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Yilmaz O, Koca D, Sahin ME, Avcilar T. Sex determination in budgerigars using radiographic pelvimetry. Vet Med Sci 2024; 10:e1340. [PMID: 38117606 PMCID: PMC10766023 DOI: 10.1002/vms3.1340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 11/11/2023] [Accepted: 12/03/2023] [Indexed: 12/22/2023] Open
Abstract
BACKGROUND The purpose of this study was to assess the pelvimetric values obtained from radiographic pelvis images of budgerigars in terms of sexual dimorphism. The objectives included determining linear osteometric and angle measurements of the pelvis, as well as calculating the length-to-width ratios among different pelvimetric measurements. Additionally, the study aimed to reveal the correlations between age and body weight with both the pelvimetric measurements and ratio measurements in these animals. METHODS In this study, measurements of linear distance, angle and length-to-width ratios were obtained from ventrodorsal images of the pelvis in a sample of 60 budgerigars, consisting of 30 males and 30 females. Subsequently, the statistical analysis of the obtained measurement values was performed. RESULTS When analysing the morphometric measurement values based on sex, it was observed that all linear measurements (L1, L2, L3, L4, L5, L6, L7, L8, L9, L10 and L11) were higher in males, whereas the angle measurements (A1, LA2 and RA2) were found to be significantly greater in females (p < 0.05). Additionally, both male and female budgerigars exhibited a greater pre-acetabular length of the ilium compared to the post-acetabular length. Moreover, there were mostly positive significant correlations between age and body weight with the pelvic measurement values in both sexes (p < 0.05). CONCLUSIONS The obtained biometric measurement values from pelvimetric X-ray images in budgerigars were analysed to assess sexual dimorphism. Furthermore, this study presents fundamental morphometric data that can be valuable for clinical, taxonomic, phylogenetic, ornithological, allometric and characterization studies of budgerigars.
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Affiliation(s)
- Osman Yilmaz
- Department of AnatomyFaculty of Veterinary MedicineVan Yuzuncu Yil UniversityVanTurkey
| | - Davut Koca
- Department of Obstetrics and GynecologyFaculty of Veterinary MedicineVan Yuzuncu Yil UniversityVanTurkey
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2
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Schmitz Ornés A, Ducay RL, Fulmer AG, Hauber ME. Coloniality and development impact intraclutch consistency of avian eggs: a comparative analysis of the individual repeatability of eggshell size and shape metrics. THE SCIENCE OF NATURE - NATURWISSENSCHAFTEN 2023; 110:12. [PMID: 36943536 DOI: 10.1007/s00114-023-01840-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 02/19/2023] [Accepted: 02/21/2023] [Indexed: 03/23/2023]
Abstract
In oviparous animals, egg morphology is considered an aspect of the extended phenotype of the laying mother and, thus, can be directly assessed for consistency both within and between individual females. Despite a recently renewed interest in the evolution and mechanics of avian eggshell morphology, we still lack a large-scale, comparative understanding of which egg traits are individually plastic and whether individual consistency is shaped by ecological and life history traits at the species level. Here, we aimed to understand whether intraclutch repeatability per se of different eggshell metrics is an evolving trait that responds to selection pressures from socio-ecological contexts across a diverse group of avian species for which clutch-level eggshell morphology data were available to us. Coloniality, ontogeny, and incubation period had significant impacts on the comparative patterns of relative individual repeatability among two egg metrics (i.e., size and shape), whereas other life history traits (including adult size, clutch size, nest type, migration, breeding latitude, host status of brood parasitism) did not have statistical impacts. Our results also demonstrate that individual consistency has a more widespread phylogenetic distribution than expected by evolutionary contingency across avian diversity. Future analyses should also incorporate the effects of intra- and interspecific covariation in other morphological and physiological traits on the evolution of individual consistency, especially those relevant to egg recognition, including eggshell color and maculation.
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Affiliation(s)
- Angela Schmitz Ornés
- AG Vogelwarte, Zoological Institute and Museum, University of Greifswald, 17489, Greifswald, Germany
| | - Rebecca L Ducay
- Department of Evolution, Ecology, and Behavior, School of Integrative Biology, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
- School of Forestry and Horticulture, Southern Illinois University, Carbondale, IL, 62901, USA
| | - Andrew G Fulmer
- Department of Psychology, Fort Lewis College, Durango, CO, 81301, USA
| | - Mark E Hauber
- Department of Evolution, Ecology, and Behavior, School of Integrative Biology, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.
