Saif N Al-Bahry

Ibrahim Y Mahmoud

Maheera Al-Zadjali

Abdulkader Elshafie

Asila Al-Harthy

Wafaa Al-Alawi

ANTIBIOTIC RESISTANT BACTERIA AS BIO-INDICATOR OF POLLUTED EFFLUENT IN THE GREEN TURTLES, Chelonia mydas IN OMAN

Keywords: Bacteria, Antibiotics, Bio-indicator, Oviductal fluid, Pollution, Green turtles

Antibiotic resistant bacteria were studied as bio-indicators of marine polluted effluents during egg-laying in green turtles. A non-invasive procedure for sampling oviductal fluid was used to test for exposure of turtles to pollution in Ras Al-Hadd, Oman, which is one of the most important nesting beaches in the world. Each sample was obtained by inserting a 15 cm sterile swab gently into the cloacal vent as the sphincter muscle is relaxed and the cloacal lining is unfolded to the outside. Forty turtles were sampled. A hundred and thirty-two species of bacteria from 7 genera were isolated. The dominant isolate was Citrobacter. Among the isolates 60.6% were multiple resistant to 15 tested antibiotics. The dominant resistance to antibiotics was ampicillin followed by streptomycine and sulphamethoxazole. Sampling oviductal fluid for resistant bacteria to antibiotics is valuable way to assess exposure to polluted effluents during feeding and migratory in turtles. Polluted effluents using bacteria as bio-indicator may influence reproductive potential in this endangered species.

INTRODUCTON

Evidence of increasing resistance to antibiotics in bacteria suggests that anti-microbial drugs play a major role in the emergence of multiple resistant bacteria [START_REF] Refsdal | To treat or not to treat: a proper use of hormones and antibiotics[END_REF]. [START_REF] Berger-Bächi | Resistance mechanisms of Gram-positive bacteria[END_REF] reported that in the last few decades there was an increase in number and severity of infections arising from such bacteria. These pathogens have a tendency to accumulate multiple resistance factors under antibiotic selection Antibiotics enter the environment via different pathways. Resistant bacteria may have been selected during the process of sewage treatment and, subsequently, may reach the aquatic environment via contaminated effluents [START_REF] Kümmerer | Drugs in the environment: emission of drugs, diagnostic aids and disinfectants into wastewater by hospitals in relation to other sources[END_REF][START_REF] Hühnerfuss | Occurrence, distribution and fate of pharmaceuticals and further polar contamination in the marine environment[END_REF].

The rapid development of resistance is due to mutational events and/or gene transfer and acquisition of resistant determinants, allowing strains to survive antibiotic treatment [START_REF] Berger-Bächi | Resistance mechanisms of Gram-positive bacteria[END_REF][START_REF] Alonso | Environmental selection of antibiotic resistance genes[END_REF]. The development of antibiotics, from the sulphonamides used in the past to the powerful broad spectrum antibiotics of today, has led to a fundamental disturbance of microbial ecology [START_REF] Spratt | Antibiotic resistance: Counting the cost[END_REF]. The use of antibiotics directly selects resistant variants to different antibiotics or disinfectants [START_REF] Jeljaszewicz | Antibiotic resistance in Gram-positive cocci[END_REF]. Antibiotic resistant bacteria have been reported in wild birds and mammals, even from remote regions such as the Amazon River Basin [START_REF] Kempski | Antibiotic resistant bacteria from Clemmys guttata (spotted turtle)[END_REF]. Antibiotic resistant bacteria were also isolated from juvenile loggerhead sea turtles (Caretta caretta) in Cour Sound, North Carolina, USA [START_REF] Harms | Cloacal bacterial isolates and antimicrobial resistance patterns in juvenile loggerhead turtles in North Carolina, USA[END_REF]. Antibiotic resistant bacteria have also been found in the egg shells and egg contents of the green turtle, Chelonia mydas (Al-Bahry et al., 2009a). The source of bacterial contamination to the eggs was unknown. In the present investigation we analyzed the oviductal fluid during the egglaying process in order to find the source of contamination that we previously reported.

In this investigation a simpler non-invasive sample method was designed specifically to collect oviductal fluid in the egg-laying green turtles and to isolate bacterial flora and resistant bacteria to antibiotics.

Resistant bacteria were used as bio-indicator for the presence of the contaminated effluents in the marine turtles (Al-Bahry et al., 2009a, Al-Bahry et al., 2009b[START_REF] Foti | Antibiotic resistance of Gram negatives isolates from loggerhead sea turtles (Caretta caretta) in the central Mediterranean Sea[END_REF][START_REF] Foti | Enterobacteriaceae isolates in cloacal swabs from live-stranded internally-hooked loggerhead sea turtles, Caretta caretta, in the Central Mediterranean Sea[END_REF]. This data will be valuable in the overall assessment of pollution of feeding habitats, as well as the migratory routes of the green turtles.

MATERIALS AND METHODS

Study area.

Ras Al-Hadd Reserve is located on the Gulf of Oman and the Arabian Sea between 22 o 32'N and 59 o 45'E and 22 o 14'N and 59 o 48'E. The northern 4km of the Reserve are located on the Gulf of Oman, while the rest of the Reserve is located on the Arabian Sea.

The coastline is mostly sheltered by rocky hills. High-energy waves build a curb of sand that can rise 2m high. Approximately 20 beaches with different lengths (50m to 5.3Km) make up the Reserve. Most of these sheltered beaches are considered ideal nesting grounds for the green turtles.

Brief description of the reproductive tract in turtles:

The oviduct (the reproductive tract) is divided into four regions: infundibulum, uterine, uterus and vagina [START_REF] Alkindi | Oviductal morphology in relation to hormonal levels in the snapping turtle, Chelydra serpentine[END_REF]. The vagina is directly connected to the cloaca (Fig 2b). The gastrointestinal tract and ureters make a connection to the cloaca by the sphincter vent (Fig 2a and2b). During the egg-laying process the turtle periodically secretes clear fluid over its eggs which are synthesized by special glands of the uterus, vagina and cloaca. In this paper the term oviductal fluid is used to describe this secretion.

Sample collection:

Oviductal fluid samples were collected by inserting a 15 cm long sterile swab gently. The swab was easily inserted into the cloacal vent due to the general relaxation of the sphincter muscle as well as the unfolding of the smooth lining of the cloaca and the moist condition of the lumina (Fig 1a and1b). During the course of oviposition, the turtle discharges oviductal fluid over the eggs which keeps them moist, as the cloacal sphincter is projected into the neck of the nesting chamber without touching the rim of the nest. This method has not been used by other investigators in the egg-laying turtles. This method was specifically designed to collect bacteria during the egg-laying process. Thus, the swabbing technique was necessary in this study.

A total of forty turtles were examined. The samples from each turtle were collected after the turtle had discharged oviductal fluid over the eggs at least three times during the course of oviposition, which ensured that most residual bacterial flora in the cloaca had been flushed away. During the oviposition the cloaca was projected into the opening of the nesting chamber. The unfolded smooth cloacal lining was not contaminated with sand at anytime and we did not observe any sand grains on the swabs (Fig 1a and1b). The cloacal vent folds in after egg-laying is completed.

Isolation of bacteria:

Four swabs were taken from each turtle, three being used to inoculate the following selective media; selenite-F, alkaline peptone and lactose broth-containing Durham tubes.

The other swab was directly streaked on nutrient agar. All media used in this study were obtained from Oxoid, UK.

The contents were then incubated in a portable incubator at 37°C for 24-48 hours. After inoculation, the tubes were streaked on the corresponding differential, selective media; Salmonella-Shigella (SS), thiosulfate-citrate-bille-sucrose (TCBS), and eosie-methyleneblue (EMB) agars respectively. The plates were also incubated at 37°C for 24-48 hours.

