Abstract
Ammonites are extinct molluscs belonging to Class Cephalopoda which lived during the Mesozoic Era. Their usefulness in Jurassic and Cretaceous paleontology and biostratigraphy studies has been widely proved. They have been studied by several authors worldwide to achieve information regarding their habitats and the climate of the world in past eras. A probabilistic analysis of the paleo-environmental causes that generated complex suture lines in ammonites has been made by means of coherent upper conditional previsions defined with respect to Hausdorff outer measures. In particular, studies have centered on the role of hydrostatic pressure.
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18 January 2017
An erratum to this article has been published.
References
Arkell WJ, Furnish WM, Kummel B, Miller AK, Moore RC, Schindewolf OH, Sylvester-Bradley PC, Wright W (1957) Teatrise on Invertebrate Paleontology. Part L, Mollusca, Cephalopoda, Ammonoidea. Geological Soc. of America University of Kansas Press 4:1–490
C\(\acute{\rm e}\)saro E (1905) Remarques sur la courbe de von Koch. Atti della Reale Accademia delle Scienze Fisiche e Matematiche di Napoli 12:1–12
Checa A, Martin-Ramos D (1989) Growth and function of spines in the Jurassic ammonites Aspidoceras. Palaeontology 32(3):645–655
Choquet G (1953) Theory of capacities. Ann de l’Institut Four 5:131–295
Damiani G (1986) Significato funzionale dell’evoluzione dei setti e delle linee di sutura dei nautiloidi e degli ammonoidi. In Pallini G, et al. (eds) Atti I Conv. Int. F.E.A., Pergola, 86
Damiani G (1989) I frattali e le linee suturali delle ammoniti. Le Scienze 60–68
Damiani G (1990) Computer simulation of some ammonoid suture lines. In: Pallini, et al. (eds) Atti II Conv. Int. F.E.A., Pergola 1987, 221–228
de Finetti B (1972) Probability, induction and statistics. Wiley, New York
de Finetti B (1974) Theory of probability. Wiley, London
Denneberg D (1994) Non-additive measure and integral. Kluwer Academic Publishers
Di Cencio A (2007) Aspetti sedimentologici e paleontologici dei sedimenti toarciani nellarea del bacino umbro-marchigiano-sabino: cause dei cambiamenti dellambiente deposizionale ai passaggi Pliensbachiano-Toarciano e Toarciano-Aaleniano. Universit “G. d’Annunzio”, Chieti PhD Thesis, 1–356
Di Cencio A (2015a) Position of spines in Toarcian ammonites. Correlation with shape of shell and complexity of sutural line. Hypothesis of life style. XV Edizione delle Giornate di Paleontologia, 27–29 Maggio, Palermo
Di Cencio, A. (2015b) The systematic and taxonomic revision of the Pleydellia-group ammonites from the Minette ironstones (Late Toarcian), southern Luxembourg. XV Edizione delle Giornate di Paleontologia, 27–29 Maggio, Palermo
Di Cencio A, et Doria S (2015) Probabilistic analysis of sutural lines developed in ammonites. An example: lower Jurassic Hammatocerataceae. In: Augustin D, Miranda Q (eds) ISIPTA ’15—Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications, 20–24 July 2015, Pescara (Italy)
d’Orbigny A (1842) Description zoologique et Geologique de tous les Animaux molluques et rayonns. Terrains Jurassiques, Atlas 51
Doria S (2007) Probabilistic independence with respect to upper and lower conditional probabilities assigned by Hausdorff outer and inner measures. Int J Approx Reason 46:617–635
Doria S (2012) Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure. Ann Operat Res, pp 33–48
Dubins LE (1975) Finitely additive conditional probabilities, conglomerability and disintegrations. Ann Probab 3:89–99
