Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-18T13:14:33.325Z Has data issue: false hasContentIssue false

Allometric and fractal exponents indicate a connection between metabolism and complex septa in ammonites

Published online by Cambridge University Press:  08 April 2016

Juan Antonio Pérez-Claros*
Affiliation:
Departamento de Ecología y Geología (Área de Paleontología), Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos s/n, Málaga 29071, Spain. E-mail: [email protected]

Abstract

Sutural perimeters of 301 Late Jurassic ammonites scale as the 3/8 power of phragmocone volume. This implies that septal surface grows as the ¾ power of body mass, the exponent of Kleiber's law (1932), one of the best-established empirical laws in biology, which is well known to be the scaling exponent of basal metabolic rate. Sutural complexity, as measured by fractal dimensions, emerges from the relationship between sutural perimeter and phragmocone volume, thus supporting the interpretations of septal folding as a mechanism for the increase in septal surface and as demanded by metabolic and physiologic processes (e.g., respiration or body chamber transport). The implications of these results strongly suggest that ammonite septa were involved in more than a simple structural support.

Type
Articles
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Banavar, J. R., Damuth, J., Maritan, A., and Rinaldo, A. 2002. Supply-demand balance and metabolic scaling. Proceedings of the National Academy of Sciences USA 99:1050610509.CrossRefGoogle ScholarPubMed
Bayer, U. 1977. Cephalopoden-Septen, Teil 1. Konstruktions-morphologie des Ammoniten-Septums. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 154:290366.Google Scholar
Bayer, U., and McGhee, G. R. 1984. Iterative evolution of Middle Jurassic ammonite faunas. Lethaia 17:116.Google Scholar
Boyajian, G. E., and Lutz, T. 1992. Evolution of biological complexity and its relation to taxonomic longevity in the Ammonoidea. Geology 20:983986.2.3.CO;2>CrossRefGoogle Scholar
Collins, D., Ward, P. D., and Westermann, G. E. G. 1980. Function of cameral water in Nautilus. Paleobiology 6:168172.CrossRefGoogle Scholar
Damuth, J. 2001. Scaling of growth: plants and animals are not so different. Proceedings of the National Academy of Sciences USA 98:21132114.CrossRefGoogle Scholar
Daniel, T. L., Helmuth, B. S., Saunders, W. B., and Ward, P. 1997. Septal complexity in ammonoid cephalopods increased mechanical risk and limited depth. Paleobiology 23:470481.Google Scholar
Denton, E. J., and Gilpin-Brown, J. B. 1966. On the buoyancy of pearly Nautilus. Journal of the Marine Biological Association of the United Kingdom 46:723759.Google Scholar
Dodds, P. S., Rothman, D. H., and Weitz, J. S. 2001. Re-examination of the “3/4-law” of metabolism. Journal of Theoretical Biology 209:927.Google Scholar
Hammer, Ø. 1999. The development of ammonoid septa: an epithelial invagination process controlled by morphogens? Historical Biology 13:153171.Google Scholar
Hassan, M. A., Westermann, G. E. G., Hewitt, R. A., and Dokainish, M. A. 2002. Finite-element analysis of simulated ammonoid septa (extinct Cephalopoda): septal and sutural complexities do not reduce strength. Paleobiology 28:113126.Google Scholar
Henderson, R. A. 1984. A muscle attachment proposal for septal function in Mesozoic ammonites. Palaeontology 27:461486.Google Scholar
Henderson, R. A., Kennedy, W. J., and Cobban, W. A. 2002. Perspectives of ammonite paleobiology from shell abnormalities in the genus Baculites. Lethaia 35:215230.Google Scholar
Hewitt, R. A. 1996. Architecture and strength of the ammonoid shell. Pp. 297339in Landman, et al. 1996.Google Scholar
Hewitt, R. A., and Westermann, G. E. G. 1987. Function of complexly fluted septa in ammonoid shells II. Septal evolution and conclusions. Neues Jahrbuch für Geologie und Palaöntologie, Abhandlungen 174:135169.Google Scholar
Hewitt, R. A., and Westermann, G. E. G. 1997. Mechanical significance of ammonoid septa with complex sutures. Lethaia 30:205212.Google Scholar
Jacobs, D. K., and Chamberlain, J. A. Jr. 1996. Buoyancy and hydrodynamics in ammonoids. Pp. 169224in Landman, et al. 1996.Google Scholar
Kleiber, M. 1932. Body size and metabolism. Hilgardia 6:315353.Google Scholar
Kröger, B. 2002. On the efficiency of the buoyancy apparatus in ammonoids: evidences from sublethal shell injuries. Lethaia 35:6170.Google Scholar
Landman, N. H., Tanabe, K., and Davis, R. A., eds. 1996. Ammonoid paleobiology. Plenum, New York.Google Scholar
Lewy, Z. 2002. The function of the ammonite fluted septal margins. Journal of Paleontology 76:6369.2.0.CO;2>CrossRefGoogle Scholar
Mandelbrot, B. 1983. The fractal geometry of nature, 2d ed. W. H. Freeman, New York.Google Scholar
McMahon, T. A., and Bonner, J. T. 1983. On size and life. W. H. Freeman, New York.Google Scholar
