males. Although there was negligible difference between tibiotarsi proximal and distal widths of females and males (1.1% and 0.9%, respectively; see above), there was much more absolute variation within the proximal regions of the tibiotarsi in the females (30.4%). However, the low sample size for the morphs, 10 and 9, respectively, for large and small morphs, likely has resulted in some of these metrics not reflecting those of their source populations well.

Estimated Body Mass
The assessments of algorithms for body mass estimation using femora and tibiotarsi least-shaft circumference measurements from D. stirtoni are presented in Table S3A-B. Body mass estimates based on mid-shaft circumference measurements of 50 individual femora were made using four separate algorithms. All of these data were normally distributed (Table S3A). A statistical assessment of the similarity of the means of the masses from these four algorithms indicated that Anderson et al.'s (1985) algorithm for body mass estimation gave significantly different estimates (P D 7.72E-06; Table S3A) to those from the algorithms proposed by Campbell and Marcus (1992), Dickison (2007), and Field et al. (2013). Consequently, Anderson et al.'s (1985) algorithm was not used in further analyses. There was no significant difference (see Table S3A) between the estimates for body mass based on femora returned by the algorithms of Campbell and Marcus (1992), Dickison (2007), and Field et al. (2013), which are all comparable because mid-shaft circumference equals least-shaft circumference in D. stirtoni. A comparison between the average estimated body mass from these three algorithms and that from each individual algorithm indicated that Field et al.'s (2013) algorithm gave mass estimates that differed least from the average estimated body mass (P D 0.999; Table S3A). These estimates suggest that unsexed individuals of D. stirtoni have a mass averaging 491 kg, with a range of about 298-728 kg. The estimated body mass based on femora using Field et al.'s (2013) algorithm for females (group 2, including NTM P4879) and males (group 1, excluding NTM P4879) were significantly different (P D 1.13E-06; Table 2; Figs. 5, 6). These estimates based on femora suggest that male individuals of D. stirtoni had a mass averaging 584 kg (439-728 kg) and females an average mass of 441 kg (317-560 kg).
Body mass estimations based on least-shaft circumference measurements of 46 individual tibiotarsi were made using the algorithms of Campbell and Marcus (1992) and Dickison (2007). The resultant data were not normally distributed (Table S3B), and a non-parametric Kruskal-Wallis assessment of the similarity of mean body masses derived from these two methods indicated that they were not significantly different (Table S3B). The mean of the average body mass estimates from the two algorithms for each individual was not significantly different to that from each algorithm (P D 0.69; Table S3B). These estimates suggest that unsexed individuals of D. stirtoni have a mass averaging 480 kg, with a range of about 345-646 kg. The estimated body mass based on tibiotarsi using the average estimates from the two algorithms showed that the male and female mass ranges were significantly different (P D 0.015; Table 2; Figs. 5, 7). These estimates based on tibiotarsi suggest that male individuals of D. stirtoni had a mass averaging 528 kg (451-610 kg) and females an average mass of 451 kg (370-543 kg).
Mass estimates based on least-shaft circumference measurements for femora gave somewhat higher values than those from tibiotarsi, but the difference was not significantly different for females (P D 0.701; Table 2). For the larger and non-normally distributed males, the Kruskal-Wallis non-parametric analyses of mass estimates using femora and tibiotarsi were somewhat significantly different (P D 0.014; Table 2). In summary, the mean body mass estimation based on both femora and tibiotarsi showed that males were significantly larger than females in D. stirtoni (Table 2; Figs. 5-7).

DISCUSSION
In this study, we investigated the fossil population of Dromornis stirtoni from Alcoota in the Northern Territory in Australia. We used landmark coordinates in addition to actual measurements to assess the patterns of size variation in the leg bones in this sample. To expand the available data and maximize inferences concerning the population, we estimated missing landmarks on a proportion of the bones that had more than 50% of the potential landmarks preserved. The distances computed from the landmark coordinates in Dromornis stirtoni were found to be not significantly different to the data physically measured between the same points in most cases (Table S1). The main exceptions were two length measurements for the tibiotarsi, which may relate to a discrepancy between what was measured and the landmarks chosen in the images of these very large bones. Nevertheless, the data are consistent and comparable within the one method. The enlarged data sets, where missing landmarks in fragmentary fossils were estimated, provided more analytical power than by using physical measurements alone. Patterns and shape variation were more discernible, allowing for the identification of intraspecific variation across especially the femora and tibiotarsi.
