Skip to main content
SpringerLink
Log in

Theoretical Modelling of the Molluscan Shell: What has been Learned From the Comparison Among Molluscan Taxa?

  • Chapter
  • First Online:
Ammonoid Paleobiology: From anatomy to ecology

Part of the book series: Topics in Geobiology ((TGBI,volume 43))

Abstract

The molluscan shell has been the subject of extensive theoretical work for over a century. From geometrical models to mechano-chemical models, a wide range of models exist that highlight the principles underlying coiling and the ornamentation in molluscan shells. Here, I review these theories, focusing on the comparison between different clades of molluscs with an external shell, namely cephalopods, bivalves, and gastropods. The models using a fixed axis -qualified as “form models”- facilitate the analysis of morphospace occupation and functional/ developmental constraints at a high phylogenetic level, whereas moving reference models—qualified as “growth models”- facilitate the quantitative study of allometry and phenotypic plasticity at lower phylogenetic levels. This review highlights the advantages and limitations of each framework and shows that comparative theoretical and experimental studies are very informative with regards to the evolutionary conserved rules underlying accretionary growth.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ackerly SC (1989) Kinematics of accretionary shell growth, with examples from brachiopods and molluscs. Paleobiology 15:147–164

    Google Scholar 

  • Ackerly SC (1992) Morphogenetic regulation in the shells of bivalves and brachiopods—Evidence from the geometry of the spiral. Lethaia 25:249–256

    Google Scholar 

  • Aldridge AE (1998) Brachipod outline and the importance of the logarithmic spiral. Paleobiology 24/2:215–226

    Google Scholar 

  • Bayer U (1970) Anomalien bei Ammoniten des Aaleniums und Bajociums und ihre Beziehung zur Lebensweise. N Jahrb Geol Paläont Abh 135:19–41

    Google Scholar 

  • Bayer U (1977) Cephalopod septa I. Constructional morphology of the ammonite septum. N Jahrb Geol Paläont Abh 154:19–41

    Google Scholar 

  • Bayer U (1978) Morphogenetic programs, instabilities and evolution: a theoretical study. N Jahrb Geol Paläont Abh 156:226–261

    Google Scholar 

  • Black R, Turner SJ, Johnson MS (1994) The early life history of Bembicium vittatum Philippi, 1846 (Gastropoda, Littorinidae). Veliger 37:393–399

    Google Scholar 

  • Bond PN, Saunders WB (1989) Sublethal injury and shell repair in upper Mississippian ammonoids. Paleobiology 15:414–428

    Google Scholar 

  • Bretos M (1980) Age-determination in the keyhole Limpet Fissurella crassa Lamarck (Archaeogastropoda, Fissurellidae) based on shell growth rings. Biol Bull 159:606–612

    Google Scholar 

  • Bucher H (1997) Caractères périodiques et modes de croissance des ammonites: comparaison avec les gastéropodes. Geobios 20:85–99

    Google Scholar 

  • Bucher H, Guex J (1990) Rythmes de croissance chez les ammonites triasiques. Bulletin des Laboratoires de Geologie, Mineralogie, Geophysique et du Musee géologique de l’Université de Lausanne 308:191–209

    Google Scholar 

  • Bucher H, Landman NH, Klofak SM, Guex J (1996) Mode and rate of growth in ammonoids. In: Landman NH, Tanabe K, Davis RA (eds) Ammonoid paleobiology. Plenum, New York

    Google Scholar 

  • Buckman SS (1887–1907) Monograph of the ammonites of the inferior Oolite series. Palaeontographical Society, London, p. 456

    Google Scholar 

  • Burnaby TP (1966) Allometric growth of ammonoid shells: a generalization of logarithmic spiral. Nature 209:904–906

    Google Scholar 

  • Checa A (1991) Sectorial expansion and shell morphogenesis in mollusks. Lethaia 24:97–114

    Google Scholar 

  • Checa A, Aguado R (1992) Sectorial expansion analysis of irregularly coiled shells: application to the recent gastropod Distorsio. Palaeontology 35:913–925