Swabs were also taken from cloacal lumen of five nesting turtles after these turtles finished laying and burying their eggs and began their movement toward the sea. During this time the smooth cloacal lining had returned to its normal inside and folded position (Fig 2a and2b). The turtle was then turned on its back, the cloacal vent was cleaned of sand, disinfected and a swab inserted into the cloaca (Fig 1c). However, there was difficulty in inserting the swab beyond 2-3 cm as the cloaca was withdrawn toward the inside and there was a general constriction in both the cloacal sphincter and the cloacal chamber. Even though the area around the sphincter was aseptically cleaned before insertion of the swab, there were still grains of sand on the swab when retracted from the cloaca. Therefore, this procedure was not used in this study and the data collected was used only for comparison with the data from the present swabbing procedure.

Sand samples:

Five sand samples near the turtle nests were collected aseptically and were then streaked on nutrient agar plates. The data were used for comparison with the results of egg-laying and the post egg-laying turtles.

Direct Oviductal Fluid Collection

Oviductal fluid was collected in 15-ml sterile test tubes as the turtle periodically discharged the oviductal fluid. The test tubes were then placed in an ice box and transported to the lab for microbiological analysis. A total of five turtles were sampled.

Identification of the isolates:

Characteristic colonies were selected and the isolates were identified biochemically by the standard Analytical Profile Index (API) system (New York). The API 20E system was used for identifying Enterobacteriaceae and the fermentative bacteria, while the API 20NE system was used for the identification of Vibrio and Aeromonas and other nonfermentative bacteria. Colonies from nutrient agar plates of the suspected Gram positive bacteria were identified by their cellular morphology using Gram and spore staining techniques.

Antibiotic susceptibility test:

One hundred and thirty-two bacterial isolates were tested for their susceptibility to antibiotics, using the disk diffusion method [START_REF] Bauer | Antibiotic susceptibility testing by standard single disk method[END_REF]) and according to the guidelines of the National Committee for Clinical Laboratory Standards (NCCLS). The cultures were incubated for 18-24 hours at 37 o C and the inhibition zones were measured.

Fifteen antibiotics were used: Amikacin (Ak) 30µg, Ampicillin (Amp) 10µg, Carbencillin (Cn) 100µg, Cephotaxin (Ctx) 30µg, Chloramphenicol (C) 30µg, Gentamycin (Gm) 10µg, Kanamycin (K) 30µg, Minocylin (Min) 30µg, Nalidixic acid (Na) 30µg, Neomycin (N) 30µg, Sulphamethyoxazole (Smx) 30µg, Streptomycin (S) 10µg. Tetracyclin (Te) 30µg, Tobramycin (Tob) 10µg, and Trimethoprim (Tmp) 5µg. Inhibition zone diameters were measured after 24 hours of incubation at 37°C. An Escherichia coli strain (ATCC 25922) and Pseudomonas aeruginosa strain (ATCC 27853) were used as controls for the disk diffusion assay.

RESULTS

A total of 132 species of bacteria from 7 genera were isolated from the swabs of the The isolates from the oviductal fluids were tested against fifteen antibiotics. All the isolates that were resistant to more than one antibiotic were considered to be multiple resistant bacteria. It was shown that 60.6% of these isolates were resistant to the tested antibiotics. The percentages/ratio of the multiple resistant isolates to the number of antibiotics were as follows: (11%:1), (16.7%:2), (38.9%:3), (13.9%:4), (5.6%:9), (5.6%:10), and (5.6%:11), and (2.8%:12) antibiotics (Fig. 4). Among the isolates, the highest resistance to antibiotics was Pseudomonas aeruginosa, which showed resistance to twelve antibiotics.

The majority of the isolates were resistant to ampicillin, streptomycin, and sulphamethoxazole (Fig. 5).

DISCUSSION

In this study, a swabbing technique was used for isolation of bacteria from the oviductal fluid during the egg-laying process. This procedure allows the examiner to insert a swab that reaches the vaginal lumen easily from where the fluid is secreted. The relaxation response observed during oviposition while the turtle was laying its eggs made it easier to insert the swab into the reproductive tract. This method is gentle and does not disturb the turtles during egg-laying and ensures that the samples are directly collected from the oviductal lumen with minimal contamination. The unfolding of the smooth cloacal lining occurred throughout the period of oviposition in all of the 40 turtles we observed. In the post egg-laying turtle the swab did not go beyond 2-3 cm. During this time, the oviductal fluid was not secreted and the swabbing was limited to the cloaca.

In this study, the oviductal fluid in the egg-laying turtles was heavily contaminated with bacterial flora. A total of 132 species from 7 genera were present. Over half of the isolates were Citrobacter spp. Moreover, isolates from the discharged oviductal fluid samples collected directly from the cloacal vent during oviposition were similar to that of the swabbing procedure. However, because of the unpredictability of the timing of oviductal fluid discharge, we did not rely on this procedure.

Isolates from the turtles that had already laid and buried their eggs were entirely different from the egg-laying turtles with exception of Citrobacter and Pseudomonas which were significantly lower than in egg-laying turtles. The dominant isolates in the post egglaying turtles were Bacillus spp. Surprisingly, the isolates taken from the sand near the nest showed a remarkable similarity to the isolates from turtles that had already buried their eggs, with Bacillus spp being the dominant. In both post egg-laying turtles and sand samples, there were close percentages for Micrococcus, Staphylococcus, and Pseudomonas spp.

Based on the present findings, it appears that the most likely source of contamination in the post egg-laying turtles was from the sand as the turtle was crawling or resting on the sand in a cyclical pattern while burying the eggs [START_REF] Alkindi | Oviductal morphology in relation to hormonal levels in the snapping turtle, Chelydra serpentine[END_REF]. The swabs were heavily contaminated with grains of sand, even though the plastron around the cloacal vent was disinfected and cleaned of sand prior to swabbing. Apparently, the grains of sand can find entry through the cloacal vent during the egg burying process. In addition, forcing the swab through the cloacal vent was difficult and harmful to the post egg-lying turtles due to the general constriction of the cloacal vent and the cloacal wall.

The present results indicate that swabbing after egg-laying does not represent the actual endogenous bacterial flora in the oviductal fluid, since the swab was restricted to only 2-3 cm beyond the cloacal vent. Moreover, vaginal glands which secrete oviductal fluid are located in the vaginal lumen [START_REF] Alkindi | Comparative study of the nesting behavior of green turtle, Chelonia mydas, during high and low population density periods at Ras Al-Hadd Reserve, Oman[END_REF] and secrete fluid only when the turtle lays eggs. Furthermore, the fluid which was collected directly from the vent while the turtle was discharging had similar results of bacterial flora to that of the swabbing technique during egg-laying. The close similarities between bacterial flora from the swabbing technique and the direct fluid collection is a clear indication that the isolates came from the same origin.

After ovulation, the eggs remain in the uterus for about two weeks for the shelling process which involves the formation of eggshell and eggshell membrane. Histological examination has revealed that there are secretory glands throughout the reproductive tract, secreting fluid during the process of eggshell formation and oviposition [START_REF] Alkindi | Oviductal morphology in relation to hormonal levels in the snapping turtle, Chelydra serpentine[END_REF]. During this time the eggs have enough time to be exposed to the contaminated oviductal fluid (Al-Bahry, 2009a).

In the green turtle, the eggs were collected directly from the cloacal vent while the turtles were burying eggs. Examination of freshly laid eggs revealed that the bacterial flora can penetrate all egg components, including eggshell, eggshell membrane, albumen and yolk (Al-Bahry 2009a).

