Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T08:50:06.112Z Has data issue: false hasContentIssue false

A new approach to modeling of foraminiferal shells

Published online by Cambridge University Press:  08 April 2016

Jarosław Tyszka
Affiliation:
Institute of Geological Sciences, Polish Academy of Sciences, Cracow Research Center, ul. Senacka 1, 31-002 Kraków, Poland. E-mail: [email protected]
Paweł Topa
Affiliation:
Institute of Computer Sciences, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland. E-mail: [email protected]

Abstract

The emergence of shell forms in the growth of foraminifera is an essential problem in the morphogenesis of these microorganisms. We present a model of foraminiferal shells that applies a moving-reference system. Previous models have referred to fixed-reference axes and have neglected apertures. Our model focuses on real morphologic characteristics and follows stepwise natural biological processes. It introduces apertures based on minimization of the local communication path and applies three parameters, which are either predetermined or selected at random from given ranges. Expression of stochastic parameters mimics phenotypic variability of a shell. We also present a detailed description of the method with examples of simulated shells and the first step toward analyses of the theoretical morphospace. The morphospace is divided into certain regions (phases) separated by transitional planes (phase transitions). Further prospects for foraminiferal modeling, which should focus on more in-depth models based on realistic intracellular dynamics, are also presented.

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

Ackerly, S. C. 1989. Kinematics of accretionary shell growth, with examples from brachiopods and molluscs. Paleobiology 15:147164.Google Scholar
Berger, W. H. 1969. Planktonic foraminifera: basic morphology and ecologic implications. Journal of Paleontology 6:13691383.Google Scholar
Brasier, M. D. 1980. Microfossils. Allen and Unwin, London.Google Scholar
Brasier, M. D. 1982. Foraminiferid architectural history; a review using the MinLOC and PI methods. Journal of Micropalaeontology 1:95105.Google Scholar
Brummer, G. J. A., Hemleben, C., and Spindler, M. 1986. Planktonic foraminiferal ontogeny and new perspectives for micropaleontology. Nature 319:5052.Google Scholar
De Renzi, M. 1988. Shell coiling in some larger foraminifera: general comments and problems. Paleobiology 14:387400.Google Scholar
De Renzi, M. 1995. Theoretical morphology of logistic coiling exemplified by tests of genus Alveolina (larger foraminifera). Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 195:241251.Google Scholar
Hammer, Ø. 1998. Regulation of astogeny in halysitid tabulates. Acta Palaeontologica Polonica 43:635651.Google Scholar
Hemleben, C., Spindler, M., and Anderson, O. R. 1989. Modern planktonic Foraminifera. Springer, New York.Google Scholar
Hohenegger, J. 1999. Larger foraminifera-microscopical green-houses indicating shallow-water tropical and subtropical environments in the present and past. Kagoshima University Research Center for the Pacific Islands, Occasional Papers 32:1945.Google Scholar
Holbourn, A., Kuhnt, W., and Erbacher, J. 2001. Benthic foraminifers from Lower Albian black shales (Site 1049, ODP Leg 171): evidence for a non “uniformitarian” record. Journal of Foraminiferal Research 31:6074.CrossRefGoogle Scholar
Hottinger, L. 1978. Comparative anatomy of elementary shell structures in selected larger foraminifera. Pp. 203266in Hedley, R. H. and Adams, C. G., eds. Foraminifera, Vol. 3. Academic Press, London.Google Scholar
Hottinger, L. 1986. Construction, structure, and function of foraminiferal shells. In Leadbeater, B. S. C. and Riding, R., eds. Biomineralization in lower plants and animals. Systematics Association Special Volume 30:222235. Clarendon, Oxford.Google Scholar
Hottinger, L. 2000. Functional morphology of benthic foraminiferal shells, envelopes of cells beyond measure. Micropaleontology 46(Suppl. 1):5786.Google Scholar