    Google Scholar 

  • Checa AG, García-Ruiz JM (1996) Morphogenesis of the septum in ammonoids. In: Landman NH, Tanabe K, Davis RA (eds) Ammonoid Paleobiology. Topics in Geobiology 13. Plenum, New York

    Google Scholar 

  • Checa AG, Jiménez-Jiménez AP (1997) Regulation of spiral growth in planorbid gastropods. Lethaia 30:257–269

    Google Scholar 

  • Checa AG, Company M, Sandoval J, Weitschat W (1996) Covariation of morphological characters in the Triassic ammonoid Czekanowskites rieberi. Lethaia 29:225–235

    Google Scholar 

  • Checa AG, Jiménez-Jiménez AP, Rivas P (1998) Regulation of spiral coiling in the terrestrial gastropod Sphincterochila: an experimental test of the road-holding model. J Morph 235:249–257

    Google Scholar 

  • Checa AG, Okamoto T, Keupp H (2002) Abnormalities as natural experiments: a morphogenetic model for coiling regulation in planispiral ammonites. Paleobiology 28:127–138

    Google Scholar 

  • Chirat R, Enay R, Hantzpergue P, Mangold C (2008) Developmental integration related to buoyancy control in nautiloids: evidence from unusual septal approximation and ontogenetic allometries in a Jurassic species. Palaeontology 51:251–261

    Google Scholar 

  • Chirat R, Moulton DE, Goriely A (2013) Mechanical basis of morphogenesis and convergent evolution of spiny seashells. PNAS USA 110:6015–6020

    Google Scholar 

  • Clements R, Liew TS, Vermeulen JJ, Schilthuizen M (2008) Further twists in gastropod shell evolution. Biol Lett 4:179–182

    Google Scholar 

  • Cortie MB (1989) Models for mollusk shell shape. S Afr J Sci 85:454–460

    Google Scholar 

  • Dagys AS, Weitschat W (1993) Extensive intraspecific variation in a Triassic ammonoid from Siberia. Lethaia 26:113–121

    Google Scholar 

  • Dagys A, Bucher H, Weitschat W (1999) Intraspecific variation of Parasibirites kolymensis Bychkov (Ammonoidea) from the lower Triassic (Spathian) of Arctic Asia. Mitt Geol-Paläont Inst Univ Hamb 83:163–178

    Google Scholar 

  • De Baets K, Bert D, Hoffmann R, Monnet C, Yacobucci MM, Klug C (2015) Ammonoid intraspecific variability. This volume

    Google Scholar 

  • Dera G, Eble GH, Neige P, David B (2008) The flourishing diversity of models in theoretical morphology: from current practices to future macroevolutionary and bioenvironmental challenges. Paleobiology 34/3:301–317

    Google Scholar 

  • Dommergues JL, Laurin B, Meister C (1996) Evolution of ammonoid morphospace during the early Jurassic radiation. Paleobiology 22:219–240

    Google Scholar 

  • Eble GJ (1999) Developmental and non-developmental morphospaces in evolutionary biology. In: Chapman RE, Rasskin-Gutman D, Wills M (eds) Morphospace concepts and applications. Cambridge University Press, Cambridge

    Google Scholar 

  • Engeser TS (1990) Major events in cephalopod evolution. Major evolutionary radiations. Syst Assoc Spec 42:119–138

    Google Scholar 

  • Ermentrout B (1998) Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61:353–430

    Google Scholar 

  • Ermentrout B, Campbell J, Oster G (1986) A model for shell patterns based on neural activity. Veliger 28:369–388

    Google Scholar 

  • Fowler DR, Meinhardt H, Prusinkiewicz P (1992) Modeling Seashells. Comput Graphics 26:379–387

    Google Scholar 

  • García-Ruiz JM, Checa A, Rivas P (1990) On the origin of ammonoid sutures. Paleobiology 16:349–354

    Google Scholar 

  • Gerber S, Neige P, Eble GJ (2007) Combining ontogenetic and evolutionary scales of morphological disparity: a study of early Jurassic ammonites. Evol Dev 9:472–482