Recent investigators have shown that ovaries and oviducts in chickens may be infected with microbes, which can be deposited inside the eggs before they are laid [START_REF] Wang | Bacterial penetration into eggs washed with various chemicals and stored at different temperatures and times[END_REF][START_REF] Berrang | Eggshell membrane structure and penetration by Salmonella typhimurium[END_REF]. This is known as vertical transmission. Also, the eggs can become horizontally contaminated with microbes if they are mixed with contaminated fecal material or other sources in the environment [START_REF] Catalano | Destruction of Salmonella enteritidis by high pH and rapid chilling during simulated commercial egg processing[END_REF].

In this study, no Escherichia coli were found either in the oviductal fluid samples during the egg laying period. This may suggest that during the swabbing procedure the samples were not contaminated by fecal materials. However, we do not rule out the possibilities of fecal contamination when the fluid passes through the cloacal chamber. Other investigators have isolated fecal coliforms in non-egg laying turtles [START_REF] Foti | Antibiotic resistance of Gram negatives isolates from loggerhead sea turtles (Caretta caretta) in the central Mediterranean Sea[END_REF][START_REF] Harms | Cloacal bacterial isolates and antimicrobial resistance patterns in juvenile loggerhead turtles in North Carolina, USA[END_REF][START_REF] Santoro | Aerobic bacterial flora of nesting green turtles (Chelonia mydas) from Tortuguero National Park, Costa Rica[END_REF].

In this study we used antibiotic resistant bacteria as bio-indicators of polluted effluents contaminating marine habitats and migratory routes. More than 60% of the isolates were resistant to antibiotics. The antibiotic resistant bacteria in marine turtles were used as bioindicators of marine pollution by contaminated effluents (Al-Bahry et al., 2009a;[START_REF] Foti | Antibiotic resistance of Gram negatives isolates from loggerhead sea turtles (Caretta caretta) in the central Mediterranean Sea[END_REF]. We hope that this non-invasive swabbing method will complement the previous method in assessing the degree of pollution in feeding and migratory habitats of marine turtles.

In this study, high levels of multi-drug resistance for Pseudomonas aeruginosa were found, and that resistance to ampicillin was the highest among the tested isolates.

Preliminary study by [START_REF] Harms | Cloacal bacterial isolates and antimicrobial resistance patterns in juvenile loggerhead turtles in North Carolina, USA[END_REF] reported high levels of multi-drug resistance among Pseudomonas aeruginosa isolates in the juvenile loggerhead sea turtles, (Caretta caretta) and resistance to penicillin and cephotaxin was almost 100%.

The development of multiple resistance to antibiotics is believed to be a result of widespread release of disinfectants and pharmaceutical products related to agriculture, human and veterinary practices [START_REF] Guardabassi | Antibiotic resistance in Acinetobacter spp. isolated from sewers receiving waste effluent from a hospital and a pharmaceutical plant[END_REF][START_REF] Kempski | Antibiotic resistant bacteria from Clemmys guttata (spotted turtle)[END_REF], Kümmerer, 2009a, Kümmerer, 2009b). The extensive use of antibiotics in both human and veterinarian medicine, together with agricultural runoff and coastal development, results in an increase in antibiotic resistant bacteria. Thus, marine animals are exposed to antibiotic residues and to multiple antibiotic resistant bacteria (Al-Bahry et al., 2009aand b, Foti et al., 2009, Kumerer, 2009a and b;[START_REF] Miranda | Antibiotic resistant bacteria in fish from the Concepcion Bay, Chile[END_REF]Zemelman, 2001, Schmidt et al., 2000). It was also reported that antibiotic resistant bacteria from pelagic fish captured in the Concepcion Bay, Chile revealed a high incidence of resistance found among the isolates [START_REF] Miranda | Antibiotic resistant bacteria in fish from the Concepcion Bay, Chile[END_REF]. Al-Bahry et al., (2009b) reported that there is strong evidence that infection of fish by antibiotic resistant bacteria is directly related to the treated sewage effluent. Multiple resistant bacteria to antibiotics remain viable in sewage treated effluent even after disinfection and was disseminated in the marine environment (Al-Bahry et al., 2009c). [START_REF] Hühnerfuss | Occurrence, distribution and fate of pharmaceuticals and further polar contamination in the marine environment[END_REF], reported that the use of pharmaceuticals can find its way into the environment via different pathways. Compounds applied in human medicine and their metabolites are released through urine and feces into sewer systems.

The presence of antibiotic resistant bacteria in marine animals, such as the green turtle, acts as an indicator of pollution in marine habitats. The Ministry of Regional Municipalities, Environment and Water Resources [START_REF] Mrmewr | Marine Pollution and Coastal Zone Management Section: Indian Ocean South-East Asian Marine Turtle Memorandum of Understanding[END_REF], observed that the migration patterns of the green turtles involve a wide geographical region including the Arabian Gulf, Arabian Sea and the northern sector of the Indian Ocean. Thus, the green turtles are exposed to different polluted effluents in their feeding grounds as well as their migratory routes. Thus, it is not practical to survey all the localities along the migratory routes for the presence of pollution. Therefore, monitoring the presence of the antibiotic resistant bacteria is more practical and valuable for detection of the magnitude of pollution along the migratory routes.

Ras Al-Hadd Reserve, Oman, hosts one of the largest nesting population in the world for the green turtles. Thousands of turtles migrate to the region to nest year round [START_REF] Alkindi | Comparative study of the nesting behavior of green turtle, Chelonia mydas, during high and low population density periods at Ras Al-Hadd Reserve, Oman[END_REF]. Thus, choosing this species is particularly helpful in monitoring environmental marine pollution in the northern sector of the Indian Ocean. Accordingly, the present investigation will be of value to trace the sources of polluted effluents which are impacting habitats specifically along the migratory routes of marine turtles.

International cooperation is urgently needed for the implementation of the conservation programs for the preservation of this endangered species.

  oviductal fluid collected from 40 turtles during the egg-laying process. All the samples contained bacteria. The percentage frequencies of the isolates in the swabs were as follows: Citrobacter spp. (51.4%), Pasteurella spp. (16.3%), Pseudomonas spp. (11.6%), Salmonella spp. (11.6%), Proteus spp. (4.7%), Aeromonas spp. (2.1%), and Shigella spp.(2.3%). Citrobacter spp dominated the other isolates (Fig 3). The frequency percentage of bacteria in the turtles isolated from the cloacal vent of the post egg-laying turtles were Bacillus spp (72.1%), Micrococcus spp. (9.6%), Staphylococcus spp (8.9%), Pseudomonas spp (5.1%) and Citrobacter spp. (4.3%). The swabs were contaminated with grains of sand. The sand isolates were Bacillus spp (82.1%), Micrococuus spp (7.6%) Staphylococcus spp (6.7%) and Pseudomonas spp (3.6%). Bacterial flora from the oviductal fluid, collected directly in the discharge from the cloacal vent of the nesting turtles, was similar to the bacteria isolated from the swab samples. These isolates were: Citrobacter spp. (47.5%), Pasteurella spp. (16.7%), Pseudomonas spp. (14.8%), Salmonella spp. (14.5%), Proteus spp. (5.3%), Aeromonas spp. (1.2%). Direct fluid collection was not used because of the unpredictable timing of the oviductal fluid discharge and the chance of possible external contamination. Escherichia coli were not present in either the swab samples or the oviductal fluids.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Swabbing technique of oviductal fluid collection in green turtles; a and b = during egg-laying, note the unfolded smooth cloacal lining; c = swabbing of constricted cloacal sphincter muscle showing plastron view during post egg-laying.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Percentage frequency of bacteria isolated from the oviductal fluids. A=Citrobacter spp, B=Pasteurella spp, C=Salmonella spp, D=Pseudomonas spp, E=Proteus spp, F=Aeromonas spp, G=Shigella spp

Fig. 5 :

 5 Fig. 5: Percentage frequencies of resistant bacteria to specific antibiotic. Amp = Ampicillin, S = Streptomycin, Smx = Sulphamethoxazole, Te = Tetracycline, Cn = Carbenicillin, K = Kanamycin, Min = Minocyline, Ctx = Cephotaxime, Na = Nalidixic acid, C = Chloramphenicol, Tmp = Trimethoprim, Ak = Amikacin, Tob = Tobramycin, Gm = Gentamicin, N=Neomycin.