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3
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Frank TM, Dodson P, Hedrick BP. Form and function in the avian pelvis. J Morphol 2022; 283:875-893. [DOI: 10.1002/jmor.21479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Revised: 03/08/2022] [Accepted: 04/16/2022] [Indexed: 11/09/2022]
Affiliation(s)
- Tanner M. Frank
- Department of Integrative Biology University of California‐Berkeley Berkeley California USA
| | - Peter Dodson
- Department of Biomedical Sciences, School of Veterinary Medicine University of Pennsylvania Philadelphia Pennsylvania USA
- Department of Earth and Environmental Science, School of Arts and Sciences University of Pennsylvania Philadelphia Pennsylvania USA
| | - Brandon P. Hedrick
- Department of Cell Biology and Anatomy School of Medicine, Louisiana State University Health Sciences Center New Orleans Los Angeles USA
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4
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Montgomerie R, Hemmings N, Thompson JE, Birkhead TR. The Shapes of Birds' Eggs: Evolutionary Constraints and Adaptations. Am Nat 2021; 198:E215-E231. [PMID: 34762571 DOI: 10.1086/716928] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
AbstractWe studied the shapes of eggs from 955 extant bird species across the avian phylogeny, including 39 of 40 orders and 78% of 249 families. We show that the elongation component of egg shape (length relative to width) is largely the result of constraints imposed by the female's anatomy during egg formation, whereas asymmetry (pointedness) is mainly an adaptation to conditions during the incubation period. Thus, egg elongation is associated with the size of the egg in relation to both the size of the female's oviduct and her general body conformation and mode of locomotion correlated with pelvis shape. Egg asymmetry is related mainly to clutch size and the structure of the incubation site, factors that influence thermal efficiency during incubation and the risk of breakage. Importantly, general patterns across the avian phylogeny do not always reflect the trends within lower taxonomic levels. We argue that the analysis of avian egg shape is most profitably conducted within taxa where all species share similar life histories and ecologies, as there is no single factor that influences egg shape in the same way in all bird species.
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5
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Ducatez S, Field DJ. Disentangling the avian altricial-precocial spectrum: Quantitative assessment of developmental mode, phylogenetic signal, and dimensionality. Evolution 2021; 75:2717-2735. [PMID: 34608994 DOI: 10.1111/evo.14365] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Revised: 08/30/2021] [Accepted: 09/06/2021] [Indexed: 01/12/2023]
Abstract
The altricial-precocial spectrum describes patterns of variation in avian developmental mode that greatly influence avian life histories. Appraising a given species' position on this spectrum is therefore fundamental to understanding patterns of avian life history evolution. However, evaluating avian developmental mode remains a relatively subjective task reliant on untested assumptions, including the notion that developmental strategies are distributed along a single dimension of statistical variation. Here, we present a quantitative multivariate framework that objectively discriminates among meaningfully different modes of avian development. We gathered information on seven hatchling and post-hatching traits for up to 4000 extant bird species, and find that most traits related to developmental mode show high phylogenetic signal and little intraclade variation, allowing unknown values to be reliably interpolated. Principal component analyses (PCAs) of these traits illustrate that most variation in hatchling state can be quantified along one dimension of trait space. However, our PCAs also reveal an important second dimension explaining variation in post-hatching behavior, enabling factors related to hatchling state and post-hatching behavior to be disentangled. In order to facilitate future macroevolutionary studies of variation in avian developmental strategies, as well as explorations of covariation between developmental mode and other aspects of avian biology, we present PC scores for 9993 extant avian species.
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Affiliation(s)
- Simon Ducatez
- Department of Earth Sciences, University of Cambridge, Cambridge, UK.,Institut de Recherche pour le Développement (IRD), UMR 241 EIO (Ecosystèmes Insulaires Océaniens), Papeete, Tahiti, French Polynesia
| | - Daniel J Field
- Department of Earth Sciences, University of Cambridge, Cambridge, UK.,Museum of Zoology, University of Cambridge, Cambridge, UK
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6
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Fischer B, Grunstra NDS, Zaffarini E, Mitteroecker P. Sex differences in the pelvis did not evolve de novo in modern humans. Nat Ecol Evol 2021; 5:625-630. [PMID: 33767411 DOI: 10.1038/s41559-021-01425-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Accepted: 02/24/2021] [Indexed: 01/31/2023]
Abstract
It is commonly assumed that the strong sexual dimorphism of the human pelvis evolved for delivering the relatively large human foetuses. Here we compare pelvic sex differences across modern humans and chimpanzees using a comprehensive geometric morphometric approach. Even though the magnitude of sex differences in pelvis shape was two times larger in humans than in chimpanzees, we found that the pattern is almost identical in the two species. We conclude that this pattern of pelvic sex differences did not evolve de novo in modern humans and must have been present in the common ancestor of humans and chimpanzees, and thus also in the extinct Homo species. We further suggest that this shared pattern was already present in early mammals and propose a hypothesis of facilitated variation as an explanation: the conserved mammalian endocrine system strongly constrains the evolution of the pattern of pelvic differences but enables rapid evolutionary change of the magnitude of sexual dimorphism, which in turn facilitated the rapid increase in hominin brain size.