    Google Scholar 

  • Gerber S, Eble GJ, Neige P (2008) Allometric space and allometric disparity: a developmental perspective in the macroevolutionary analysis of morphological disparity. Evolution Int J Org Evolution 62:1450–1457

    Google Scholar 

  • Gierer A, Meinhardt H (1972) Theory of biological pattern formation. Kybernetik 12:30–39

    Google Scholar 

  • Goodwin BC (1988) Problems and prospects in morphogenesis. Experientia 44:633–637

    Google Scholar 

  • Gould SJ (1984) Morphological channeling by structural constraint: convergence in styles of dwarfing and gigantism in Cerion, with a description of two new fossil species and a report on the discovery of the largest Cerion. Paleobiology 10:172–194

    Google Scholar 

  • Gould SJ (1989) A developmental constraint in Cerion, with comments of the definition and interpretation of constraint in evolution. Evolution 43:516–539

    Google Scholar 

  • Guex J (1967) Contribution à l’étude des blessures chez les ammonites. Bull géologique de Lausanne 165:1–23

    Google Scholar 

  • Guex J (1968) Sur deux conséquences particulières des traumatismes du manteau des ammonites. Bull de la Societé vaudoise des sciences naturelles 70:121–126

    Google Scholar 

  • Guex J, Koch A, O’Dogherty L, Bucher H (2003) A morphogenetic explanation of Buckman’s law of covariation. Bulletin de la Société géologique de France 174:603–606

    Google Scholar 

  • Guzman LF, Rios CF (1987) Age and growth of the sub-antarctic limpet Nacella (Patinigera) magellanica magellanica (Gmelin, 1791) from the Strait of Magellan, Chile. Veliger 30:159–166

    Google Scholar 

  • Hammer Ø (2000) A theory for the formation of commarginal ribs in mollusc shells by regulative oscillation. J Molluscan Stud 66(3):383–392

    Google Scholar 

  • Hammer Ø, Bucher H (1999) Reaction-diffusion processes: application to the morphogenesis of ammonoid ornamentation. Geobios 32:841–852

    Google Scholar 

  • Hammer Ø, Bucher H (2005a) Models for the morphogenesis of the molluscan shell. Lethaia 38:111–122

    Google Scholar 

  • Hammer Ø, Bucher H (2005b) Buckman’s first law of covariation: a case of proportionality. Lethaia 38:67–72

    Google Scholar 

  • Hammer Ø, Bucher H (2006) Generalized ammonoids hydrostatics modelling, with application to Intornites and intraspecific variation in Amaltheus. Paleontol Res 10:91–96

    Google Scholar 

  • Hayami I, Okamoto T (1986) Geometric regularity of some oblique sculptures in pectinid and other bivalves: recognition by computer simulations. Paleobiology 12:433–449

    Google Scholar 

  • Hoffmann R, Keupp H (2015) Ammonoid Paleopathology. In: Klug C (ed) Ammonoid Paleobiology, Chapter 21

    Google Scholar 

  • Hutchinson JMC (1989) Control of gastropod shell shape: the role of the preceding whorl. J Theor Biol 140:431–444

    Google Scholar 

  • Hutchinson JMC (1990) Control of gastropod shell form via apertural growth rates. J Morph 206:259–264

    Google Scholar 

  • Huxley JS, Teissier G (1936) Terminology of relative growth. Nature 137:780–781

    Google Scholar 

  • Iijima A (2001) Growth of the intertidal snail, Monodonta labio (Gastropoda, Prosobranchia) on the Pacific coast of central Japan. Bull Mar Sci 68:27–36

    Google Scholar 

  • Illert C (1987) Formulation and solution of the classical problem. I. Shell geometry. Nuovo Cimento 9:791–813

    Google Scholar 

  • Illert C (1989) Formulation and solution of the classical problem. II. Tubular three-dimensional seashell surfaces. Nuovo Cimento 11:761–780

    Google Scholar 

  • Illert C (1990) Nipponites mirabilis: a challenge to seashell theory. Nuovo Cimento D 12:1405–1421

    Google Scholar 

  • Jackson DJ et al (2006) A rapidly evolving secretome builds and patterns a sea shell. BMC Biol 4:40