Acknowledgement:

We thank Mr Majid Al-Khanjari, for his technical assistance in preparation of the drawings.


W C H Parr

A Ruto

C Soligo
email: c.soligo@ucl.ac.uk

H J Chatterjee
email: h.chatterjee@ucl.ac.uk

Allometric shape vector projection: A new method for the identification of allometric shape characters and trajectories applied to

Keywords: scaling, canonical sampling, laser scanning, principal components analysis, allometry

HAL is a

Introduction

The geometric morphometric method combines Galton's multivariate techniques, which are based on covariance matrices of a number of measurements designed to capture the metrics of a biological object, with D'Arcy Thompson's direct visualisations of simple geometric transformations leading to differing biological forms [START_REF] Thompson | On Growth and Form[END_REF]. The key to the geometric morphometric method is to identify discrete homologous 'landmark' points, which can be identified reliably across the sample. Landmarks enable individual biological forms to be described as well as mathematically defining the morphological transformations that warp one form to the shape of another. However, in complex biological forms such as post-cranial bones and whole bodies, and particularly in three dimensional analyses, truly homologous landmarks are difficult to locate in sufficient abundance to accurately describe the form of the object [START_REF] Gunz | Landmarks in Three Dimensions[END_REF]. In such cases Bookstein [START_REF] Bookstein | Morphometric Tools for Landmark Data: Geometry and Biology[END_REF] advocates the use of type III landmarks. Gunz et al [START_REF] Mitteroecker | Advances in Geometric Morphometrics[END_REF] and Mittereocker et al [START_REF] Adams | Geometric Morphometrics: Ten Years of Progress Following the 'Revolution[END_REF] have applied type III semi-landmarks across the surface of skulls to create slid semi-landmarks [START_REF] Adams | Geometric Morphometrics: Ten Years of Progress Following the 'Revolution[END_REF].

The use of the landmark based methods of geometric morphometrics for describing shape differences between specimen samples habitually contains the following steps [6, 7, 8 9, 10]: selection of homologous landmark points on all specimens within a sample, alignment of specimens by standardisation (centering by translation, rotational transformation and scaling) of landmark coordinate points before examination of the remaining shape differences between specimens by Principal Components (PC) analysis [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF]. For 2D and 3D landmarks and semi-landmarks, scaling is commonly achieved by division of coordinates by the centroid size, as described in Gower [START_REF] Gower | Generalized Procrustes analysis[END_REF] and Rohlf and Slice [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF]. The centroid of each specimen is calculated as the mean of the specimen's coordinates and the centroid size is represented by the squared root of sum of squared distances to each of the coordinate points from the centroid [START_REF] Gower | Generalized Procrustes analysis[END_REF]. Scaling aims to remove the effects of geometric scaling in the data. Any residual differences in the measurements or coordinate data of different specimens after translation, scaling and rotation will therefore correspond to shape rather than shape, size and orientation [START_REF] Gower | Generalized Procrustes analysis[END_REF] as shape is defined as the aspects of form remaining once size has been removed [START_REF] Mosimann | Size allometry: Size and shape variables with characterizations of lognormal and generalized gamma distributions[END_REF][START_REF] Van Der Linde | Inferring the Nature of Allometry from Geometric Data[END_REF]. However, in some cases, such as analyses concerned with intra-specific allometric shape characters, it may be advantageous not to scale the data sets before performing PC analysis. If an analysis of the un-scaled data is performed, then PC 1 is likely to identify 'size' as the major difference between bone specimens in a sample. Crucially however 'size' will incorporate geometric size differences between specimens and also all of the size correlated morphological differences in the specimens [START_REF] Ruto | Comparing Principal and Independent Modes of Variation in 3D Human Torso Shape using PCA and ICA[END_REF][START_REF] Ruto | Dynamic human body modeling and animation[END_REF][START_REF] Parr | Evolutionary and functional anatomy of the hominoid astragalus-new approaches using laser scanning technologies and 3D analyses[END_REF].

Harcourt-Smith [START_REF] Harcourt-Smith | Form and Function in the Hominoid Tarsal Skeleton[END_REF] and Hellier and Jeffrey [START_REF] Hellier | Morphological Plasticity in the Juvenile Talus[END_REF] analysed allometry in the astragalus of human and non-human apes. Both studies took landmark and semi-landmark 3D coordinates as their initial data. Following Procrustes superimposition (translation, rotation and scaling), a PC analysis was performed and the size proxy (centroid size in Harcourt-Smith [START_REF] Harcourt-Smith | Form and Function in the Hominoid Tarsal Skeleton[END_REF] and femur length in Hellier and Jeffrey [START_REF] Hellier | Morphological Plasticity in the Juvenile Talus[END_REF]) was correlated with PC scores. In this way, the authors determined how much of the shape difference captured in each PC was the result of size differences between astragali, i.e. reflected allometric shape variation. This methodology generally resulted in relatively low correlations (r < +/-0.4) between size and individual PCs and many PCs being minimally correlated with size. Therefore, no single PC identified shape differences in the astragali that were solely the result of size differences. This makes it difficult to identify exactly which shape differences in the astragali are the results of size differences alone.

Aims

This paper aims to further the geometric morphometric tool set available to biologists interested in understanding 3D allometric shape change. As Van der Linde and Houle [START_REF] Van Der Linde | Inferring the Nature of Allometry from Geometric Data[END_REF] point out, biologists frequently use visualisations of the patterns of covariances identified by their morphometric analyses to understand the nature of the variation in biological shapes they are examining. The method introduced here has been specifically designed to allow visualization of complex 3D shape changes that are related to differences in size (i.e. allometric shape changes) in bones, or other 3D objects, that do not have many readily identifiable Type I or II landmarks [START_REF] Bookstein | Morphometric Tools for Landmark Data: Geometry and Biology[END_REF] that are truly biologically homologous and can be repeatedly located across most of their surfaces throughout a sample [START_REF] Gunz | Landmarks in Three Dimensions[END_REF]. The subject of this study is the modern human astragalus; a particularly globular bone, which is devoid of Type I landmarks [START_REF] Harcourt-Smith | Form and Function in the Hominoid Tarsal Skeleton[END_REF][START_REF] Hellier | Morphological Plasticity in the Juvenile Talus[END_REF][START_REF] Lewis | Functional Morphology of the Evolving Hand and Foot[END_REF]. The new methodology presented in this study of canonical sampling of whole surface morphology in conjunction with allometric vector identification and projection aims to isolate allometric shape characters in adult human astragali.

Methods

The astragali examined for this study were housed in the Department of Palaeontology at the Natural History Museum (NHM) in London. A total of 59 adult human astragali were included in the study, with 24 from confirmed males, 29 from confirmed females and 6 unknowns. Male and female status was confirmed either by grave records or by gender records determined from skeletal morphology and kept by the NHM. Specimens were chosen that did not show any osteological signs of pathologies such as bone breakages or osteoarthritis. Table 1 shows the population breakdown of the astragali used in this study. The sample was composed of different ethnic groups as the aim of this study was to identify general allometric shape characters that apply to the species Homo sapiens, rather than of a specific ethnic group. Adult specimens were selected as having full epiphyseal fusion of the long bones.