Analyses of the enlarged data sets based on actual and estimated landmarks showed that Dromornis stirtoni is clearly dimorphic, with significant differences in the robustness of leg elements between the morphs resulting in bimodal distribution for several variables and in multivariate plots. The enlarged sample size generated from estimated landmark coordinates revealed most measurements to have a greater absolute range than those found from measurable fossils (e.g., D. stirtoni femora: 352-476 vs. 365-435 mm, respectively; Table 1A) and tarsometatarsi: 359-506 vs. 350-480 mm, respectively; Table 1A). This is predictable given the larger sample sizes enabled by landmarking incomplete specimens and estimating coordinates for showing the outer compacted cortical bone, and an inner, perimedullary layer of medullary bone that is more spongy in texture and extends into the medullary cavity. The white arrow demarcates the tide line (extent of bone resorption during medullary expansion) and the subsequent endosteal deposition of medullary bone. The dashed-line-framed region is illustrated in B under cross-polarized light with a lambda filter and shows the woven texture of the medullary bone and the rich vascularization evident; C, NTM P3053 shows the periosteally formed cortical bone tissue and the absence of medullary bone in the medullary cavity. The white arrow indicates the resorptive margin of the medullary cavity. Abbreviation: m, medullary cavity. formerly larger or smaller bones than those that are complete and can be physically measured. These refined population statistics for lengths and widths of the femora, tibiotarsi, and tarsometatarsi allow a better understanding of size variation in the population. The application of this landmark estimation technique has maximized data retrieval from fragmentary material, which is normally neglected and considered taxonomically uninformative, yet can be studied using numerical quantitative approaches (Arbour and Brown, 2014;Bastir et al., 2014).
Tibiotarsi of D. stirtoni displayed negligible variation in their proximal and distal widths between the morphs (Table 1B) and the PCAs showed that most variation in this element was related to absolute size (see Fig. 3G-I). However, the poorer resolution of the modal groups using tibiotarsal width measurements may relate to the limited sample size. Importantly, our data show that individual measurements of the proximal width of femora are the better discriminators of dimorphism in D. stirtoni. These data, in revealing two separate groups, support the observation made by Murray and Vickers-Rich (2004:75) that the "considerable" size range observed for fossils of D. stirtoni was suggestive of the species probably being sexually dimorphic.
Medullary Bone-We used the presence of medullary bone in specimens of the smaller, less robust morph to confirm that this was the female. Medullary bone was found in three out of four femora and one out of three tibiotarsi from the small morph for D. stirtoni. Conversely, no evidence of medullary bone was found in larger specimens of the more robust morph. One exception was a specimen assigned to the more robust group by the cluster analysis, but it was the smallest in that group. However, the presence of medullary bone in this specimen suggests that it is a large mature female (and not a small male). Our findings therefore show that females were the smaller morph, and that all the large dromornithid fossils found at Alcoota were representative of a single sexually dimorphic species.
As medullary bone is an ephemeral deposition of calcium produced upon ovulation in anticipation of reproduction (Schweitzer et al., 2005), the presence of these structures suggests that the female bird died prior to egg laying. Medullary tissue is rapidly resorbed during egg production and is therefore either absent or minimal at the end of the reproductive season (Schweitzer et al., 2007). This evidence shows that at least some female birds died during the early part of, or leading up to, the reproductive season. In emus in Australia, this is about May-June, so that incubation goes through winter and chicks hatch in spring to take advantage of the seasonal flush of food (Davies, 2002;Dzialowski and Sotherland, 2004). The fact that some birds were physiologically able to commence breeding in the months leading up to their death suggests that the drought event hypothesized to have generated the mortality leading up to the fossil FIGURE 5. Box plot of Dromornis stirtoni femora (including NTM P4879 as female) and tibiotarsi estimated body masses grouped by sex according to cluster analysis group designations (Fig. 3A, B). Mass estimates for femora are based on Field et al. (2013); those for tibiotarsi are based on the average of estimates for each specimen using algorithms from Campbell and Marcus (1992) and Dickison (2007). Whiskers indicate range, box is standard deviation, and horizontal line is the median. Estimated body mass data grouped by sex according to cluster analysis group designations (Fig. 3A, B): femora based on Field et al. (2013), and tibiotarsi based on the average of estimates for each specimen using algorithms from Campbell and Marcus (1992) and Dickison (2007). Normality of distribution was tested by the Shapiro-Wilk test, where P-values (P) > 0.05 indicate that data are normally distributed. Comparative statistics include t-test assessments of normally distributed data and Kruskal-Wallis test assessments of non-parametric data where P-values (P) > 0.05 indicate no significant difference was found between means. Abbreviations: EBM, estimated body mass; SD, standard deviation; Tib, tibiotarsi.
accumulation (Murray and Megirian, 1992:213) was likely not one lasting in the order of years. Extant emu will delay breeding when short of food and abort entirely in the event of drought, cassowary breeding coincides with the maximum availability of fruit, and all anseriform breeding activities are contingent on rainfall and the availability of food (Marchant and Higgins, 1990). Many other birds will breed only when food and rainfall are conducive (see Boag and Grant, 1981;Brown and Li, 1996;Morrison and Bolger, 2002;Chase et al., 2005;Preston and Rotenberry, 2006;McCreedy and Van Riper, 2014). Therefore, it seems unlikely dromornithids would invest in egg generation if they were stressed by prolonged food and water shortages. Body Mass-The body mass of each sex was estimated by a variety of methods using both femora and tibiotarsi and conservatively these show that the mean body mass of male D. stirtoni (584 and 528 kg from femora and tibiotarsi, respectively) was significantly larger than that of females (441 and 451 kg; Table 2). The sexes therefore differed by about 80-140 kg, a difference that certainly would have been conspicuous in life.