    Google Scholar 

  • Jackson DJ, Worheide G, Degnan BM (2007) Dynamic expression of ancient and novel molluscan shell genes during ecological transitions. BMC Evol Biol 7:160

    Google Scholar 

  • Jacobs DK, Landman NH (1993) Nautilus—a poor model for the function and behavior of ammonoids? Lethaia 26:101–111

    Google Scholar 

  • Johnson MS, Black R (2008) Adaptive responses of independent traits to the same environmental gradient in the intertidal snail Bembicium vittatum. Heredity 101:83–91

    Google Scholar 

  • Kavanagh KD, Evans AR, Jernvall J (2007) Predicting evolutionary patterns of mammalian teeth from development. Nature 449:427–432

    Google Scholar 

  • Kemp P, Bertness MD (1984) Snail shape and growth rates: evidence for plastic shell allometry in Littorina littorea. PNAS USA Biol Sci 81:811–813

    Google Scholar 

  • Kennedy WJ, Cobban WA (1976) Aspects of ammonite biology, biogeography, and biostratigraphy. Spec Pap in. Palaeontology 17:1–94

    Google Scholar 

  • Klingenberg CP (1998) Heterochrony and allometry: the analysis of evolutionary change in ontogeny. Biol Rev 73:79–123

    Google Scholar 

  • Klug C (2001) Life-cycles of some Devonian ammonoids. Lethaia 34:215–233

    Google Scholar 

  • Klug C, Hoffmann R (2015) Ammonoid Septa and Sutures. This volume

    Google Scholar 

  • Klug C, Korn D, Landman NH, Tanabe K, De Baets K, Bert D, Naglik C (2015) Describing ammonoid conchs. This volume

    Google Scholar 

  • Korn D (2012) Quantification of ontogenetic allometry in ammonoids: ontogenetic allometry in ammonoids. Evol Dev 14:501–514

    Google Scholar 

  • Korn D, Klug C (2003) Morphological pathways in the evolution of early and middle Devonian ammonoids. Paleobiology 29:329–348

    Google Scholar 

  • Korn D, Klug C (2007) Conch form analysis, variability, morphological disparity, and mode of life of the Frasnian (Late Devonian) ammonoid Manticoceras from Coumiac (Montagne Noire, France). In: Landman NH, Davis RA, Mapes RH (eds) Cephalopods present and past: new insights and fresh perspectives. Springer Science & Business Media, New York

    Google Scholar 

  • Kröger B (2002) On the efficiency of the buoyancy apparatus in ammonoids: evidences from sublethal shell injuries. Lethaia 35:61–70

    Google Scholar 

  • Landman NH, Waage KM (1986) Shell abnormalities in scaphitid ammonites. Lethaia 19:211–224

    Google Scholar 

  • Linsley RM (1977) Some “laws” of gastropod shell form. Paleobiology 3:196–206

    Google Scholar 

  • Linsley RM (1978) Shell form and the evolution of gastropods. Am Sci 66:432–441

    Google Scholar 

  • Løvtrup S, Løvtrup M (1988) The morphogenesis of molluscan shells: a mathematical account using biological parameters. J Morph 197:53–62

    Google Scholar 

  • McGhee GR (1978) Analysis of shell torsion phenomenon in Bivalvia. Lethaia 11:315–329

    Google Scholar 

  • McGhee GR (1980) Shell form in the biconvex articulate Brachiopoda: a geometric analysis. Paleobiology 6:57–76

    Google Scholar 

  • McGhee GR (1999) Theoretical morphology. Columbia University, New York

    Google Scholar 

  • McGhee GR (2001) The question of spiral axes and brachiopod shell growth: a comparison of morphometric techniques. Paleobiology 27:716–723

    Google Scholar 

  • Meinhardt H (1995) The algorithmic beauty of sea shells. Springer, Berlin

    Google Scholar 

  • Meinhardt H (2008) Models of biological pattern formation: from elementary steps to the organization of embryonic axes. Curr Top Dev Biol 81:1–63

