Multivariate analysis of the sexual dimorphism of the hip bone in a modern human population and in early hominids

A large sample of hip bones of known sex coming from one modern population is studied morphologically and by multivariate analysis to investigate sexual dimorphism patterns. A principal component analysis of raw data shows that a large amount of the hip bone sexual dimorphism is accounted for by size differences, but that sex-linked shape variation is also very conspicuous and cannot be considered an allometric consequence of differences in body size between the sexes. The PCA of transformed (“shape”) variables indicates that the female hip bones are different in those traits associated with a relatively larger pelvic inlet (longer pubic bones, a greater degree of curvature of the iliopectineal line, and a more posterior position of the auricular surface), as well as a broader sciatic notch. The analysis of nonmetric traits also shows marked sexual dimorphism in the position of the sacroiliac joint in the iliac bone, in the shape of the sciatic notch, in pubic morphology, and in the presence of the pre-auricular sulcus in females. When the australopithecine AL 288-1 and Sts 14 hip bones are included in the multivariate analysis, they appear as “ultra-females.” In particular these early hominids exhibit extraordinarily long pubic bones and iliopectineal lines, which cannot be explained by allometry. © 1994 Wiley-Liss, Inc.     

The variation of the cross-sectional shape in the long bones of birds and mammals

The transverse and sagittal diameters of the long bones were measured in a sample of 53 species of eutherian mammals and 36 species of birds. The scaling of the transverse and sagittal diameters of each bone to body mass was calculated. For each bone the ratio of sagittal/transverse diameter was calculated, as an expression of the cross-sectional shape of the bones. The distributions of the ratios were not significantly different from normality in all the avian bones and in the mammalian femur and tibia. In most cases, the mean of the distribution was significantly different from 1 (circular shape). The analysis shows that changes in the ratio can be caused by selective factors, considering the correlation predicted between the breaking moments and the radii, but at the same time the cross-sectional shape of mammalian and avian long bones may have a phylogenetic basis. Finally, the previous assumption of relationship between bone curvature and stress predictability, is also discussed.     

Muscle‐induced loading as an important source of variation in craniofacial skeletal shape

The shape of the craniofacial skeleton is constantly changing through ontogeny and reflects a balance between developmental patterning and mechanical‐load‐induced remodeling. Muscles are a major contributor to producing the mechanical environment that is crucial for “normal” skull development. Here, we use an F₅ hybrid population of Lake Malawi cichlids to characterize the strength and types of associations between craniofacial bones and muscles. We focus on four bones/bone complexes, with different developmental origins, alongside four muscles with distinct functions. We used micro‐computed tomography to extract 3D information on bones and muscles. 3D geometric morphometrics and volumetric measurements were used to characterize bone and muscle shape, respectively. Linear regressions were performed to test for associations between bone shape and muscle volume. We identified three types of associations between muscles and bones: weak, strong direct (i.e., muscles insert directly onto bone), and strong indirect (i.e., bone is influenced by muscles without a direct connection). In addition, we show that although the shape of some bones is relatively robust to muscle‐induced mechanical stimulus, others appear to be highly sensitive to muscular input. Our results imply that the roles for muscular input on skeletal shape extend beyond specific points of origin or insertion and hold significant potential to influence broader patterns of craniofacial geometry. Thus, changes in the loading environment, either as a normal course of ontogeny or if an organism is exposed to a novel environment, may have pronounced effects on skeletal shape via near and far‐ranging effects of muscular loading.     

A 3-D geometric morphometric study of intraspecific variation in the ontogeny of the temporal bone in modern Homo sapiens

This study addresses how the human temporal bone develops the population-specific pattern of morphology observed among adults and at what point in ontogeny those patterns arise. Three-dimensional temporal bone shape was captured using 15 landmarks on ontogenetic series of specimens from seven modern human populations. Discriminant function analysis revealed that population-specific temporal bone morphology is evident early in ontogeny, with significant shape differences among many human populations apparent prior to the eruption of the first molar. As early as five years of age, temporal bone shape reflects population history and can be used to reliably sort populations, although those in closer geographic proximity and molecular affinity are more likely to be misclassified. The deviation of cold-adapted populations from this general pattern of congruence between temporal bone morphology and genetic distances, identified in previous work, was confirmed here in adult and subadult specimens, and was revealed to occur earlier in ontogeny than previously recognized. Significant differences exist between the ontogenetic trajectories of some pairs of populations, but not among others, and the angles of these trajectories do not reflect genetic relationships or final adult temporal bone size. Significant intrapopulation differences are evident early in ontogeny, with differences becoming amplified by divergent trajectories in some groups. These findings elucidate how the congruence between adult human temporal bone morphology and population history develops, and reveal that this pattern corresponds closely to that described previously for facial ontogeny.     