How do these new mass estimates compare with previous ones for D. stirtoni? Those we obtained from femora (n D 50; Table  S3A) based on the algorithms from Campbell and Marcus (1992), differed from those of Murray and Vickers-Rich (2004: table 11:196), whose mass estimates were 20% heavier (mean D 626.9 kg, range D 397.1-829.1 kg, n D 17) than the mean from this study (501.5 kg, range D 303.9-744.5 kg, n D 50; Table S3A), which may be explained by errors in their use of the algorithm (Nguyen et al., 2010). The mean of mass estimates reported by Nguyen et al. (2010:table 4) for femora of D. stirtoni (519.5 kg, range D 341.9-713.9 kg, n D 17) were similar to the results of our study. However, the greater range in mass values reported here was likely due to our larger sample size.
A range of other methods have been used to estimate mass of D. stirtoni. The mass estimates reported here greatly exceed those reported by Jennings (1990: fig 76:177) of 320-370 kg, which were derived from an allometric algorithm using body length. Murray and Vickers-Rich (2004) also estimated body mass for D. stirtoni as 574 kg, using water displacement of a 1/10 size scale model of a 2.7-m-tall individual. In the present study, measured tibiotarsi had a maximum length of 87 cm, although larger ones had an estimated maximum length of 100 cm (Table S2B). Murray and Vickers-Rich (2004) proposed that a tibiotarsus length of 83 cm scaled to a height of almost 3 m. Thus, conservatively, if one used the maximum length of tibiotarsi (87 cm) as actually measured (Table S1B), a mass estimation in the vicinity of a metric ton might be predicted for D. stirtoni (see Murray and Vickers-Rich, 2004:table 14:202), rather more than the maximum estimate of 744.5 kg (Table S3A) found here using femora, or 632.1 kg (Table S3B) using tibiotarsi. This model method therefore appears to overestimate mass. Murray and Vickers-Rich (2004:203) discussed the limitations of this method, primarily identifying the paucity of data regarding the distributions of individual body masses within extant populations of large mammals and birds. This is why mean mass provides a better and more valid estimate for a species than selecting the largest specimen, which is often well outside the 95% percentile range (e.g., Worthy et al., 2005; re Dinornis moa in New Zealand) and hardly representative of the species.
Several different algorithms for mass estimation based on femoral skeletal measurements have been proposed in the literature.  Table S3A). Individuals were attributed to male (group 1) and female (group 2) by cluster analysis of the femora landmark coordinate data (Fig. 3A, D) with the sex of group 2 identified as female by the presence of medullary bone, with the exception of the misassigned specimen NTM P4879 ( ) identified as female by medullary bone.
For the current data sets, no significant difference was found in the mass estimates (Table S3A) between the algorithms of Campbell and Marcus (1992), Dickison (2007, excl. kiwi), and Field et al. (2013), but that of Anderson et al. (1985) underestimated the body mass of D. stirtoni significantly (Table S3A) compared with the other methods. Murray and Vickers-Rich (2004:205) also found that the Anderson et al. (1985) algorithm underestimated body masses when applied to measurements for the Magpie goose (Anseranas semipalmata).
Mass estimates were also obtained from least-shaft circumference measurements of tibiotarsi (Campbell and Marcus, 1992; Table S3B). Nguyen et al. (2010) reported equivalent mass estimates for D. stirtoni of 491.4 kg, with a range of 450.5-567.6 kg, which were very similar to those of this study (477 kg, range of 348.9-632.1 kg; Table S3B). As for femora, the range for tibiotarsi in this study was greater, due to the larger number of specimens (n D 46 vs. 4). In general, the mean body mass estimations based on tibiotarsi are 4.9% lower than those based on femora (477 vs. 501.5 kg; Table S3A-B). Campbell and Marcus (1992) argued that the femur provides a more reasonable mass estimation because it more accurately represents the morphological adaptations required for the weight of the bird. However, it is evident from the present comparisons of a large data set that mass estimations using Campbell and Marcus's (1992) algorithms are biased towards femora measurements producing heavier estimations than tibiotarsi measurements in D. stirtoni.