Kaandorp, J. A. 1994. A formal description of radiate accretive growth. Journal of Theoretical Biology 166:149161.Google Scholar
Kaandorp, J., and Kuebler, J. E. 2001. Algorithmic beauty of seaweeds, sponges and corals. Springer, Heidelberg.Google Scholar
Łabaj, P., Topa, P., Tyszka, J., and Alda, W. 2003. 2D and 3D numerical models of the growth of foraminiferal shells. Lecture Notes in Computer Science 2657:669678.Google Scholar
Lindenmayer, A. 1968. Mathematical models for cellular interactions in development, I & II. Journal of Theoretical Biology 18:280315.Google Scholar
Lipps, J. H. 1993. Fossil prokaryotes and protists. Blackwell Scientific, Boston.Google Scholar
Loeblich, A. R., and Tappan, H. 1987. Foraminiferal genera and their classification. Van Nostrand Reinhold, New York.Google Scholar
McGhee, G. R. Jr. 1999. Theoretical morphology: the concept and its application (Perspectives in Paleobiology and Earth History Series). Columbia University Press, New York.Google Scholar
Okamoto, T. 1988. Analysis of heteromorphy ammonoids by differential geometry. Palaeontology 31:3552.Google Scholar
Opalach, A., and Gascuel, M. P., eds. 1995. Introduction to modelling and animation using implicit surfaces. Computer Graphics International '95, Course Notes No. 3, Leeds, U.K.Google Scholar
Prusinkiewicz, P., and Lindenmayer, A. 1990. The algorithmic beauty of plants. Springer, New York.Google Scholar
Raup, D. M. 1961. The geometry of coiling in gastropods. Proceedings of the National Academy of Sciences USA 47:602609.Google Scholar
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. Journal of Paleontology 40:11781190.Google Scholar
Raup, D. M., and Michelson, A. 1965. Theoretical morphology of the coiled shell. Science 147:12941295.Google Scholar
Rhumbler, L. 1909. Die Foraminiferen (Thalamophoren) der Plankton-Expedition der Humboldt-Stiftung. Lipsius and Tischer, Kiel.Google Scholar
Scott, G.H. 1974. Biometry of the foraminiferal shell. Pp. 55151in Hedley, R. H. and Adams, C. G., eds. Foraminifera, Vol. 1. Academic Press, London.Google Scholar
Seilacher, A. 1991. Self-organizing mechanisms in morphogenesis and evolution. Pp. 251271in Schmidt-Kittler, N. and Vogel, K., eds. Constructional morphology and evolution. Springer, Berlin.Google Scholar
Signes, M., Bijma, J., Hemleben, C., and Ott, R. 1993. A model for planktic foraminiferal shell growth. Paleobiology 19:7191.Google Scholar
Stearns, S. C. 1992. The evolution of life histories. Oxford University Press, Oxford.Google Scholar
Stroustrup, B. 1997. The C++ Programming Language, 3d ed.Addison-Wesley Longman, Murray, N.J.Google Scholar
Thomson, D'A. W. 1919. On growth and form. Complete revised edition, 1992. Dover, New York.Google Scholar
Topa, P., and Tyszka, J. 2002. Local minimization paradigm in numerical modelling of foraminiferal shells. Lecture Notes in Computer Science 2329:97106.Google Scholar
Tyszka, J. 2004. Analysis of test ontogenesis (ATO) in small foraminifera: implications from Pseudonodosinella. In Bubik, M. and Kaminski, M. A., eds. Proceedings of the seventh international workshop on agglutinated foram inifera. Grzybowski Foundation Special Publication 8:471483. Grzybowski Foundation, Kraków and London.Google Scholar
Tyszka, J., Topa, P., and Saczka, K. 2005. State-of-the-art in modelling of foraminiferal shells: searching for an emergent model. In Tyszka, J., Oliwkiewicz-Miklasińska, M., and Gedl, P., eds. Methods and applications in micropalaeontology. Studia Geologica Polonica 124:143157.Google Scholar
Webb, L. P., and Swan, A. R. C. 1996. Estimation of parameters of foraminiferal test geometry by image analysis. Paleontology 39:471475.Google Scholar
Woo, M., Neider, J., and Davis, T. 1997. OpenGL programming guide. Addison-Wesley, Reading, Mass.Google Scholar
Supplementary material: PDF

Tyszka and Topa supplementary material

Supplementary materials

Download Tyszka and Topa supplementary material(PDF)
PDF 943 KB