Mutvei, H. 1967. On the microscopic shell structure in some Jurassic ammonoids. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 129:157166.Google Scholar
Mutvei, H., and Reyment, R. A. 1973. Buoyancy control and siphuncle function in ammonoids. Palaeontology 16:623636.Google Scholar
Newell, N. D. 1949. Phyletic size increase, an important trend illustrated by fossil invertebrates. Evolution 3:103124.CrossRefGoogle ScholarPubMed
Okamoto, T. 1996. Theoretical modeling of ammonoid morphology. Pp. 225251in Landman, et al. 1996.Google Scholar
Olóriz, F., and Palmqvist, P. 1995. Sutural complexity and bathymetry in ammonites: fact or artifact? Lethaia 28:167170.Google Scholar
Olóriz, F., Palmqvist, P., and Pérez-Claros, J. A. 1997. Shell features, main colonized environments, and fractal analysis of sutures in Late Jurassic ammonites. Lethaia 30:191204.Google Scholar
Olóriz, F., Palmqvist, P., and Pérez-Claros, J. A. 1999. Recent advances in morphometric approaches to covariation of shell features and the complexity of sutures lines in Late Jurassic ammonites, with references to the major environments colonized. Pp. 273293in Olóriz, F. and Rodríguez-Tovar, P. J., eds. Advancing research on living and fossil cephalopods. Plenum, New York.Google Scholar
Olóriz, F., Palmqvist, P., and Pérez-Claros, J. A. 2002. Morphostructural constraints and phylogenetic overprint on sutural frilling in Late Jurassic ammonites. Lethaia 35:158168.Google Scholar
Osserman, R. 1978. The isoperimetric inequality. Bulletin of the American Mathematical Society 84:11821238.Google Scholar
Pérez-Claros, J. A., Palmqvist, P., and Olóriz, F. 2002. First and second order levels of suture complexity in ammonites: a new methodological approach using fractal analysis. Mathematical Geology 34:323342.Google Scholar
Peters, R. H. 1983. The ecological implications of body size. Cambridge University Press, Cambridge.Google Scholar
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. Journal of Palaeontology 40:11781190.Google Scholar
Raup, D. M., and Chamberlain, J. A. Jr. 1967. Equations for volume and center of gravity in ammonoid shells. Journal of Palaeontology 41:566574.Google Scholar
Reyment, R. A. 1958. Some factors in the distribution of fossil cephalopods. Stockholm Contributions in Geology 1:97184.Google Scholar
Saunders, W. B. 1995. The ammonoid suture problem: relationships between shell and septum thickness and suture complexity in Paleozoic ammonoids. Paleobiology 21:343355.CrossRefGoogle Scholar
Saunders, W. B., and Shapiro, E. A. 1986. Calculation and simulation of ammonoid hydrostatics. Paleobiology 12:6479.Google Scholar
Saunders, W. B., and Work, D. M. 1996. Shell morphology and suture complexity in Upper Carboniferous ammonoids. Paleobiology 22:189218.Google Scholar
Saunders, W. B., and Work, D. M. 1997. Evolution of shell morphology and suture complexity in Paleozoic prolecanitids, the rootstock of Mesozoic ammonoids. Paleobiology 23:301325.Google Scholar
Saunders, W. B., Work, D. M., and Nikolaeva, S. V. 1999. Evolution of complexity in Paleozoic ammonoid sutures. Science 288:760763.Google Scholar
Seilacher, A. 1975. Mechanische simulation und funktionelle evolution des Ammoniten-Septums. Paläontologische Zeitschrift 49:268286.Google Scholar
Seilacher, A., and LaBarbera, M. 1995. Ammonites as Cartesian divers. Palaios 10:493506.Google Scholar
Tanabe, K., Landman, N. H., and Weitschat, W. 1993. Septal necks in Mesozoic Ammonoidea: structure, ontogenetic development, and evolution. In House, M. R., ed. The Ammonoidea: environment, ecology and evolutionary change. Systematic Association Special Volume 47:5784. Clarendon, Oxford.Google Scholar
Tanabe, K, Mapes, R. H., Sasaki, T., and Landman, N. H. 2000. Soft-part anatomy of the siphuncle in Permian prolecanitid ammonoids. Lethaia 33:8391.Google Scholar
Ward, P. D. 1982. The relationship of siphuncle size to emptying rates in chambered cephalopods: implications for cephalopods paleobiology. Paleobiology 8:426433.Google Scholar
Ward, P. D. 1987. The natural history of Nautilus. Allen and Unwin, Boston.Google Scholar
Weitschat, W., and Bandel, K. 1991. Organic components in phragmocones of Boreal Triassic ammonoids: implications for ammonoid biology. Paläontologische Zeitschrift 65:269303.Google Scholar
West, G. J., Brown, J. H., and Enquist, B. J. 1999. The fourth dimension of life: fractal geometry and the allometric scaling of organisms. Science 284:16771679.Google Scholar
Westermann, G. E. G. 1975. Model for origin, function and fabrication of fluted cephalopod septa. Paläontologische Zeitschrift 49:235253.Google Scholar
Westermann, G. E. G. 1990. New developments in ecology of Jurassic-Cretaceous ammonoids. Pp. 459478in Pallini, G., Cecca, F., Cresta, S., and Sanantonio, M., eds. Atti del secondo convegno internazionale, Fossili, Evoluzione, Ambiente, Pergola 1987. Tecnostampa, Otra Vetere, Italy.Google Scholar