    Google Scholar 

  • Meinhardt H, Gierer A (1974) Applications of a theory of biological pattern formation based on lateral inhibition. J Cell Sci 15:321–346

    Google Scholar 

  • Meinhardt H, Gierer A (2000) Pattern formation by local self-activation and lateral inhibition. Bioessays 22:753–760

    Google Scholar 

  • Meinhardt H, Klingler H (1988) A model for pattern formation of shells of mollusks. J Theor Biol 126:63–89

    Google Scholar 

  • Meister C (1988) Ontogeny and evolution of the Amaltheidae (Ammonoidea). Eclogae Geol Helv 81:763–841

    Google Scholar 

  • Monnet C, Bucher H (2005) New middle and late Anisian (Middle Triassic) ammonoid faunas from northwestern Nevada (USA): taxonomy and biochronology. Fossils Strata 52:1–60

    Google Scholar 

  • Monnet C, De Baets K, Yacobucci MM (2015) Buckman’s rules of covariation. In: Klug C, Korn D, De Baets K, Kruta I, Mapes RH (eds) Ammonoid paleobiology: from macroevolution to paleogeography. Springer, Dordrecht

    Google Scholar 

  • Morita R (1991a) Finite element analysis of a double membrane tube (DMS-tube) and its implication for gastropod shell morphology. J Morph 207:81–92

    Google Scholar 

  • Morita R (1991b) Mechanical constraints on aperture form in gastropods. J Morph 207:93–102

    Google Scholar 

  • Morita R (1993) Development mechanics of retractor muscles and the “Dead Spiral Model” in gastropod shell morphogenesis. N Jahrb Geol Paläont Abh 190:191–217

    Google Scholar 

  • Morita R (2003) Why do univalve shells of gastropods coil so tightly? A head-foot guidance model of shell growth and its implication on developmental constraints. In: Sekimura T, Noji S, Ueno N, Maini PK (eds) Morphogenesis and pattern formation in biological systems: experiments and models. Springer, Tokyo

    Google Scholar 

  • Moseley H (1838) On the geometrical forms of turbinated and discoid shells. Philos Trans R Soc Lond 128:351–370

    Google Scholar 

  • Moulton DE, Goriely A (2014) Surface growth kinematics via local curve evolution. J Math Biol 68:81–108

    Google Scholar 

  • Moulton DE, Goriely A, Chirat R (2012) Mechanical growth and morphogenesis of seashells. J Theor Biol 311:69–79

    Google Scholar 

  • Murray JD (1989) Mathematical biology. Springer, Berlin

    Google Scholar 

  • Neige P, Brayard A, Gerber S, Rouget I (2009) Ammonoids (Mollusca, Cephalopoda): recent advances and contributions to evolutionary paleobiology. Comptes Rendus Pale 8:167–178

    Google Scholar 

  • Okamoto T (1988a) Analysis of heteromorph ammonoids by differential geometry. Palaeontology 31:37–51

    Google Scholar 

  • Okamoto T (1988b) Changes in life orientation during the ontogeny of some heteromorph ammonoids. Paleontology 31:281–294

    Google Scholar 

  • Okamoto T (1988c) Developmental regulation and morphological saltation in the heteromorph ammonite Nipponites. Paleobiology 14/3:272–286

    Google Scholar 

  • Okamoto T (1996) Theoretical modeling of ammonoid morphology. In: Landman NH, Tanabe K, Davis RA (eds) Ammonoid Paleobiology. Topics in Geobiology, 13. Plenum, New York

    Google Scholar 

  • Oster GF, Shubin N, Murray JD, Alberch P (1988) Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny. Evolution 42(5):862–884

    Google Scholar 

  • Pappas JL, Miller DJ (2013) A Generalized approach to the modeling and analysis of 3D surface morphology in organisms. PLoS ONE 8(10):e77551. doi:10.1371/journal.pone.0077551

    Google Scholar 

  • Pérez-Claros JA, Olóriz F, Palmqvist P (2007) Sutural complexity in Late Jurassic ammonites and its relationship with phragmocone size and shape: a multidimensional approach using fractal analysis. Lethaia 40:253–272