Patterns of morphological integration in the appendicular skeleton of mammalian carnivores

We investigated patterns of evolutionary integration in the appendicular skeleton of mammalian carnivores. The findings are discussed in relation to performance selection in terms of organismal function as a potential mechanism underlying integration. Interspecific shape covariation was quantified by two‐block partial least‐squares (2B‐PLS) analysis of 3D landmark data within a phylogenetic context. Specifically, we compared pairs of anatomically connected bones (within‐limbs) and pairs of both serially homologous and functional equivalent bones (between‐limbs). The statistical results of all the comparisons suggest that the carnivoran appendicular skeleton is highly integrated. Strikingly, the main shape covariation relates to bone robustness in all cases. A bootstrap test was used to compare the degree of integration between specialized cursorial taxa (i.e., those whose forelimbs are primarily involved in locomotion) and noncursorial species (i.e., those whose forelimbs are involved in more functions than their hindlimb) showed that cursors have a more integrated appendicular skeleton than noncursors. The findings demonstrate that natural selection can influence the pattern and degree of morphological integration by increasing the degree of bone shape covariation in parallel to ecological specialization.     

Univariate and multivariate methods for sexing the sacrum

Metric data on 200 sacra of known sex, age and race are analyzed to determine the usefulness of conventional observations for determining sex in this bone. Results of the univariate analysis show that significant sex differences in the sacrum involve primarily the top portion of the bone for both whites and blacks. However, measurements of curvature are important sex differences in the sample of blacks. A new index relating the S1 body to sacral breadth is proposed as more useful in classifying the bones by sex than indices involving other measurements. Discriminant analysis shows that the sample of whites can be analyzed significantly better by this method than by using an index. The choice of univariate or multivariate method must depend on the condition of the bone, and will be influenced to some extent by the race from which the sample is drawn.     

Avian wing proportions and flight styles: first step towards predicting the flight modes of mesozoic birds

We investigated the relationship between wing element proportions and flight mode in a dataset of living avian species to provide a framework for making basic estimates of the range of flight styles evolved by Mesozoic birds. Our results show that feather length (f(prim)) and total arm length (ta) (sum of the humerus, ulna and manus length) ratios differ significantly between four flight style groups defined and widely used for living birds and as a result are predictive for fossils. This was confirmed using multivariate ordination analyses, with four wing elements (humerus, ulna/radius, manus, primary feathers), that discriminate the four broad flight styles within living birds. Among the variables tested, manus length is closely correlated with wing size, yet is the poorest predictor for flight style, suggesting that the shape of the bones in the hand wing is most important in determining flight style. Wing bone thickness (shape) must vary with wing beat strength, with weaker forces requiring less bone. Finally, we show that by incorporating data from Mesozoic birds, multivariate ordination analyses can be used to predict the flight styles of fossils.     

Patterns of morphological discrimination in selected human tarsal elements

A suite of measurements was collected from the talus, calcaneus, navicular, and cuboid of humans from Southern China, Victorian Britain, Roman Britain, and Zulu tribes people from the Republic of South Africa. Univariate and multivariate statistical analyses of dimensions of individual foot bones revealed subtle but distinct patterns of morphological discrimination on the basis of sex and size on the one hand, and geographical relationships on the other. These differences are largely expressed in the first three canonical variates of the multivariate analyses: the first axis expresses both sex and size differences, and the second and third, geographical group differences. Confirmation of morphological patterns obtained from individual multivariate analyses was provided by an integrated analysis of the four tarsal elements together. However, the integrated analysis also gave larger separations with discriminations along different axes. Thus the three geographical groups (Zulus, Southern Chinese, and the two British groups together) were separated by first and third variates. The discrimination of sex and size differences was found in the second axis, mirroring what was found in the first axes of the individual studies. This axis reversal implies that in examining all bones together, there is enough redundant information about sex and size in each individual bone that they are relegated to a second axis. It likewise implies that the data referring to geographic discriminations provided by each individual bone are not redundant; they sum in the integrated analysis, and therefore contribute to the overall analysis to a greater extent, with increased clarity.     