Ratite species can display disproportionate asymmetry of the femoral cross-section, that is, it is not round or circular, but rather can be elongated on some axis. Worthy and Holdaway (2002:152) noted that the femora of the elephant bird Aepyornis maximus Geoffroy St-Hilaire, 1851, of Madagascar, had an "unusual thickening" to compensate for the rotational stresses associated with an unusually wide pelvis structure. Similar asymmetry has been observed in femora of moa, especially the robust Pachyornis elephantopus Owen, 1856, and has been related to lateral forces on the femur as the bird swayed from foot to foot (Worthy and Holdaway, 2002). Murray and Vickers-Rich (2004) observed that the femora of dromornithids have a relatively greater diameter than do tibiotarsi and are somewhat craniocaudally compressed, and that this is associated with a thinner cortical bone in the femur. This is particularly obvious in Genyornis newtoni where individual skeletal associations (not available in material of D. stirtoni) show that the femur is disproportionately robust compared with the tibiotarsus (Stirling and Zietz, 1896). It is possible that a relatively thinner cortical bone in these femora is being offset by increased shaft circumference, or a "least mass solution" (Campbell and Marcus, 1992:405), where the same sectional strength is achieved across a hollow femur by an increase in shaft circumference and a reduction of cortical bone wall thickness (Murray and Vickers-Rich, 2004). Campbell and Marcus (1992:402) found that the log femur to log tibiotarsus circumference comparisons for their "long legged group" departed from an isometric slope (of 1.0) by more than 0.01 in the lower confidence bounds, implying that femur circumference increased faster relative to tibiotarsus circumference for larger birds than what their geometric scaling would predict. If this trend is characteristic of dromornithids, then mass estimation based on femoral circumference may overestimate actual mass for them and tibiotarsi may be better used for interspecific comparison of body mass in large birds.
Regardless of which tool is the most accurate predictor of body mass, it is evident that D. stirtoni was enormous, with the FIGURE 7. Estimated mass based on Dromornis stirtoni tibiotarsi using least-shaft circumference and the average of two algorithms from Campbell and Marcus (1992) and Dickison (2007) (Table S3B). Individuals were attributed to male (group 1) and female (group 2) by cluster analysis of the tibiotarsi landmark coordinate data (Fig. 3B), with the sex of group 2 identified as female by the presence of medullary bone. largest individual about twice the mass of the smallest (344.6-645.8 kg; tibiotarsi; Table S3B). They were 10-fold larger than the extant emu (range 18-48 kg, n D 22; see Davies, 2002:213). Even if these algorithms resulted in an overestimate for mass, observations of living birds show that in any one individual, mass varies by at least 50% dependent on seasonal condition (Handford and Mares, 1985;Campbell and Marcus, 1992;Davies, 2002), so it is very likely that these estimates overlap the reality. As discussed by Murray and Vickers-Rich (2004:209), the true mass of the majority of D. stirtoni individuals would most likely fall somewhere in the middle of the predicted ranges (Figs. 5-7).
Aepyornis maximus is often described as having been the heaviest bird to have lived, and most authors will cite Amadon's (1947) estimate of 438 kg as support. Campbell and Marcus (1992:409) estimated the mean mass of A. maximus as 526 kg using femora (n D 8) and suggested that Amadon's (1947) method utilizing femur cross-sectional area underestimated the mass of this taxon. To test these previous estimates in context with our data for D. stirtoni, we used the algorithms of Campbell and Marcus (1992) and the hind-limb circumferences given for Aepyornis by Monnier (1913:140), who did not specify how many femora and tibiotarsi were measured, but provided metrics of the absolute range for four Aepyornis spp. Additionally, A. maximus and A. medius likely belong to a single dimorphic species: these taxa were noted by Worthy and Holdaway (2002:153) as distinguishable only by size. We therefore included Monnier's (1913:140) circumference ranges for A. medius in our data for A. maximus (Table S3C). Our median result of about 528 kg for the femora of A. maximus is almost identical to the 526 kg estimate of Campbell and Marcus (1992:409), and is very similar to our unsexed femur results for D. stirtoni (501.5 kg, n D 50; Table S3A), but with D. stirtoni having a greater range (303.9-744.5 vs. 341.9-713.9 kg; Table S3A-C). Results for tibiotarsi suggest that A. maximus had less robust tibiotarsi (median D 360.6 kg, range D 242.9-478.3 kg; Table S3C) than D. stirtoni (mean D 477 kg, range D 348.9-632.1 kg; Table S3B) and was similar to Genyornis newtoni (see above) in the sense that A. maximus femora seem disproportionally robust compared with their tibiotarsi. These results, taken in context with our argument (see above) that tibiotarsi provide the most reasonable interspecific assessment of body mass in large birds, suggest that Dromornis stirtoni can be argued to likely be the heavier of the two taxa (477 vs. 361 kg; Table S3B-C).