A Konica Minolta Vivid 910 surface laser scanner was used to capture the entire surface morphology of each astragalus. The scanner is accurate to X: ±0.22mm, Y: ±0.16mm, Z: ±0.10mm. Surface data are initially captured and processed using the scanner's associated software package, Polygon Editing Tool [START_REF] Pet | Polygon Editing Tool[END_REF] before being further edited in RapidForm 2006 [START_REF]RapidForm 2006[END_REF]. The initial astragalus scans resulting from PET would often have small holes or other scanning artefacts due to the merging process not succeeding in integrating the initial scans flawlessly. These holes were filled using RapidForm 2006 [START_REF]RapidForm 2006[END_REF] with either the hole filling tool or the defeature tool (for scanning artefacts). The hole filling and defeature tools use the curvature of the model around the hole or scanning artefact to re-mesh the model's surface so that the result is consistent with the surrounding model's surface. The resulting shells (Figure 1), or virtual 3D bones, are made up of point clouds and triangles. The points have x, y, z coordinates in 3D space, and the triangles are created by joining these 3D points (for detailed method see Parr [START_REF] Parr | Evolutionary and functional anatomy of the hominoid astragalus-new approaches using laser scanning technologies and 3D analyses[END_REF]).

Canonical sampling

The canonical sampling process aims to give an accurate representation of the whole surface morphology of astragali. The procedure for canonically sampling the astragali is as follows. The bones are aligned with their length running along the x-axis (in 3D space), their widths running along the y-axis, and their depths along the z-axis. This is achieved by rotating each model so that the principal axes are aligned with the global 3D axes, with principal axis 1 aligned to the global x-axis, principal axis 2 aligned with the global y-axis, and principal axis 3 aligned with the global z-axis. All remaining differences in orientation of the bones are then minimised by ICP (Iterative Closest Point) registration of all of the specimens [START_REF] Besl | A method for registration of 3-D shapes[END_REF]. This process is similar to a Procrustes registration, except that the ICP algorithm does not need each bone model to have the same number of points, or the points to be homologous [START_REF] Besl | A method for registration of 3-D shapes[END_REF]. ICP registration relies on matching the surface morphology of the bone models and ensures that they are in similar orientations. Note that at this point the astragali models have not been scaled. Each 3D bone model is then divided up into 50 slices along its length. Each of these 50 slices is then sampled 50 times along its circumference; this forms the canonical sample [START_REF] Ruto | Dynamic human body modeling and animation[END_REF][START_REF] Buxton | Point distribution models of human body shape from a canonical representation of 3D scan data[END_REF][START_REF] Douros | Web-based software tools for 3d body database access and shape analysis[END_REF]. Bone models of varying length are still sampled into the same number of slices (50), with the slices spread evenly from the posterior to the anterior extremes of the bone model [START_REF] Ruto | Comparing Principal and Independent Modes of Variation in 3D Human Torso Shape using PCA and ICA[END_REF][START_REF] Ruto | Dynamic human body modeling and animation[END_REF][START_REF] Buxton | Point distribution models of human body shape from a canonical representation of 3D scan data[END_REF][START_REF] Douros | Web-based software tools for 3d body database access and shape analysis[END_REF]. Slices of varying circumference are sampled into the same number of radial points (50) based on a fixed radial segmentation. Therefore, repeating the sampling process always produces the identical result as each bone is sampled using the identical slice and radial segmentation process [START_REF] Ruto | Comparing Principal and Independent Modes of Variation in 3D Human Torso Shape using PCA and ICA[END_REF][START_REF] Ruto | Dynamic human body modeling and animation[END_REF]. This canonical sampling process was described by Ruto [START_REF] Ruto | Dynamic human body modeling and animation[END_REF], Ruto et al.

[13], Buxton et al [START_REF] Buxton | Point distribution models of human body shape from a canonical representation of 3D scan data[END_REF], Douros et al [START_REF] Douros | Web-based software tools for 3d body database access and shape analysis[END_REF]. The process is different from processes used by Polly [START_REF] Polly | Adaptive zones and the Pinniped ankle. A three dimensional Quantitative analysis of Carnivoran Tarsal Evolution[END_REF], Gunz et al [START_REF] Mitteroecker | Advances in Geometric Morphometrics[END_REF], Mittereocker et al [START_REF] Adams | Geometric Morphometrics: Ten Years of Progress Following the 'Revolution[END_REF], which are variations of template optimisation, in that rather than laying a grid over one aspect of a bone's surface, the canonical sampling process uses the 3D points that make up the original bone model's surface. The canonical representations for this study are made up of 50 rows of canonical points, with each row having 50 points in it, resulting in an initial 2500 canonical points describing the whole bone surface. The canonical samples were sub-sampled (every third canonical point dropped) to reduce point density, but not to the extent of loosing overall surface morphology resolution. To avoid over-sampling the posterior end, which is narrower than the rest of the astragalus, the first row was further point reduced by keeping only every fourth point. The final canonical samples used consisted of 1617 points [START_REF] Parr | Evolutionary and functional anatomy of the hominoid astragalus-new approaches using laser scanning technologies and 3D analyses[END_REF].

The canonical points are spatially rather than biologically homologous. For example, canonical point 1 in the 25th row of the canonical sampling cylinder will always be half-way along the length of the 3D virtual bone model. This is different to landmarks or pseudo-landmarks for which the stated aim is to be biologically equivalent, but is similar to slid semi-landmarks [START_REF] Gunz | Landmarks in Three Dimensions[END_REF]. However, the spatial equivalence of the canonical points conveys biological meaning in a similar way as traditional linear measurements of distances, where these are not anchored at either end by structurally homologous points (such as, e.g., maximal cranial width). For instance, it is conceivable that someone could describe a particular projection on a bone in a ratio form: in specimen A the projection occurs at 1/4 the length of the bone, whereas in B the same projection occurs at 3/4 the length of the bone. Similarly if there is a difference in the position of a canonical landmark between specimens A and B, we know this corresponds to a difference in morphology between bones A and B, which allows for quantification of differences in the surface morphologies of A and B.

Acquiring size related shape (allometric) characteristics

The resulting canonical models were Procrustes aligned (translated and rotated, but not scaled). PC analysis was performed on the un-scaled canonical models. The expectation was that the first PC identified by this analysis would represent size related shape variation, including both geometrically and allometrically scaled characters. The extent to which PC 1 identifies size related shape variation was tested by regression analysis of specimen PC 1 scores on centroid size, with a high R 2 value (> 0.9) indicating a strong correlation with size. In order to test for a major influence (other than size) on residual variation in PC1 scores, we performed t-tests on the means of the residual values for males vs. females and for individuals from populations that are typically shod vs. those from populations that are typically unshod. Next, the eigenvectors for PC 1 were used, in conjunction with the maximum and minimum PC 1 scores, to calculate and draw the PC 1 positive and negative extreme astragalus shapes. This concluded the first stage of the analysis, resulting in a large bone shape and a small bone shape.

The second stage of the analysis was to identify the allometric shape characters. This was achieved by first performing a Procrustes size adjustment followed by rotational transformation and translation of the two (i.e. large and small) PC 1 extreme shape models defined in the first stage [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF][START_REF] Gower | Generalized Procrustes analysis[END_REF]. Following this step the two PC 1 extreme shape models have a centroid size of 1, have the same orientation, are centred on the origin ({x, y, z} = {0, 0, 0}) and consist of 1617 spatially homologous 3D coordinate points. All calculations were performed in Mathematica [START_REF][END_REF] using code developed according to algorithms in Rohlf and Slice [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF]. At this stage the size adjusted PC 1 extreme shape models were in 3D point cloud form. For visualisation purposes these can be converted to 'solid' polygon models by triangulation between the 3D coordinate points. This was performed in Rapidform 2006 [START_REF]RapidForm 2006[END_REF].