A new morphometric analysis of the hominid pelvic bone

This study is based upon a new morphometric technique providing both size and shape variables. It has been applied to 189 pelvic bones of extant humans and African apes as well as to 13 hominid pelvic bones of various taxonomic status. The main aim of this work is to include such fossil bones in the same study in order to set a synthetic comparison of their shape in the light of the yardstick given by the African ape/human pelvic bone comparison. To do so, ratio diagrams are chosen because they are simple and very expressive tools with which to present such comparisons. Shape differences are very well illustrated and quantified by this technique. The ilium appears to be the most different of the three parts of the pelvic bone. Compared to these differences, discrepancies between fossil hominid and extant human bones are of a totally different scale. This shows the architectural unity related to the acquisition of bipedalism by hominids. It is nonetheless possible to detect two levels of difference. The first separates Australopithecus from Homo and could be seen as reflecting locomotor differences between both genera. The second splits both Homo erectus and Neanderthal from modern human pelvic bones. It appears from the hominid fossil record of pelvic bones that two periods of stasis exist and are separated by a period of very rapid evolution corresponding to the emergence of the genus Homo. We are of the opinion that the same could be true for the split between African ape and hominid lineages at the end of the Miocene.     

Long bone growth variation among Arikara skeletal populations

Long bone growth variation among skeletal samples has had limited application to ecological studies of archaeological groups, in spite of its well-known sensitivity to health and nutritional status. In this study we examine long bone growth variation among ten samples of Arikara skeletal groups, all located in the Middle Missouri subarea of South Dakota and ranging in time from A.D. 1600 to 1832. The samples are analyzed by variant, an archaeological taxonomic unit below Tradition. Children's long bones between about 0.5 and 11.9 years of age were analyzed by means of regression using the model, bone length =b₀ + b₁ (age) + b₂ (log₁₀ age). The three variants, Extended Coalescent, Postcontact Coalescent, and Disorganized Coalescent, differ from one another with regard to health and nutritional status. Extended Coalescent groups probably experienced periods of undernutrition due to unfavorable climatic conditions prevailing at the time. Postcontact Coalescent groups experienced more favorable health and nutrition due to improved climatic conditions and introduction of the horse. Disorganized Coalescent groups were exposed to undernutrition and high levels of morbidity, due to introduction of epidemic diseases, depopulation, and intertribal conflict. Analysis of slopes shows significant heterogeneity among variants for humerus, radius, and tibia, but not femur. In general, the Postcontact Coalescent is characterized by slighter greater rates of increase with age and longer bone lengths for each age than is Extended Coalescent. Disorganized Coalescent exhibits lower rates of increase, particularly in later childhood, with shorter bone lengths in late childhood. Disorganized Coalescent also presents longer radius and humerus lengths than the other two variants in early childhood, an unexpected finding. This may be partly, but not entirely, explained by differential bone response to stress along the lines of maturity gradients.     

Inter‐ and intraspecific variation in the surface pattern of the dermal bones of two sturgeon species

Archaeological bone remains of sturgeon (Acipenser sturio/Acipenser oxyrinchus) from northwestern Europe are often identified to species on the basis of their surface morphology and then used to reconstruct the spatial distribution of the two species through time. The dermal bones of A. sturio are said to have an exterior surface pattern consisting of tubercles, while those of A. oxyrinchus are said to display alveoli. In the present paper, the validity of the surface pattern as a species‐specific characteristic is critically assessed. To this purpose, dermal plates from modern, genetically identified museum specimens were studied and the surface morphology observed in a series of archaeological remains was compared with the genetic identifications obtained on these same remains. The analyses show that the surface pattern of dermal bones is related to the size of the individual, with the pattern of small A. oxyrinchus being similar to that of A. sturio. In addition, variations in the surface pattern among the bones of a single individual and within the same bone have been observed. These findings explain previous conflicting results between morphological and genetic identifications and allow the formulation of some recommendations for more accurate morphological identification of isolated archaeological sturgeon dermal bones.     