Comparisons were made between D. stirtoni and the largest known terrestrial bird of South America. Brontornis burmeisteri Moreno and Mercerat, 1891 once believed to be a carnivorous phorusrhacid (see Alvarenga and H€ ofling, 2003, and references therein) but now considered to have anseriform affinities (Agnolin, 2007), is estimated to have weighed around 350-400 kg, or 15-20% less than A. maximus (Alvarenga and H€ ofling, 2003:59). Dromornis stirtoni would certainly have been heavier than any Brontornis specimen known. Worthy et al. (2005:387) provide mass estimations for the largest of all New Zealand moas: Dinornis robustus Owen, 1846 (range D 61-275 kg, n D 99; appendix 1; fig. 4) from the Canterbury region of the South Island. Although these data are not directly comparable with ours because Worthy et al. (2005) used Prange et al.'s (1979 algorithm based on femur length for their assessment, Dromornis stirtoni was clearly considerably heavier than any moa taxa.
Dromornis stirtoni and Aepyornis maximus were the two heavyweights of the Cenozoic avifauna, but which was truly the heaviest remains to be clarified conclusively, and is contingent on acquiring additional specimens of A. maximus.
Sex Ratios-The sex ratio in avian species can be quite revealing of breeding behavior and life history (Hardy, 1997;Sheldon, 1998;Cockburn et al., 2002;Allentoft et al., 2010). The calculated sex ratios for D. stirtoni based on cluster analysis group assigned fossils with more than 50% of landmarks present, differed by element. For femora (n D 34), the male/female ratio was 0.8:1, for tibiotarsi (n D 19) the ratio was 1.1:1, and for tarsometatarsi (n D 29) the ratio was 3.1:1. Clearly only one ratio can pertain to the species, indicating that some form of bias is differentially operating on each element. Although hydraulic sorting may have contributed, we prefer the hypothesis that the disparity in ratios is due to differential preservation caused by differences in resistance to both weathering prior to burial and fracturing after burial. Larger femora and tibiotarsi are more fragile and are likely to be subject to greater disruptive forces caused by the heaving and shifting of the unconsolidated silts that enclose them. Accentuating this difference is the presence of medullary bone in many of the females, which serves to increase internal shaft thickness and robusticity. In contrast, smaller tarsometatarsi are differentially broken up and more greatly damaged. There exist more tibiotarsi specimens in the collection (n D 59; Appendix 2) than other elements of D. stirtoni, affording a greater sample size: body mass estimates derived from least-shaft circumference measurements from 46 tibiotarsi indicated a bimodal distribution (Fig. 2C), and although not all these specimens were landmarked, we note that tibiotarsi shaft circumferences and the mass estimates derived from this measurement are likely to be least affected by breakage of the bone. Hence, the sex ratio from this element is more likely to reflect the population than the other two bones; therefore, it seems that in the sample of D. stirtoni from Alcoota, the ratio is close to 1:1, and so they are similar to ratites, where the normal sex ratio is in the vicinity of 1 male for every 1.14 females (Bunce et al., 2003;Worthy et al., 2005).
However, does this ratio represent the actual population ratio or is it somehow related to intrinsic site factors? These data provide no indication that the Alcoota site during the late Miocene preferentially incorporated one morph over the other, either because of differential availability of sexes to the site or through entrapment mechanisms biasing towards one sex. The former, via a seasonal segregation of sexes, has been used to explain the marked preponderance of females over males for Dinornis robustus in the Pyramid Valley moa deposit (Holdaway and Worthy, 1997), compared with contemporaneous nearby deposits with normal proportions of male fossils, e.g., Bell Hill Vineyard (Allentoft et al., 2010). Essentially, Holdaway and Worthy (1997) and Allentoft et al. (2010) argued that females held territory over summer months in the resource-rich margins of the Pyramid Valley lake site, whereas males and the young they were tending were elsewhere, creating a segregation much like in cassowaries today (Handford and Mares, 1985;Davies, 2002).
Given that the sex ratio of D. stirtoni approaches 1:1 and that these birds are common, the question arises; is there a bias for these giant birds over smaller birds in the Alcoota deposits? Our analysis reveals minimally 31 D. stirtoni (tibiotarsi MNI; Appendix 2), rather more than the 23 Ilbandornis woodburnei and 16 I. lawsoni so far recorded (see Worthy et al., 2016). The Ilbandornis species are much smaller birds that differ only a little in size and together they outnumber D. stirtoni, precluding any bias towards the larger bird. This is also supported by the presence of numerous smaller mammals in the deposits. Considering the dromornithid sample as a whole, it appears more likely that the taphonomy of the site has differentially impacted on the various elements, biasing for smaller femora, but against smaller tarsometatarsi. The processes to which the bones were exposed, from death and decay around a waterhole to their eventual concentration in channel deposits by flood events (Murray and Megirian, 1992), easily explain the deviation from a 1:1 ratio for these elements.