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Affiliation(s)
- Barbara Fischer
- Department of Evolutionary Biology, Unit for Theoretical Biology, University of Vienna, Vienna, Austria.
| | - Nicole D S Grunstra
- Department of Evolutionary Biology, Unit for Theoretical Biology, University of Vienna, Vienna, Austria.,Konrad Lorenz Institute for Evolution and Cognition Research, Klosterneuburg, Austria.,Mammal Collection, Natural History Museum Vienna, Vienna, Austria
| | - Eva Zaffarini
- Department of Cell Biology and Anatomy, University of Calgary, Calgary, Alberta, Canada
| | - Philipp Mitteroecker
- Department of Evolutionary Biology, Unit for Theoretical Biology, University of Vienna, Vienna, Austria.,Konrad Lorenz Institute for Evolution and Cognition Research, Klosterneuburg, Austria
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7
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Bjarnason A, Benson R. A 3D geometric morphometric dataset quantifying skeletal variation in birds. ACTA ACUST UNITED AC 2021. [DOI: 10.18563/journal.m3.125] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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8
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Blackburn DG, Stewart JR. Morphological research on amniote eggs and embryos: An introduction and historical retrospective. J Morphol 2021; 282:1024-1046. [PMID: 33393149 DOI: 10.1002/jmor.21320] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2020] [Revised: 12/31/2020] [Accepted: 01/01/2021] [Indexed: 12/21/2022]
Abstract
Evolution of the terrestrial egg of amniotes (reptiles, birds, and mammals) is often considered to be one of the most significant events in vertebrate history. Presence of an eggshell, fetal membranes, and a sizeable yolk allowed this egg to develop on land and hatch out well-developed, terrestrial offspring. For centuries, morphologically-based studies have provided valuable information about the eggs of amniotes and the embryos that develop from them. This review explores the history of such investigations, as a contribution to this special issue of Journal of Morphology, titled Developmental Morphology and Evolution of Amniote Eggs and Embryos. Anatomically-based investigations are surveyed from the ancient Greeks through the Scientific Revolution, followed by the 19th and early 20th centuries, with a focus on major findings of historical figures who have contributed significantly to our knowledge. Recent research on various aspects of amniote eggs is summarized, including gastrulation, egg shape and eggshell morphology, eggs of Mesozoic dinosaurs, sauropsid yolk sacs, squamate placentation, embryogenesis, and the phylotypic phase of embryonic development. As documented in this review, studies on amniote eggs and embryos have relied heavily on morphological approaches in order to answer functional and evolutionary questions.