Ontogeny and phylogeny of the pelvis in Gorilla, Pongo, Pan, Australopithecus and Homo

To examine the evolutionary differences between hominoid locomotor systems, a number of observations concerning the growth of the pelvis among the great apes as compared to modern and fossil hominids are reported. We are interested in the size and shape of the coxal bones at different developmental stages across species that may elucidate the relationship between ontogeny and phylogeny (i.e., heterochrony) in the hominoid pelvis. Our hypotheses are: (1) do rates of absolute growth differ?, (2) do rates of relative growth differ?, and (3) does heterochrony explain these differences? Bivariate and multivariate analyses of pelvic dimensions demonstrate both the diversity of species-specific ontogenetic patterns among hominoids, and an unequivocal separation of hominids and the great apes. Heterochrony alone fails to account for the ontogenetic differences between hominids and the great apes. Compared to recent Homo,Australopithecus can be described as 'hyper-human' from the relative size of the ischium, and short but broad ilium. Australopithecus afarensis differs from Australopithecus africanus by its relatively long pubis. In multivariate analyses of ilium shape, the most complete coxal bone attributed to Homo erectus, KNM-ER 3228, falls within the range of juvenile and adult Australopithecus, whereas Broken Hill falls within the range of modern Homo, suggesting that the modern human ilium shape arose rather recently. Among the great apes, patterns of pelvic ontogeny do not exclusively separate the African apes from Pongo.     

Heritability of quantitative variation at the group-specific component (Gc) locus

Human group-specific component (Gc) is the plasma transport protein for vitamin D; in addition, polymorphic electrophoretic variants of Gc are found in all human populations. Because of its physiologic importance and in view of the extensive genetic variation at the Gc locus, we have determined the heritability of quantitative variation in Gc by comparing a series of monozygotic (MZ) and dizygotic (DZ) twins of known Gc genotype. The series included 31 MZ twin pairs, 13 DZ twin pairs, and 45 unrelated controls. Since Gc concentration is increased by estrogens, pregnant women and women taking oral contraceptives were excluded. We found no age-related differences in Gc concentration or differences between males and females, but the concentrations of Gc in the three electrophoretically determined genotypes were significantly different from each other. Using classical methods of heritability analysis, the overall heritability of variation in Gc concentration is approximately 70%. Heritability in males is greater than in females, probably reflecting the additional environmental effect of estrogens in women. To determine if the differences in Gc concentration between the three genotypes explain the high heritability, a new variance decomposition procedure was developed following classical methods in quantitative genetics. Application of this method suggests that 19% of the total variation in Gc concentration, combining both sexes, is due to electrophoretic differences between individuals (30% in females and 20% in males). Thus, the genetic component of variation in Gc concentration can be decomposed into a major gene component--the result of electrophoretic variation at the structural locus--and a second, unexplained, polygenic component.     

Developmental basis of limb length in rodents: evidence for multiple divisions of labor in mechanisms of endochondral bone growth

SUMMARY Mammals are remarkably diverse in limb lengths and proportions, but the number and kind of developmental mechanisms that contribute to length differences between limb bones remain largely unknown. Intra- and interspecific differences in bone length could result from variations in the cellular processes of endochondral bone growth, creating differences in rates of chondrocyte proliferation or hypertrophy, variation in the shape and size of chondrocytes, differences in the number of chondrocytes in precursor populations and throughout growth, or a combination of these mechanisms. To address these questions, this study compared cellular mechanisms of endochondral bone growth in cross-sectional ontogenetic series of the appendicular skeleton of two rodent species: the mouse ( Mus musculus ) and Mongolian gerbil ( Meriones unguiculatus ). Results indicate that multiple cellular processes of endochondral bone growth contribute to phenotypic differences in limb bone length. The data also suggest that separate developmental processes contribute to intraspecific length differences in proximal versus distal limb bones, and that these proximo-distal mechanisms are distinct from mechanisms that contribute to interspecific differences in limb bone length related to body size. These developmental "divisions of labor" are hypothesized to be important features of vertebrate limb development that allow (1) morphology in the autopods to evolve independently of the proximal limb skeleton, and (2) adaptive changes in limb proportions related to locomotion to evolve independently of evolutionary changes in body size.     