Dimorphism Ratios-As for sex ratios, the dimorphism ratio (DR) based on the mass of each sex (Livezey and Humphrey, 1984;Livezey, 1993Livezey, , 1996aLivezey, , 1996bLivezey, , 1997) allows predictions to be made concerning breeding biology (see Tables S4, S5). We compared the DR in D. stirtoni with those of ratites and anseriforms, respectively, the groups to which dromornithids were (Rich, 1975(Rich, , 1979, and are currently, considered related (Murray and Megirian, 1998;Murray and Vickers-Rich, 2004). McCracken et al. (2000) argued that sexual dimorphism ratios within waterfowl were generally well below 1.4:1 (male:female). All the available sexed mass data for Australian anseriforms return DRs below 1.4:1 except for the musk duck (Biziura lobata), which is 1.55:1 (Table S4; see also Livezey and Humphrey, 1984:374), thus supporting this observation. Interestingly, the anseranatid magpie goose Anseranas semipalmata displays a relatively high DR of 1.34:1 (Table S4) in comparison with other basal anseriforms. The disparity between the size of males and females in the musk duck is associated with (see below) the development of a lek mating system (McCracken et al., 2000). All other basal anatids (see Gonzalez et al., 2009), e.g., oxyurines such as the freckled duck Stictonetta naevosa (DR D 1.15:1) and the pinkeared duck Malacorhynchus membranaceus (DR D 1.17:1), display low dimorphism ratios (Table S4), as do dendrocygnines such as the wandering whistling duck Dendrocygna arcuata (DR D 1.18:1) and the plumed whistling duck D. eytoni (DR D 0.99:1). Similarly, the Cape Barren goose Cereopsis novaehollandiae has a low dimorphism ratio (DR D 1.03:1). All of these taxa are considered primitive members of the Australian anseriform fauna (Worthy, 2009). Additionally, all these Australian anatids have male-dominated SSD associated with the almost universal occurrence of sustained and long-term monogamy reinforced by ritualized display, vigorous defense of nest and young, and shared parental care (Table S5).
In contrast, data for Australasian ratites (Table S4) show that all extant ratite birds display strong RSSD, e.g., brown kiwi Apteryx australis (DR D 0.83:1), little spotted kiwi A. owenii (DR D 0.83:1), and great spotted kiwi A. haastii (DR D 0.7:1) all show similar levels of RSSD, almost identical to the RSSD displayed by the Australian emu Dromaius novaehollandiae (DR D 0.85:1). The excellent preservation of extinct New Zealand moa remains allowed Worthy et al. (2005) to provide mass data by sex for two species of Dinornis, one from the North Island: Dinornis novaezealandiae Owen, 1843 (DR D 0.51:1), and one from South Island: D. robustus (DR D 0.51:1), dimorphism ratios that compare with that of the extant southern cassowary Casuarius casuarius (DR D 0.53:1). However, these data for C. casuarius are based on only three individuals (two male, one female). Similarly, mass data by sex for wild ostrich Struthio camelus (DR D 1.15:1) are limited, do not provide an indication of the number of specimens measured, and thus should be considered cautiously. Sexed mass data for farmed South American rhea Rhea americana albescens (DR D 1.28:1) provide an insight into what may be the wild state for rhea (Table S4; Navarro et al., 2005). These data show that rhea display a similar DR to ostrich (see above) at 15 months of age, but additional assessments of wild rhea sexed mass data are necessary to appreciate their DR when fully sexually mature, which according to Davies (2002:205) is around 3-4 years of age. Comparisons of ratite data with anseriform data show clear distinctions between these clades (Tables S4, S5). Ratites display strong RSSD and associated with that is almost exclusive male incubation and parental care (Table S5). Ostriches are anomalous in that they display SSD and shared incubation, nest defense, and parental care (Davies, 2002; Table S5).
Dromornis stirtoni has a DR of 1.17:1, which is most similar to those of the anatids D. arcuata, S. naevosa, M. membranaceus, and Anas castanea (chestnut teal), and very similar to the those of the anserines Branta canadensis (Canada goose) and Cygnus atratus (black swan), and the anatine Tadorna tadornoides (Australian shelduck) (Table S4).
Sexual Dimorphism and Breeding Biology-In general, two explanations are given for the evolution of sexual dimorphism: sexual selection or intraspecific niche divergence (Shine, 1989;Green, 2000), although Blanckenhorn (2005) argues that intraspecific foraging niche divergence is of less importance. In their study of the musk duck (Biziura lobata), McCracken et al. (2000) found that male emancipation from parental care and the evolution of a lek mating system led to fixation of larger body size (see also Livezey and Humphrey, 1984:376). The differences seen in the morphology of these ducks was not the result of niche divergence, but due to sexual selection.