The third stage of the analysis assessed which areas of the size adjusted PC 1 extreme shape models exhibit the greatest degrees of size correlated shape change. This was achieved by first calculating the magnitudes of all of the distances between the homologous points. Following this, the 250 homologous points which showed the greatest differences in 3D position, as indicated by having the greatest magnitude of distance, were selected. 3D arrows were then drawn between all of these 250 homologous points, starting at what was the original 'small' PC 1 extreme shape and ending at what was the original 'big' PC 1 extreme model. Only the largest 250 vectors were selected for illustration, as displaying all 1617 vectors would have been visually confusing. This effectively created a vector map of the areas of the PC 1 astragali models exhibiting the most pronounced size related (allometric) shape changes, and indicated in which 3D direction these allometric shape changes occur. Examination of the allometric vector maps, rather than the movements of individual landmarks, conveys the information about the allometric shape characters. This is because the canonical points and allometric vector maps give information on spatial differences between the surfaces of astragali models rather than movements of biologically homologous points on the bones differences as is the case with true landmarks.

Allometric vector identification and extrapolation method validation

To test whether using the allometric projection as the model for the shape of an astragalus of a particular size is more accurate than using the mean astragalus shape of a sampled population, additional astragali models were created. These models were created by warping the mean astragalar shape for the canonically sampled astragali along the allometric vectors to create an astragalus shape predicted by the allometric vectors for each original canonical astragalus according to its size. We can then ascertain to what degree (mathematically) the shape of an adult human astragalus can be predicted using the allometric vector projection technique. The model pairs (original canonical astragalus and allometric projection) were Procrustes aligned with one another (translated and rotationally transformed but not scaled as the model pairs have the same centroid size) before the mean squared difference (MSdiff) in canonical landmark positions were calculated. The MSdiff is an overall (average) measurement (in mm) of how close two models are to one another in shape. In the present analyses, MSdiffs vary from 0.67 to 2.50mm. The MSdiff was also calculated for the original models paired with scaled mean shape models (these model pairs were Procrustes rotated and translated and had the same centroid sizes). MSdiffs varied from 0.84 to 3.07mm; greater maxima and minima than for the allometric projections paired with the original models. In 47 out of the 59 models (80%) the MSdiffs were lower between the Procrustes aligned original and their corresponding allometric projection than between the same Procrustes aligned original and the mean shape, showing that in the majority of cases the astragalus model created by allometric projection was closer than the mean astragalus model's shape to the actual astragalus model's shape.

To test for differences in allometric vectors between males and females, which could, for example, result from the subtle differences in gait between males and females [START_REF] Wang | Comparison of inverse-dynamics musculo-skeletal models of AL 288-1 Australopithecus afarensis and KNM-WT 15000 Homo ergaster to modern humans, with implications for the evolution of bipedalism[END_REF], the male and female astragali were analysed separately. The PC scores were regressed against centroid size separately for the male and female groups. This suggests that projection along allometric vectors can be used to create more accurate models than a species mean shape in cases where an allometric stage is not documented and, hence, both justifies the use of allometric shape vector projections as a tool for quantifying allometric shape change in relatively feature-less bones such as the astragalus and opens the possibility of extrapolating allometric shape variation beyond the range of existing samples.

Results

Method validation

Principal Components Analysis of un-scaled (but translated and rotated) canonically sampled astragali resulted in the first 10 PCs describing 90.75 % of total variance. Of these, PC1 described 71.18% of total variance, followed by PC2 with 8.67% and PC3 with 2.18% of total variance. Regression of PC 1 against centroid size resulted in a very strong correlation (R 2 = 0.999, confidence level = 0.99) suggesting that PC 1 is strongly associated with size and size correlated shape variation (Figure 2). Regressions of PCs 2-10 gave very low R 2 values (max = PC2: 0.00221, min = PC7: 2.12x10 -7 ). This suggests that PC 1 captures nearly all of the total size related shape variation. For the separate analyses of male and female astragali, Figure 3 shows that in both cases PC 1 identifies size and size correlated shape (male R 2 = 0.997, female R 2 = 0.998) and that males are larger than females as the y intercept of the regression line for males is -12.594 [99% CIs = -13.013, -12.175] as opposed to females where the y intercept = -10.914 [99% CIs = -11.158, -10.670]). Additionally, the scaling exponents for the regression lines (male = 0.0148 [99% CIs = 0.0143, 0.0153], female = 0.0147 [99% CIs = 0.0144, 0.0151]) are very similar (not significantly different at a P = 0.01 level). This indicates that the relationship of PC 1 with centroid size is essentially the same in both male and female groups.

Results of the method as applied to adult human astragali

The variation in size between the two extreme shapes shown in Figure 4 indicates that PC 1 isolated size differences in the astragali. The allometric shape characters identified by PC 1 for the astragalus are illustrated by the diagrams shown in Figures 5, 6 and7. In Figures 5 and6 the 250 canonical landmarks that differ the most between the PC 1 extreme shape models are identified by red arrows running from the blue (original small model) to the yellow (original big) model. These groupings of arrows (the allometric vector maps) illustrate the main regions of allometric shape differences between small and large astragali models.

The main regions of allometric shape differences, from the dorsal view, are: the lateral head, medial facet and medial trochlea, the anterior lateral trochlea, the lateral projection and posterior trochlea regions of the astragalus (see the clustering of red 3D arrows in the dorsal view of the size adjusted PC 1 extreme shape models as shown in Figure 5A and see Figure 1 for annotations for the different facets and regions of the astragalus; see Video 1 for an animation of the allometric shape change from the dorsal view). From the plantar view the allometric shape variations are: the posterior and anterior calcaneal facet regions, the posterior region of the sustentaculum facet, the medial region of the head and the lateral projection regions of the astragalus (see Figure 5B and Video 2).

From the anterior view (Figure 6A) the main regions of allometric shape difference are the lateral head region, the medial facet and the anterior lateral region of the trochlea facet.

From the posterior view (Figure 6B and Video 3) they are the anterior and posterior regions of the calcaneal facet and the posterior regions of the trochlea and lateral facets. The main regions of allometric shape differences from the medial view (Figure 7A), are: the posterior region of the trochlea facet and the anterior region of the medial facet and from the lateral view (Figure 7B and Video 4): the posterior calcaneal facet and lateral head (and neck) regions.

Discussion

Canonical sampling

The methodology featured in Adams et al [START_REF] Adams | Geometric Morphometrics: Ten Years of Progress Following the 'Revolution[END_REF] and Gunz et al [START_REF] Gunz | Landmarks in Three Dimensions[END_REF], described in Mitteroecker and Gunz [START_REF] Mitteroecker | Advances in Geometric Morphometrics[END_REF], used, a variation of template optimisation, which consists of decimating the 3D point cloud of a reference skull until it is represented by only a few roughly evenly spaced semi-landmarks and warping this template to the shape of another specimen. An important difference between template optimisation and canonical sampling techniques is that canonical sampling gives a more accurate representation of an object because the final subset of data is a subset of each object's original points. Template optimisation gives as close an approximation to this as possible, based on optimising the shape of a template to match the object. This optimisation process finds a least squares fit for corresponding landmarks on template and object, while maintaining the template's topology (connectivity or relationship between the template's points). This connectivity can limit the positioning accuracy of a template's landmarks on an object and thus lead to a less accurate object representation when compared against the object's original point set For the purposes of object shape representation, each method is slightly different as outlined below.

Template Optimisation (TO):

1. TO provides a means of placing landmarks on a shape based on a predefined template with an existing topology.

2. The resulting landmarks are approximate positions on the target shape (in other words, the landmarks are not taken from the original model) but are optimised to give a least squares fit between the template shape and target object shape.