Falconer KJ (1896) The geometry of fractals sets. Cambridge University Press
Ferri R, Venturi F (2001) Ammoniti liassici dellAppennino Centrale. Tibergraph,Citt di Castello (PG), 1–272
Innamorati G, Battista F, Citton P, Romano M, Di Cencio A (2015) Occurrence of graphoceratid - Pleydellia buckmani Maubeuge, 1947 - in the Umbria-Marche domain and its biostratigraphic constraints. XV Edizione delle Giornate di Paleontologia, 27–29 Maggio, Palermo
Janensch W (1902) Die Jurensisschischten des Elsass. Abhandl. Z. Spezialkarte v. Elsass-Lothringen, Strassburg 5:1–151
Kovacs Z (2009) Toarcian-Aalenian Hammatoceratinae (Ammonitina) from the Gerecse Mts (NE Transdanubian Range, Hungary). Fragm Paleontol Hung 5:1–72
von Koch H (1904) Sur une courve continue sans tangente, obtenue par une construction geometrique elementaire. Arkiv for Matematik Astronomioch Fysick 1:681–704
Martinez Gutierrez G (1992) Hammatoceratinae (Ammonitina) del Toarciense superiore y Aaleniense en la cordillera Iberica. Thesis, Dep. Pal. Univ. Madrid, pp 1–398
Maubeuge PL (1947) Sur quelques ammonites de l“Aalnien Ferrugineux” du Luxembourg et sur l’chelle stratigraphique de la formation ferrifre franco-belgo-luxemburgeoise. Inst. Grand Ducal de Luxembourg, Section Sci. natur., Luxembourg, XVII, 73–87
Nicosia U, Pallini G, Schiavinotto F (1978) Non time consuming method to reproduce ammonoid sutures. Boll Soc Paleont Ital 16(1):125–128
Orsina L (2000) Teorema delle contrazioni e sistemi di funzioni iterate
Pallini G, Elmi S, Gasparri F (2003) Late Toarcian late Aalenian ammonites assemblage from Mt. Magaggiaro (Western Sicily, Italy). Geologica Romana 37:1–66 (Roma)
Perez-Claros JA, Palmqvist P, Oloriz F (2002) First and second order of suture complexity in ammonites: a new methodological approach using fractal analysis. Math Geol 34(3):313–343
Regazzini E (1985) Finitely additive conditional probabilities. Rend Sem Math Fis Milano 55:69–89
Regazzini E (1987) De Finetti’s coherence and statistical inference. Ann Stat 15(2):845–864
Rogers CA (1970) Hausdorff measures. Cambridge University Press
Rulleau L (2008) Les Nautilus du Lias et du Dogger de la rgion Lyonnaise. Sect Geol Paleont Com Enter Lafarge 1–149
Santantonio M (1994) Pelagic carbonate platforms in the geologic record: their classification, and sedimentary and paleontotectonic evolution. AAPG Bull 78(1):122–141
Venturi F, Rea G, Silvestrini G, Bilotta M (2010) Ammoniti. Un viaggio geologico nelle montagne Appenniniche. Porzi editoriali 1–367, Perugia
Venturi F, Rossi S (2003) Subasio, Origine e vicende di un Monte Appenninico. Porzi editoriali 1–112, Perugia
Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, London
Acknowledgements
The authors are grateful to Alain Faber, Robert Weis and Ben Thuy of Natural History Museum of Luxembourg for permission to study some of the material here discussed. We thank late Giovanni Pallini (University of Chieti) for introducing one of the authors to science of ammonites and Nino Mariotti (University of Rome) for discussion.
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An erratum to this article is available at https://doi.org/10.1007/s11004-017-9674-1.
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Di Cencio, A., Doria, S. Probabilistic Analysis of Suture Lines Developed in Ammonites: The Jurassic Examples of Hildocerataceae and Hammatocerataceae. Math Geosci 49, 737–750 (2017). https://doi.org/10.1007/s11004-016-9666-6
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DOI: https://doi.org/10.1007/s11004-016-9666-6