In the late Miocene at Alcoota, resources would have been more abundant than they are in the area today and bulk feeders such as dromornithids would have ranged over a large area. Therefore, SSD was more likely associated with mate competition than resource partitioning, and in this context, congregation at a limited resource such as a water hole may have provided opportunity for the development of a lek or display arena, where males could congregate and attract females for mating. However, the DR for D. stirtoni suggests that these birds did not have lek behavior, because at 1.33:1 based on femora and 1.17:1 from tibiotarsi (Table S4), this is well below recorded heavily skewed values for animals with lek behavior (Emlen and Oring, 1977;Ribeiro et al., 2015). Thus, as exclusive maternal care of the young, male defense of their right to mate with females and elaborate male display are allied with lek behavior, D. stirtoni likely did not have such behaviors. Similarly, polygyny can be excluded for D. stirtoni, because this is associated with marked sexual dimorphism (Payne, 1984;Dunn et al., 2001;Ribeiro et al., 2015).
The DR for D. stirtoni falls just outside the range of what Livezey (1996a:79) proposed as the "evidently primitive mean ratio of 1.05 to 1.15" for waterfowl. These data suggest that D. stirtoni most likely had a mating system typical of Anserinae, characterized by long-term monogamy, mutual display, shared parental care, and aggressive defense of nests (Livezey, 1996b; see also Table S5).
Incubation Behavior-The average size of the sexes is also predictive of incubation behavior, and it is well known that the strength of eggshell is related to the mass of the incubating bird (Deeming and Birchard, 2008;Birchard and Deeming, 2009). The male D. stirtoni was on average heavier than the female and more robustly built; some became much larger than any females. It is therefore certain that the smaller sex, hence the female D. stirtoni, incubated the eggs, in contrast to the smaller males incubating the eggs in moa (Worthy and Holdaway, 2002:184) and most other ratites (Davies, 2002:49; see also Table S5).
There is a marked lack of fossils of small juvenile or chick bones recovered from Alcoota, with only three D. stirtoni chick bones (two femora and one tibiotarsus) known (Murray and Vickers-Rich, 2004). Similarly, half grown to adult-sized juvenile specimens are equally rare (W.D.H., pers. observ.), implying that few subadult birds were present at the site. This raises the possibility that the chicks reached their full-grown size in months and hence were speculated to have grown to full size within 2 years (Murray and Vickers-Rich, 2004), much as emus (Davies, 2002) and almost all extant birds (Marchant and Higgins, 1990) do. However, such a lack of juvenile specimens may alternatively mean one of two things: (1) the young were not near the site because of seasonal segregation, as inferred for D. robustus at Pyramid Valley (Holdaway and Worthy, 1997); or (2) that they had a very low frequency in the population. Further sites are needed to discriminate between these options. Additionally, the hydraulic sorting process may have biased against survival of the soft and small bones of juveniles. There is no eggshell in the deposit, and this similarly may have several explanations: (1) the deposit was highly seasonal in nature and sampled the pre-laying period, as evidenced by the presence of medullary bone in some specimens; (2) the dromornithids were laying and brooding elsewhere; and (3) the matrix and depositional history is not conducive to survival of calcium carbonate from eggshell, to the extent that any that was incorporated into the deposits has dissolved away. In support of this, we note that there exists not a trace of snail shell, charophyte oogonia, or any yabby (decapod) depocenters, all of which are abundant calcium carbonate structures in inland waters of all types (W. D.H. et al., pers. observ.).
Life Strategy-The question of how fast the dromornithids grew to full size is similarly unresolved. The New Zealand moa Dinornis spp. accelerated juvenile growth rate relative to the growth rate of other moa taxa, in order to reach a large size as quickly as possible (Turvey et al., 2005;Olson and Turvey, 2013). After juveniles of Dinornis spp. had reached near full size, maturation processes slowed and they then took up to a further 8 years to reach actual adult size and sexual maturity. The case of Dinornis spp. is an extreme manifestation of the K-selected life history strategy, which is typified by a long life span, coupled with a low mortality rate, and full maturity took a long time, even up to a decade to complete. Such animals tend to live near the carrying capacity of the habitat and have no predators as adults. Additionally, breeding populations are near saturation levels most of the time and show high adult survivorship. Populations can withstand juvenile 'cropping,' but breeding adults are replaced slowly and losses of large breeding adults can cause species vulnerability (Worthy and Holdaway, 2002:545). This contrasts markedly with emus, which can suffer dramatic mortality in bad seasons and rebound by producing many fast-maturing offspring when favorable conditions return (Davies, 2002:215). The few juveniles or subadult specimens recovered from Alcoota hint at the possibility of a K-selected life history strategy for D. stirtoni. If so, it is possible that dromornithids were long-lived species, had few young, and employed a similar strategy to that of Dinornis spp. in that the populations were made up of a core of older, breeding birds.