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Affiliation(s)
- Daniel G Blackburn
- Department of Biology and Electron Microscopy Center, Trinity College, Hartford, Connecticut, USA
| | - James R Stewart
- Department of Biological Sciences, East Tennessee State University, Johnson City, Tennessee, USA
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9
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Nagy J, Hauber ME, Hartley IR, Mainwaring MC. Correlated evolution of nest and egg characteristics in birds. Anim Behav 2019. [DOI: 10.1016/j.anbehav.2019.10.015] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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10
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Abourachid A, Castro I, Provini P. How to walk carrying a huge egg? Trade-offs between locomotion and reproduction explain the special pelvis and leg anatomy in kiwi (Aves; Apteryx spp.). J Anat 2019; 235:1045-1056. [PMID: 31432515 PMCID: PMC6875947 DOI: 10.1111/joa.13072] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/13/2019] [Indexed: 11/30/2022] Open
Abstract
Kiwi (Aves; genus Apteryx) are famous for laying an enormous egg in comparison with their relatively small body size. Considering the peculiar gait of this flightless bird, we suspected the existence of morpho-functional trade-offs between reproduction and locomotion. To understand how structural constraints, imposed by a large egg size, might influence the terrestrial locomotion of Apteryx, we analysed the anatomy of the limb osteomuscular system in two species of kiwi (Apteryx mantelli and Apteryx owenii). We performed detailed dissections and brought to light specific anatomical features of kiwi, in comparison with other ratites and neognathous birds. Our osteological study revealed a strongly curved pelvis, a rigid tail, and enlarged ribs. Our myology study showed an unusual location of the caudofemoralis muscle origin and insertion. The insertion of the pars pelvica along the entire caudal face of the femur, contrasts with the proximal insertion usually seen in other birds. Additionally, the pars caudalis originates along the entire tail, whereas it only inserts on the uropygium in the other birds. To interpret these specificities from a functional point of view, we built three-dimensional osteomuscular models based on computed tomography scans, radiographies and our dissections. We chose three postures associated with reproductive constraints: the standing position of a gravid compared with a non-gravid bird, as well as the brooding position. The 3D model of the brooding position suggested that the enlarged ribs could support the bodyweight when leaning on the huge egg in both males and females. Moreover, we found that in gravid females, the unusual shape of the pelvis and tail allowed the huge egg to sit ventrally below the pelvis, whereas it is held closer to the rachis in other birds. The specific conformation of the limb and the insertions of the two parses of the caudofemoralis help to maintain the tail flexed, and to keep the legs adducted when carrying the egg. The caudal location of the hip and its flexed position explains the long stance phase during the strange gait of kiwi, revealing the functional trade-off between reproduction and locomotion in this emblematic New Zealand bird.
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Affiliation(s)
- Anick Abourachid
- Département Adaptations du VivantUMR Mécanismes adaptatifs et évolution (MECADEV) Muséum National d'Histoire Naturelle/CNRSParis Cedex 05France
| | - Isabel Castro
- Wildlife and Ecology GroupMassey UniversityPalmerston NorthNew Zealand
| | - Pauline Provini
- Département Adaptations du VivantUMR Mécanismes adaptatifs et évolution (MECADEV) Muséum National d'Histoire Naturelle/CNRSParis Cedex 05France
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11
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Yang TR, Engler T, Lallensack JN, Samathi A, Makowska M, Schillinger B. Hatching Asynchrony in Oviraptorid Dinosaurs Sheds Light on Their Unique Nesting Biology. Integr Org Biol 2019; 1:obz030. [PMID: 33791544 PMCID: PMC7671163 DOI: 10.1093/iob/obz030] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Dinosaur nesting biology has been an intriguing research topic, though dinosaur behaviors were relatively less illuminated because of the constraints of the fossil record. For instance, hatching asynchrony, where eggs in a single clutch hatch at different times, is unique to modern neoavian birds but was also suggested to be present in oviraptorid dinosaurs based on a possible partial clutch of four embryo-containing eggs from Mongolia. Unfortunately, unequivocal evidence for the origination of these eggs from a single clutch is lacking. Here we report a new, better preserved partial oviraptorid clutch with three embryo-containing eggs—a single egg (Egg I) and a pair (Egg II/III)—from the Late Cretaceous Nanxiong Group of Jiangxi Province, China. Geopetal features indicate that the pair of eggs was laid prior to the single egg. Neutron tomographic images in combination with osteological features indicate that the embryo of the single egg is less developed than those of the paired eggs. Eggshell histology suggests that the embryo-induced erosion in the paired eggs is markedly more pronounced than in the single egg, providing a new line of evidence for hatching asynchrony. The inferred hatching asynchrony in combination with previously surmised thermoregulatory incubation and communal nesting behaviors very likely suggests that oviraptorid dinosaurs presented a unique reproductive biology lacking modern analogs, which is contrary to the predominant view that their reproductive biology was intermediate between that of modern crocodiles and birds.