3. When assessing the shape variation of a large sample, the general shape variability of the sample can be captured using template representations of the data. However, this variability will include the representation error of the template optimisation technique used [START_REF] Ruto | Dynamic human body modeling and animation[END_REF].

Canonical sampling (CS):

1. CS provides a sample of an object's original data at predefined locations. Where no data are present at those locations, an approximation is used. It is important to note that highly accurate initial models, such as those achieved by the surface laser scanner used in this study, result in more accurate canonical representations essentially containing a larger proportion of the original data points.

2. Canonical sampling does not produce a representation error other than when approximate points are used.

3. When used for assessing shape variations, canonical sampling relies on the object shapes being similar so that sampling them at specific locations will result in representations that are similar in terms of the regions of whole shape they represent. The PC analysis will then capture the shape variability in these regions. This is the essence of the spatial homology of the canonical landmarks and why allometric vector maps are important rather than movements of individual landmarks. Template optimisation is reliant on choosing a suitable density of landmarks for each region of the original template specimen.

4. Variability between models results from actual shape variation between specimens and the representation error of the sampling procedure. The models generated by canonical sampling have a smaller representation error and hence provide a more accurate shape representation [START_REF] Ruto | Dynamic human body modeling and animation[END_REF]. Ruto [START_REF] Ruto | Dynamic human body modeling and animation[END_REF] found that for human whole body shape in a sample that would be expected to have the same shape variability, the template representation model has a larger total variation (or entropy) than the canonical representation model, thus indicating the representation error was larger in the template representation model. This confirmed that canonical sampling was a more accurate technique for assessing body shape variation. Hence, for sampling of bones such as the astragalus or 3D objects such as whole bodies [START_REF] Ruto | Dynamic human body modeling and animation[END_REF] which are naturally devoid of both Type I and Type II landmarks [START_REF] Bookstein | Morphometric Tools for Landmark Data: Geometry and Biology[END_REF] canonical sampling can be preferable to template optimisation.

Identification of allometric vectors and their use to create allometric projections

With the allometric vector method presented here, it is the allometric vector maps, which are created by drawing the 250 allometric vectors with the greatest magnitude, rather than individual landmarks, that elucidate size correlated shape changes which occur in the sample. The allometric vector maps are virtually identical if the scaled PC 1 extreme shape models are not re-aligned (results not presented). However, we recommend performing the second alignment step so as to minimise any orientation differences in the PC 1 extreme shape models. This re-alignment may not be necessary, if there are no size correlated orientation differences in the canonical representations, but it effectively minimises the magnitudes of the allometric vectors. We advise against the use of sub-set superimposition in the case of allometric vector identification [START_REF] Van Der Linde | Inferring the Nature of Allometry from Geometric Data[END_REF]. This is because sub-set superimposition, as with Procrustes resistance fit superimposition, is designed to align specimens using the landmarks that are not influenced by allometry [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF][START_REF] Van Der Linde | Inferring the Nature of Allometry from Geometric Data[END_REF][START_REF] Rohlf | Shape statistics: Procrustes Superimpositions and Tangent Space[END_REF][START_REF] Siegel | A Robust Comparison of Biological Shapes[END_REF]. However, as we identify allometric shape variation for all of the canonical landmarks, none of them can be considered suitable for use in subset superimposition. Additionally, affine superimposition is not suitable in the case of the allometric shape characters presented in this paper, as there is no obvious allometric affine transformation occurring in any axis of the astragalar shape [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF][START_REF] Van Der Linde | Inferring the Nature of Allometry from Geometric Data[END_REF].

How well the allometric projections approximated the shape of the original canonical models was calculated as the mean squared difference (MSdiff) between the location of the canonical landmarks in the original and allometric projection model. In the 12 cases where the mean shape had a lower MSdiff than the allometric projection, the difference in MSdiff between the mean and allometric projection was very slight (often 1 or 2 orders of magnitude lower than the average difference in MSdiff between the mean and allometric projection models). This indicates that using allometric projection as the model for the shape of an astragalus of a particular size is usually more accurate than using the mean astragalus shape of the sampled population. Frequently, in cases where the MSdiff for the allometric projection was greater than for the mean shape, the original astragalus exhibited fairly unique shape characters not habitually observed in the remainder of the sample.

Application of allometric vector and projection techniques in adult human astragali.

Intra-specific allometric shape characters identified in the human astragalus.

Figure 5A (dorsal view) shows that the anterior medial region of the trochlea facet and anterior lateral region of the astragalar head exhibit allometric shape change. These changes lead to the apparent decrease in horizontal astragalar neck angle with increasing size, as described by Day and Wood [START_REF] Day | Functional affinities of the Olduvai Hominid 8 talus[END_REF] and Lewis [START_REF] Lewis | Functional Morphology of the Evolving Hand and Foot[END_REF] and reduced medial facet curvature observed in the larger (yellow) model in Figure 4 when compared to the smaller (blue) PC 1 extreme shape model. The biomechanical consequence is that the path of force transmission is aligned across the trochlea facet, through the astragalar neck, to the head facet and on to the navicular, as described by Day and Wood [START_REF] Day | Functional affinities of the Olduvai Hominid 8 talus[END_REF]. Further, the reduced medial facet curvature causes less medial movement of the tibia during dorsi-flexion of the foot (during the pre toe-off stance phase of the gait). These both potentially lead to comparatively less strain in the astragalar neck of the larger individuals (as suggested by Gebo and Schwartz [START_REF] Gebo | Foot bones from omo: Implications for hominid evolution[END_REF]). The plantar view shows that the anterior (eversion) half of the calcaneal facet appears relatively smaller and re-orientated in the larger (yellow) model whereas the posterior (inversion) half of the facet appears expanded and re-orientated in the big (yellow) model (inversion and eversion facet halves defined as in Wang et al [START_REF] Wang | Contact areas and pressure distributions in the subtalar joint[END_REF]).

From this analysis alone, it is difficult to conclude what the cause of this allometric shape change is and if they have any functional consequences.

Male versus female allometric vector maps

The medial expansion of the anterior medial region of the trochlea and the consequent medial displacement of the medial facet identified in the analysis of the combined male and female samples is not identified as one of the major allometric shape differences in the dorsal view of the male allometric vector map (Figure 8A). Instead, the lateral shift (with increased size) of the medial region of the astragalus head is identified as the region of the medial aspect of the astragalus with the strongest allometric shape difference. The male allometric vector map shows that with increased size the astragalus head becomes re-aligned with the trochlea body and trochlea groove by moving laterally, rather than the trochlea body expanding medially. The lateral expansion of the head in the larger male specimens is possibly a late onset allometric growth pattern as it does not seem to 'outweigh' the medial expansion of the anterior trochlea region in the whole sample analysis. If the astragalus head and trochlea alignment is a functional requirement for efficient and safe (with respect to strains generated in the astragalus) bipedal locomotion in large individuals, then this realignment may be more extreme in larger males compared to both smaller males and females [START_REF] Day | Functional affinities of the Olduvai Hominid 8 talus[END_REF][START_REF] Gebo | Foot bones from omo: Implications for hominid evolution[END_REF]. This is because males will experience greater force transmission through the tarsal region due to greater body mass compared to females.