The Hindlimb Elements of the Maas (Aves,Dinornithidae): A Multivariate Assessment of Size and Shape

A multivariate morphometric analysis of size and shape was performed on the hindlimb skeletal elements of the extinct New Zealand moas (Dinornithidae). Investigations were undertaken of size-shape patterns within species and among moas as a group using principal components analysis; between species investigations used canonical analysis. In addition, standard allometric curve-fitting of six femur, seven tibiotarsus, and nine tarsometatarsus variables against body size was performed. Size was the major discriminator along the first principal component for all three bones in the intraspecific and whole-group analyses. Shape was the important discriminator along the second component: in the whole-group analysis of all three bones, separation was based on relative robustness of the shaft, whereas in the intraspecific analyses shaft robustness was only expressed in the analysis of the femur, there being little correspondence in the results between the intraspeci fic and whole-group analyses of the tibiotarsus and tarsometatarsus. Size was the major discriminator along the first canonical axis for the between-group investigations of the femur and tibiotarsus, but in the analysis of the tarsometatarsus shape influences were equally as important as those of size. The second canonical axis separated groups on the basis of shape differences in all three hindlimb elements. The genus Dinornis, which contains the largest species of moas, has evolved sizeshape patterns very different from those of other moas. The species of Dinornis did not follow size-dependent allometric trends and evolved proportionately thinner legs than might be expected for their body size. All other moas exhibit allometric increase in all hindlimb variables except bone lengths. Dinornis may have evolved a cursorial mode of locomotion as an adaptation for certain intraspecific behavioral interactions.     

Genetic, geographic, and environmental correlates of human temporal bone variation

Temporal bone shape has been shown to reflect molecular phylogenetic relationships among hominoids and offers significant morphological detail for distinguishing taxa. Although it is generally accepted that temporal bone shape, like other aspects of morphology, has an underlying genetic component, the relative influence of genetic and environmental factors is unclear. To determine the impact of genetic differentiation and environmental variation on temporal bone morphology, we used three-dimensional geometric morphometric techniques to evaluate temporal bone variation in 11 modern human populations. Population differences were investigated by discriminant function analysis, and the strength of the relationships between morphology, neutral molecular distance, geographic distribution, and environmental variables were assessed by matrix correlation comparisons. Significant differences were found in temporal bone shape among all populations, and classification rates using cross-validation were relatively high. Comparisons of morphological distances to molecular distances based on short tandem repeats (STRs) revealed a significant correlation between temporal bone shape and neutral molecular distance among Old World populations, but not when Native Americans were included. Further analyses suggested a similar pattern for morphological variation and geographic distribution. No significant correlations were found between temporal bone shape and environmental variables: temperature, annual rainfall, latitude, or altitude. Significant correlations were found between temporal bone size and both temperature and latitude, presumably reflecting Bergmann's rule. Thus, temporal bone morphology appears to partially follow an isolation by distance model of evolution among human populations, although levels of correlation show that a substantial component of variation is unexplained by factors considered here.     

Taphonomy of the south Brazilian Triassic herpetofauna: fossilization mode and implications for morphological studies

Skulls and limb bones of reptiles from Mid-Triassic rocks in southern Brazil show striking morphological and volumetric differences among specimens from the same taxonomic group; this is caused by early calcite cementation. Petrographic analysis of 40 thin sections of selected fossil bones demonstrates that the main agent of fossilization was precipitation of calcite and minor hematite in the pores of bones during early burial mineralization. The framework of the bones has been broken and replaced by calcite (and hematite), beginning in the spongy inner part of the bone (the cancellous bone) and gradually extending into the compact external layers. Three taphonomic groups of fossil bones are recognized: I – those almost entirely retaining their original structure and shape; II – those whose internal structure is destroyed, but which still have solid outer 'bone surface', and III – those composed of fragments of bone apatite 'floating' in a carbonate matrix. Destruction of the bone structure was caused by the displacive force of calcite crystallization, which typically occurs at shallow burial, during early diagenesis. This process occurs in the vadose zone and requires markedly alternating wet and dry seasons, which indicates a semi-arid paleoclimate for the south Brazilian Mid-Triassic, an inference consistent with other paleoclimatic data. Diagenesis can significantly alter the shape and size of bones and cause considerable morphological variation within the same fossil group, possibly leading to taxonomic misinterpretation.     

Morphological variation in a secondary contact between divergent lineages of brown trout (Salmo trutta) from the Iberian Peninsula