    Google Scholar 

  • Picken GB (1980) Distribution, growth, and reproduction of the antarctic limpet Nacella (Patinigera) Concinna (Strebel, 1908). J Exp Mar Biol Ecol 42:71–85

    Google Scholar 

  • Polly PD (2007) Development with a bite. Nature 449:413–415

    Google Scholar 

  • Raup DM (1961) The geometry of coiling in gastropods. Proc Natl Acad Sci USA 47:602–609

    Google Scholar 

  • Raup DM (1962) Computer as aid in describing gastropod shells. Science 138:150–152

    Google Scholar 

  • Raup DM (1966) Geometric analysis of shell coiling: general problems. J Paleont 40:1178–1190

    Google Scholar 

  • Raup DM (1967) Geometric analysis of shell coiling: coiling in ammonoids. J Paleont 41:43–65

    Google Scholar 

  • Raup DM, Chamberlain JA Jr (1967) Equations for volume and center of gravity in amnonoid shells. J Paleont 41:566–574

    Google Scholar 

  • Raup DM, Michelson A (1965) Theoretical morphology of the coiled shell. Science 147:1294–1295

    Google Scholar 

  • Renvoisé E, Evans AR, Jebrane A, Labruère C, Laffont R, Montuire S (2009) Evolution of mammal tooth patterns: new insights from a developmental prediction model. Evolution 63:1327–1340

    Google Scholar 

  • Reyment RA, Kennedy WJ (1991) Phenotypic plasticity in a Cretaceous ammonite analyzed by multivariate statistical methods—a methodological study. Evol Biol 25:411–426

    Google Scholar 

  • Rice SH (1998) The bio-geometry of mollusc shells. Paleobiology 24:133–149

    Google Scholar 

  • Rieber H (1972) Die Triasfauna der Tessiner Kalkalpen. XXII. Cephalopoden aus der Grenzbitumenzone (Mittelere Trias) des Monte San Giorgio (Kanton Tessin, Schweiz). Schweizerische Paläont Abh 93:1–95

    Google Scholar 

  • Salazar-Ciudad I, Jernvall J (2010) A computational model of teeth and the developmental origins of morphological variation. Nature 464:583–586

    Google Scholar 

  • Salazar-Ciudad I, Jernvall J, Newman S (2003) Mechanisms of pattern formation in development and evolution. Development 130:2027–2037

    Google Scholar 

  • Saunders WB, Shapiro EA (1986) Calculation and simulation of Ammonoid hydrostatics. Paleobiology 12:64–79

    Google Scholar 

  • Saunders WB, Swan ARH (1984) Morphology and morphologic diversity of mid-Carboniferous (Namurian) ammonoids in time and space. Paleobiology 10:195–228

    Google Scholar 

  • Savazzi E (1985) Shellgen: a basic program for the modeling of molluscan shell ontogeny and morphogenesis. Comput Geosci 11:521–530

    Google Scholar 

  • Savazzi E (1987) Geometric and functional constraints on bivalve shell morphology. Lethaia 20:293–306

    Google Scholar 

  • Savazzi E (1990) Biological aspects of theoretical shell morphology. Lethaia 23:195–212

    Google Scholar 

  • Savazzi E (1991) Constructional Morphology of strombid gastropods. Lethaia 24:311–331

    Google Scholar 

  • Schander C, Sundberg P (2001) Useful characters in gastropod phylogeny: soft information or hard facts? Syst Biol 50:136–141

    Google Scholar 

  • Schindel DE (1990) Unoccupied morphospace and the coiled geometry of gastropods: architectural constraint or geometrical covariation. In: Ross RM, Allmon WD (eds) Causes of evolution: a paleontological perspectives. University of Chicago, Chicago

    Google Scholar 

  • Schöne BR, Lega J, Flessa KW, Goodwin DH, Dettman DL (2002) Reconstructing daily temperatures from growth rates of the intertidal bivalve mollusk Chione cortezi (northern Gulf of California, Mexico). Palaeogeogr Palaeoclimat Palaeoeco 184:131–146