The plantar views in Figure 5B and6 show that the lateral region of the calcaneal facet does not exhibit as much allometric shape change in the female astragali as it does in the male astragali and in the whole human sample. As a result, the calcaneal facet appears relatively larger with respect to overall astragalus size in the females and smaller males than in the larger males (Figure 8). Similarly, the posterior region of the sustentaculum facet shows more allometric change in the whole sample and the male specimens than the female sample. These differences in allometric trajectories may be the result of ossification and growth cessation of the astragalus occurring considerably earlier than growth cessation of other foot bones and overall body growth cessation [START_REF] Scheuer | Developmental juvenile osteology[END_REF][START_REF] Humphrey | Growth patterns in the modern human skeleton[END_REF] and in different processes controlling the overall size of the astragalus (proposed to be genetic control) compared to the size of articular facets (epigenetic; the need to fit with the morphology of their articular partner). This is true in males compared to females [START_REF] Scheuer | Developmental juvenile osteology[END_REF][START_REF] Shea | Heterochrony in Primates[END_REF], and potentially larger males compared to smaller males [START_REF] Scheuer | Developmental juvenile osteology[END_REF][START_REF] Shea | Heterochrony in Primates[END_REF]. In such a scenario, larger males would grow for even longer than the smaller males (growth duration hypermorphosis [START_REF] Shea | Heterochrony in Primates[END_REF]) after astragalar growth cessation (when the morphology of the astragalar calcaneal facet is fixed). This results in the differences in allometric characteristics observed in the male compared to female calcaneal facet. Thus, Figure 8 shows that although the size correlated shape and allometric vectors identified in males and females are similar, there are differences.

Conclusion

The method developed in this study, of identifying size related, allometric, shape characteristics in canonically sampled whole bone models, was successful in identifying and isolating intra-specific allometric shape characters in the adult human astragalus, a bone which typically lacks type 1 landmarks and has, consequently, proved difficult to analyse using traditional 3D morphometric methods. The method first Procrustes rotates and translates (but does not scale at this stage) the canonical representations. PC analysis is then performed on the un-scaled, but otherwise aligned, models. PC 1 extreme shapes are calculated and then Procrustes superimposed (rotated, translated and scaled). The 250 largest allometric vectors between spatially homologous canonical points in the scaled (originally) small and (originally) large models are then calculated and displayed on the Procrustes superimposed PC extreme shapes, creating allometric vector maps. These vector maps, rather than individual landmarks, allow for the identification of the main regions, directions and amplitudes of allometric shape change in relatively featureless bones such as the astragalus. Our new method differs from previous methods, which Procrustes scaled (and aligned) data before performing Principal Components (PC) analysis. In such analyses, the size related shape characteristics are frequently spread through a number of PCs, all of which typically show fairly low correlations (r < +/-0.4) with the size (or body mass) proxy, making it hard to determine exactly which shape characteristics are purely size related.

Authors contributions

WCHP conceived of the study, undertook all data collection and analyses, and prepared the manuscript. AR performed the canonical sampling of the initial 3D scans and advised with respect to the use of principal component analysis. HJC and CS participated in data interpretation and manuscript preparation and oversaw supervision of the research. All authors have approved the final article.

Table legends Table 1

Population and sex breakdown of astragali specimens included in this study.

Figure 2

Principal Component (PC) 1 scores plotted against centroid size for the PC analysis of unscaled canonical astragali models. The PC analysis was carried out on all 59 specimens together. The plot shows male specimens as filled blue circles and female specimens as filled red squares. The mean scores for males (black M) and females (black F) are shown along with the least squares regression line and corresponding model equation.

Figure 3

Principal Component (PC) 1 scores plotted against centroid size for the separate PC analyses of un-scaled male and female canonical astragali models. Regression lines, regression equations and mean scores for the separate male and female analyses are shown.

Males are shown in blue, females in red.

Figure 4

The dorsal (A, B) and plantar (C, D) views of the Principal Component (PC) 1 extreme shapes, as identified by the PC analysis of canonical representations of the un-scaled right astragali. The blue model represents the 'small' PC 1 extreme shape. The yellow model represents the 'big' PC 1 extreme shape. In this analysis of human astragali shapes, the big (yellow model) PC 1 extreme model was at the positive end of the PC 1 spectrum, with the small (blue model) PC 1 extreme shape model at the negative end of PC 1.

Figure 5

Allometric vector maps between Procrustes scaled, translated and rotated Principal Component (PC) 1 extreme shape models (from Figure 4) viewed from dorsal (A) and plantar (B) aspects. Yellow models represent the original 'big' PC 1 extreme, blue models represent the original 'small' PC 1 extreme (as in Figure 4). The red arrows represent the largest 250 allometric vectors and run from small (blue) model to big (yellow) model.

Figure 6

Allometric vector maps between Procrustes scaled, translated and rotated Principal Component (PC) 1 extreme shape models (from Figure 4) viewed from anterior (A) and posterior (B) aspects. Yellow models represent the original 'big' PC 1 extreme, blue models represent the original 'small' PC 1 extreme (as in Figure 4). The red arrows represent the largest 250 allometric vectors and run from small (blue) model to big (yellow) model.

Figure 7

Allometric vector maps between Procrustes scaled, translated and rotated Principal Component (PC) 1 extreme shape models (from Figure 4) viewed from medial (A) and lateral (B) aspects. Yellow models represent the original 'big' PC 1 extreme, blue models represent the original 'small' PC 1 extreme (as in Figure 4). The red arrows represent the largest 250 allometric vectors and run from small (blue) model to big (yellow) model.

Figure 8

Allometric vector maps between Procrustes scaled, translated and rotated Principal Component (PC) 1 extreme shape models for males and females separately. As in Figure 5, the yellow models represent the original 'big' PC 1 extreme, blue models represent the original 'small' PC 1 extreme. The red arrows represent the largest 250 allometric vectors and run from small (blue) model to big (yellow) model.

Video 1

Dorsal view of the allometric shape change identified by our method in a right astragalus. 3D lines represent the largest 250 allometric vectors. These vectors run from blue dots to yellow dots. Blue points are in the position of the scaled original small PC1 extreme model.

Yellow points correspond to the scaled original big PC1 extreme model. Video runs from scaled small to big scaled astragalus shape.

Video 2

Plantar view of the allometric shape change identified by our method in a right astragalus.

3D lines represent the largest 250 allometric vectors. These vectors run from blue dots to 29 yellow dots. Blue points are in the position of the scaled original small PC1 extreme model.

Yellow points correspond to the scaled original big PC1 extreme model. Video runs from scaled small to big scaled astragalus shape.

Video 3

Posterior view of the allometric shape change identified by our method in a right astragalus.

3D lines represent the largest 250 allometric vectors. These vectors run from blue dots to yellow dots. Blue points are in the position of the scaled original small PC1 extreme model.

Yellow points correspond to the scaled original big PC1 extreme model. Video runs from scaled small to big scaled astragalus shape.

Video 4

Lateral view of the allometric shape change identified by our method in a right astragalus.

3D lines represent the largest 250 allometric vectors. These vectors run from blue dots to yellow dots. Blue points are in the position of the scaled original small PC1 extreme model. Yellow points correspond to the scaled original big PC1 extreme model. Video runs from scaled small to big scaled astragalus shape.

Figure 1

 1 Figure 1

Fig 1 32

 32 Fig 1

Fig 2 33

 2 Fig 2

Fig 3 34

 3 Fig 3

Fig 4 35

 4 Fig 4

Fig 5 36

 5 Fig 5

Fig 6 37

 6 Fig 6

Fig 7 Fig 8

 78 Fig 7

Acknowledgements

The authors gratefully acknowledge NERC (Award number: NER/S/A/2004/12187) and the Natural History Museum, London, for additional funding through a CASE award. The authors are extremely grateful to all of the Palaeontology curators at the Natural History Museum who generously provided access to material used in this study and allowed the use of their departmental Konica Minolta vivid 910 laser scanner. In particular, we are grateful to Robert Kruszynski for extra assistance with the specimens. Further, thanks to Andrew and Helen Parr for recent support enabling this work.