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Affiliation(s)
- T-R Yang
- Section of Paleontology, Institute of Geosciences, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 8, 53115 Bonn, Germany.,Division of Geology, National Museum of Natural Science, Guancian Road 1, 40453 Taichung, Taiwan
| | - T Engler
- Section of Paleontology, Institute of Geosciences, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 8, 53115 Bonn, Germany
| | - J N Lallensack
- Section of Paleontology, Institute of Geosciences, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 8, 53115 Bonn, Germany
| | - A Samathi
- Section of Paleontology, Institute of Geosciences, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 8, 53115 Bonn, Germany.,Biodiversity and Conservation Research Unit. Walai Rukhavej Botanical Research Institute, Mahasarakham University, 44150 Maha Sarakham, Thailand
| | - M Makowska
- Photons for Engineering and Manufacturing Group, Paul Scherrer Institute, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland
| | - B Schillinger
- Heinz Maier-Leibnitz Zentrum (MLZ), Lichtenbergstraße 1, 85748 Garching, Germany
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12
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Shatkovska OV, Ghazali M. Integration of skeletal traits in some passerines: impact (or the lack thereof) of body mass, phylogeny, diet and habitat. J Anat 2019; 236:274-287. [PMID: 31713858 DOI: 10.1111/joa.13095] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/04/2019] [Indexed: 02/05/2023] Open
Abstract
Morphological integration of the bird skeleton is of great interest because it relates to issues of specialization, plasticity, and rate of evolutionary transformations of a skeleton as a whole and its anatomical regions. Despite growing interest, the integration and modularity of the skeleton of birds, in general, remain little studied. We evaluated the change of relative sizes and integration of shapes of skull, sternum and pelvis, and factors that influence the covariation of these regions among passerines. Results of both standard and phylogenetic reduced major axis showed that the relative lengths of the most studied skeletal traits were largely determined by body mass. The length of the skull scaled isometrically on body mass, and the lengths of both synsacrum and ilium showed positive allometry. Within the skull, beak length was positively allometric, whereas cranium length was negatively allometric with body mass. We found the presence of covariation between shapes of skull, sternum and pelvis using standard partial least squares (PLS) analysis and absence of covariation between most of these blocks using evolutionary PLS analysis on phylogenetic independent contrasts. Evolutionary integration is confirmed only for shapes of skull and pelvis (dorsal view).
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Affiliation(s)
- Oksana V Shatkovska
- Department of Evolutionary Morphology, Schmalhausen Institute of Zoology of NAS of Ukraine, Kyiv, Ukraine
| | - Maria Ghazali
- Department of Evolutionary Morphology, Schmalhausen Institute of Zoology of NAS of Ukraine, Kyiv, Ukraine
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13
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Mytiai IS, Matsyura AV. Mathematical interpretation of artificial ovoids and avian egg shapes (part I). REGULATORY MECHANISMS IN BIOSYSTEMS 2019. [DOI: 10.15421/021915] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
We performed comparative analysis of curvature characteristics of bird eggs and used ovoid profiles from various authors, our own geometric profiles, and archive bird egg profiles from our database. We suggested that the possible ovoids arise by changing the curvature radii of the polar and lateral zones. We compared the constructed curves and curves presented in oological literature with the pictures of the real bird egg profiles. The volume of actual material includes 16,490 eggs from 800 species of 20 bird orders. Specially designed computer software had calculated the radius of curvature of real bird eggs from photos and drew out the half-profiles presented in our article. We supposed that the asymmetrical ovoid is the most widespread geometric egg-shaped figure, which can easily be obtained by combination of circles. We also calculated that if the ovoid diameter were taken as a unit, then the radius obtuse (infundibular) pole would be equal to its half-length, lateral (side arcs) is equal two lengths, and the cloacal arch is 1–√2/2. From this suggestion, we concluded that the length of the ovoid is 2–√2/2 and its cloacal radius is equal to the difference between the length of ovoid and its diameter (rc = L–D). We analyzed the geometry of this asymmetrical oval and came to the conclusion that this is the basic form able to generate the derivative forms. We discovered that the centres of the arcs which form it lie on one basic/supporting circle, the diameter of which is equal to the ovoid diameter. All other ovoids, which have radius equal to radius of the infundibular zone we called the real ovoids. The changes in the radii of the lateral arcs are caused by the movement of their centres along a horizontal line passing through the centre of the base circle. This causes the prolongation or shortening of the ovoids. Sizes of cloacal arcs depended on the lateral, and their centres are placed along the vertical axis. Variability of the sizes of the abovementioned arcs caused the variability of form of the bird eggs. For their classification, we have proposed to divide them into five groups: sphere-like, circle, obtuse, droplet, and cone-shaped. Further, we separated some more groups: short, shortened, normal, lengthened, and long; according to the sizes of cloacal arcs – large radius, middle radius, and small radius ovoids. As a result, we have 80 forms of real ovoids – standards which describe the varieties of bird eggs. Each of them has its own number, name, geometrical figure, polynomic equation, and correlations of ovoid parameters. This set of ovoids is sufficient to describe the specifics of any form of bird eggs.
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