    Google Scholar 

  • Schöne BR, Rodland DL, Wehrmann A, Heidel B, Oschmann W, Zhang ZJ, Fiebig J, Beck L (2007) Combined sclerochronologic and oxygen isotope analysis of gastropod shells (Gibbula cineraria, North Sea): life-history traits and utility as a high-resolution environmental archive for Kelp forests. Marine Biol 150:1237–1252

    Google Scholar 

  • Seilacher A (1970) Arbeitskonzept zur Konstruktionmorphologie. Lethaia 3:393–396

    Google Scholar 

  • Seilacher A (1991) Self-organizing mechanisms in morphogenesis and evolution. In: Schmidt-Kittler N, Vogel K (eds) Constructional Morphology and Evolution. Springer Berlin Heidelberg, pp. 251–271

    Google Scholar 

  • Shubin N, Tabin C, Carroll S (2009) Deep homology and the origins of evolutionary novelty. Nature 457:818–823

    Google Scholar 

  • Skalak R, Farrow DA, Hoger A (1997) Kinematics of surface growth. J Math Biol 35:869–907

    Google Scholar 

  • Spight T (1973) Ontogeny environment and shape of a marine snail Thais lamellosa. J Exp Mar Biol Ecol 13:215–228

    Google Scholar 

  • Spight TM, Lyons A (1974) Development and functions of the shell sculpture of the marine snail Ceratostoma foliatum. Marine Biol 24:77–83

    Google Scholar 

  • Spight TM, Birkelan C, Lyons A (1974) Life histories of large and small murexes (Prosobranchia-Muricidae). Marine Biol 24:229–242

    Google Scholar 

  • Stone JR (1995) Cerioshell: a computer program designed to simulate variation in shell form. Paleobiology 21:509–519

    Google Scholar 

  • Stone JR (1996a) Computer-simulated shell size and shape variation in the caribbean land snail genus Cerion: a test of geometrical constraints. Evolution 50:341–347

    Google Scholar 

  • Stone JR (1996b) The evolution of ideas: a phylogeny of shell models. Am Nat 148:904–929

    Google Scholar 

  • Thompson D’AW (1917) On growth and form. Cambridge University, Cambridge

    Google Scholar 

  • Truman AE (1941) The ammonite body chamber with special reference the buoyancy and mode of life of the living ammonite. Q J Geol Soc Lond 96:339–383

    Google Scholar 

  • Trussell GC (1996) Phenotypic plasticity in an intertidal snail: the role of a common crab predator. Evolution 50:448–454

    Google Scholar 

  • Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond B Biol Sci 237:37–72

    Google Scholar 

  • Ubukata T (1997) Microscopic growth of bivalve shells and its computer simulation. Veliger 40:165–177

    Google Scholar 

  • Ubukata T (2001) Morphological significance of the orientation of shell coiling and the outline of “the aperture” in bivalve molluscs. N Jahrb Geol Paläont Abhandlungen 221:249–270

    Google Scholar 

  • Ubukata T (2003) Computer modeling of microscopic features of molluscan shells. In: Sekimura T, Noji S, Ueno N, Maini PK (eds) Morphogenesis and pattern formation in biological systems: experiments and models. Springer, Tokyo

    Google Scholar 

  • Ubukata T (2005) Theoretical morphology of bivalve shell sculptures. Paleobiology 31:643–655

    Google Scholar 

  • Ubukata T, Nakagawa Y (2000) Modelling various sculptures in the Cretaceous bivalve Inoceramus hobetsensis. Lethaia 33:313–329

    Google Scholar 

  • Urdy S (2012) On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis. Biol Rev Camb Philos Soc 87:786–803

    Google Scholar 

  • Urdy S, Goudemand N, Bucher H, Chirat R (2010a) Allometries and the morphogenesis of the molluscan shell: a quantitative and theoretical model. J exp zool B 314:280–302

    Google Scholar 

  • Urdy S, Goudemand N, Bucher H, Chirat R (2010b) Growth-dependent phenotypic variation of molluscan shells: implications for allometric data interpretation. J exp zool B 314:303–326