An extreme K-selected strategy for D. stirtoni might help explain why successive dromornithid species were much smaller after the late Miocene (Murray and Vickers-Rich, 2004). The progressive widespread aridification of Australia through the Miocene (Macphail, 1997;Murray and Vickers-Rich, 2004;Crayn et al., 2006;Martin, 2006) and resultant resource limitations placed species with a K-selected life history strategy at a competitive disadvantage to those with an r-selection strategy.
Trophic Niche-The allometric effects of body size can be one of the main drivers of trophic niche divergence within a species (Shine, 1989) and result in the targeting of different trophic niches within dimorphic species (see McCracken et al., 2000). As yet there are no data that might indicate cranial differences associated with the sexes (Murray and Vickers-Rich, 2004; see also Murray and Megirian, 1998). Moreover, unlike species of Dinornis, where the males were considerably shorter than females (Bunce et al., 2003;Worthy et al., 2005), the lengths for femora and tibiotarsi between the sexes of D. stirtoni imply that the majority of the population was of similar height. Thus, the sexes in D. stirtoni are unlikely to have segregated feeding niches based on feeding height in shrubs.
The evolution of the dromornithids, and the size they attained, is suggestive of adaptation to the woodland environment that was developing in central Australia from the late Eocene (38 Ma) onward. These scleromorphic fire-sensitive woodlands or 'dry jungles' became the dominant continental floras (Murray and Vickers-Rich, 2004:333; see also Macphail, 1997;Martin, 2006) that were progressively exploited by a range of large, bulkfeeding herbivores, of which the dromornithids, and most notably Dromornis stirtoni, became one of the most conspicuous during the late Miocene. Several species of diprotodontian marsupials dominated the fauna at Alcoota, with four abundant taxa found together: Kolopsis torus Woodburne, 1967a, a sheepsized browser, Plaisiodon centralis Woodburne, 1967a, a large browsing marsupial, Dorcopsoides fossilis Woodburne, 1967b, a small browsing wallaby, and Hadronomas puckridgei Woodburne, 1967b, a large browsing kangaroo (Murray and Vickers-Rich, 2004). This diversity of small, medium, and large browsers suggests an associated diverse small-and medium-sized shrub flora (Murray and Megirian, 1992). Associated with these medium-sized browsers were less frequent larger browsers: Palorchestes painei Woodburne, 1967b, a large tapir-like marsupial, and two large diprotodontids: Pyramios alcootense Woodburne, 1967a, and Alkwertatherium webbi Murray, 1990. Alongside these diprotodontian browsers were the herbivorous birds: the large (480 kg; Table S3B) Dromornis stirtoni, able to browse at heights over 3 m, and two ostrich-sized Ilbandornis species. A much smaller casuariid ratite was also present alongside the much more abundant dromornithids (Murray and Vickers-Rich, 2004; see also Rich et al., 1991Rich et al., :1037. Divisions between the separate guilds indicate a complex and diverse browsing community operating in different, but complementary trophic niches (Murray and Vickers-Rich, 2004). Dromornis stirtoni would have been prominent in the landscape and certainly was the tallest animal in the local fauna, capable of exploiting the upper levels of the shrub and tree dominated environment more so than contemporary marsupial browsers.

CONCLUSION
In this study of dromornithids, the application of geometric morphometrics and the estimation of missing landmarks has provided a valuable technique for the recovery of additional information from fragmentary fossil material. This approach has previously provided information on shape variation exceeding what is possible using other methods (Slice, 2007;Webster and Sheets, 2010). The use of a range of morphs as comparative templates to estimate width and length measurements has allowed for comparisons at a much finer scale (Arbour and Brown, 2014;Bastir et al., 2014). Generalized Procrustes analysis permitted the reflection of differences in the size and shapes of the fossils and allowed for the identification of structural and group differences, contrasting size and shape data and functional relationships that could be statistically defined (Slice, 2007;Klingenberg and Marug an-Lob on, 2013).
Our use of geometric morphometrics and the estimation of missing landmarks has allowed the analysis of variation in fossil leg bones attributed to Dromornis stirtoni, revealing that they were derived from only one taxon and that sexual dimorphism accounted for the size variation observed in the collection.
The Alcoota fauna is the only example of the central Australian vertebrate community known from the late Miocene (8-6 Ma) (Murray and Megirian, 1992;Murray and Vickers-Rich, 2004). This assemblage has revealed a diverse browsing community populated by a combination of abundant marsupial browsers and a large community of dromornithid birds, dominated by what was the apex browsing animal in the environment-Dromornis stirtoni. Some males were truly gigantic, they likely practiced male/male competition, and maintained longterm monogamous relationships reinforced by elaborate mutual display. These dominant males were likely to have defended family groups and priority territories with a vengeance reminiscent of their former fearsome reputation.