The aim of this study was to analyze the morphological variation of brown trout (Salmo trutta) in the Duero basin, an Atlantic river basin in the Iberian Peninsula, where a spatial segregation of two divergent lineages was previously reported, based on isozyme, microsatellite and mtDNA data. In these studies, two divergent pure regions (Pisuerga and Lower-course) and several hybrid populations between them were identified. Morphological variation was evaluated in 11 populations representative of the genetic differentiation previously observed in the Duero basin, using multivariate analysis on 12 morphometric and 4 meristic traits. A large differentiation between populations was observed (interpopulation component of variance: 41.8%), similar to that previously detected with allozymes and microsatellites. Morphometric differentiation was also reflected by the high classification success of pure and hybrid individuals to their respective populations, using multivariate discriminant functions (94.1% and 79.0%, respectively). All multivariate and clustering analyses performed demonstrated a strong differentiation between the pure regions. The hybrid populations, though showing large differentiation among them, evidenced an intermediate position between the pure samples. Head and body shape traits were the most discriminant among the morphometric characters, while pectoral rays and gillrakers were the most discriminant among the meristic traits. These results confirmed the high divergence of the brown trout from the Duero basin and suggest some traits on which selection could be acting to explain the spatial segregation observed.     

Effect of CD44 deficiency on in vitro and in vivo osteoclast formation

In vitro studies have shown that CD44 is involved in the fusion process of osteoclast precursor cells. Yet, in vivo studies do not support this, since an osteopetrotic phenotype has not been described for CD44 knock-out (CD44 k.o.) mice. This discrepancy may suggest that the role of CD44 in fusion may depend on the microenvironment of osteoclast formation. We investigated osteoclast formation of CD44 k.o. and wild-type mice under three conditions: in vitro, both on plastic and on bone and in vivo by analyzing osteoclast number, and size in long bones from wild-type and CD44 k.o. mice. Bone marrow cells from wild-type and CD44 k.o. mice were analyzed for their capacity to form osteoclasts on plastic and on bone in the presence of macrophage colony stimulating factor (M-CSF) and receptor activator of NF-kB ligand (RANKL). On plastic, the number of multinucleated tartrate resistant acid phosphatase (TRAP) positive cells in CD44 k.o. cultures was twofold higher than in wild-type cultures. On bone, however, equal numbers of osteoclasts were formed. Interestingly, the total number of osteoclasts formed on bone proved to be higher than on plastic for both genotypes, strongly suggesting that osteoclastogenesis was stimulated by the bone surface, and that CD44 is not required for osteoclast formation on bone. Functional analyses showed that bone resorption was similar for both genotypes. We further studied the osteoclastogenic potential of wild-type bone marrow cells in the presence of CD44 blocking antibodies. Osteoclastogenesis was not affected by these antibodies, a further indication that CD44 is not required for the formation of multinucleated cells. Finally, we analyzed the in vivo formation of osteoclasts by analyzing long bones from wild-type and CD44 k.o. mice. Morphometric analysis revealed no difference in osteoclast number, nor in number of nuclei per osteoclasts or in osteoclast size. Our in vitro experiments on plastic showed an enhanced formation of osteoclasts in the absence of CD44, thus suggesting that CD44 has an inhibitory effect on osteoclastogenesis. However, when osteoclasts were generated on bone, no differences in number of multinucleated cells nor in bone resorption were seen. These observations are in agreement with in vivo osteoclast characteristics, where no differences between wild-type and CD44 k.o. bones were encountered. Therefore, the modulating role of CD44 in osteoclast formation appears to depend on the microenvironment.     

Three-dimensional topology optimization model to simulate the external shapes of bone

Elucidation of the mechanism by which the shape of bones is formed is essential for understanding vertebrate development. Bones support the body of vertebrates by withstanding external loads, such as those imposed by gravity and muscle tension. Many studies have reported that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that bone shape adapts to external load. In fact, by simulating this relationship through topology optimization, the internal trabecular structure of bones can be successfully reproduced, thereby facilitating the study of bone diseases. In contrast, there have been few attempts to simulate the external structure of bones, which determines vertebrate morphology. However, the external shape of bones may be reproduced through topology optimization because cells of the same type form both the internal and external structures of bones. Here, we constructed a three-dimensional topology optimization model to attempt the reproduction of the external shape of teleost vertebrae. In teleosts, the internal structure of the vertebral bodies is invariable, exhibiting an hourglass shape, whereas the lateral structure supporting the internal structure differs among species. Based on the anatomical observations, we applied different external loads to the hourglass-shaped part. The simulations produced a variety of three-dimensional structures, some of which exhibited several structural features similar to those of actual teleost vertebrae. In addition, by adjusting the geometric parameters, such as the width of the hourglass shape, we reproduced the variation in the teleost vertebrae shapes. These results suggest that a simulation using topology optimization can successfully reproduce the external shapes of teleost vertebrae. By applying our topology optimization model to various bones of vertebrates, we can understand how the external shape of bones adapts to external loads.