    Google Scholar 

  • Urdy S, Wilson LAB, Haug JT, Sánchez-Villagra MR (2013) On the unique perspective of paleontology in the study of developmental evolution and biases. Biol Theory 8:293–311

    Google Scholar 

  • Vasconcelos P, Gaspar MB, Castro M (2006) Development of indices for nonsacrificial sexing of imposex-affected Hexaplex (Trunculariopsis) Trunculus (Gastropoda: Muricidae). J Molluscan Stud 72(3):285–294

    Google Scholar 

  • Vermeij GJ (1980) Gastropod growth rate, allometry, and adult size: environmental implications. In: Rhoads DC, Lutz RA (eds) Skeletal growth of aquatic organisms: biological records of environmental change. Plenum, New York

    Google Scholar 

  • Vermeij GJ (2002) Characters in context: molluscan shells and the forces that mold them. Paleobiology 28:41–54

    Google Scholar 

  • Ward PD (1980) Comparative shell shape distributions in Jurassic-Cretaceous ammonites and Jurassic-Tertiary nautiloids. Paleobiology 6:32–43

    Google Scholar 

  • Ward PD (1985) Periodicity of chamber formation in chambered cephalopods: evidences from Nautilus macromphalus and Nautilus pompilius. Paleobiology 11:438–450

    Google Scholar 

  • Westermann GEG (1966) Covariation and taxonomy of the Jurassic ammonite Sonninia adrica (Waagen). N Jahrb Geol Paläont Abh 124:289–312

    Google Scholar 

  • Whitworth WA (1862) The equi-angular spiral, its chief properties proved geometrically. Messenger Math 1:5–13

    Google Scholar 

  • Wilson LAB, Madden RH, Kay RF, Sanchez-Villagra MR (2012) Testing a developmental model in the fossil record: molar proportions in South American ungulates. Paleobiology 38:308–321

    Google Scholar 

  • Yeap KL, Black R, Johnson MS (2001) The complexity of phenotypic plasticity in the intertidal snail Nodilittorina australis. Biol J Linn Soc 72:63–76

    Google Scholar 

  • Zhu J, Zhang YT, Alber MS, Newman SA (2010) Bare bones pattern formation: a core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution. PLoS ONE 5:e10892

    Google Scholar 

Download references

Acknowledgments

I thank Hugo Bucher (PIMUZ) for courteously providing the specimens illustrated in Fig. 6.8 and allowing them to be published here. I thank Nicolas Goudemand for fruitful discussions, as well as Takao Ubukata and an anonymous reviewer for providing useful comments during the reviewing process. This work would not have been possible without the support of the Swiss National Science Foundation (200021_124784/1 and PA00P3–136478) and the University of Zurich.

Author information

Authors and Affiliations

  1. Department of Anatomy, Department of Bioengineering and Therapeutic Sciences, University of California San Francisco, Genentech Hall, 600, 16th Street, 94143–2140, San Francisco, CA, USA

    Séverine Urdy

  2. Physics Institute, Disordered and Biological Soft Matter, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Séverine Urdy

Authors
  1. Séverine Urdy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Séverine Urdy .

Editor information

Editors and Affiliations

  1. Paläontologisches Institut und Museum, University of Zurich, Zürich, Switzerland

    Christian Klug

  2. Leibniz-Institut für Evolutions und Biodiversitätsforschung, Museum für Naturkunde, Berlin, Germany

    Dieter Korn

  3. GeoZentrum Nordbayern, Friedrich-Alexander-Universität Erlangen, Erlangen, Germany

    Kenneth De Baets

  4. Division of Paleontology, American Museum of Natural History, New York, New York, USA

    Isabelle Kruta

  5. North Carolina Museum of Natural Science, Raleigh, USA

    Royal H. Mapes

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Urdy, S. (2015). Theoretical Modelling of the Molluscan Shell: What has been Learned From the Comparison Among Molluscan Taxa?. In: Klug, C., Korn, D., De Baets, K., Kruta, I., Mapes, R. (eds) Ammonoid Paleobiology: From anatomy to ecology. Topics in Geobiology, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9630-9_6

Download citation

Publish with us

Policies and ethics

Search

Navigation