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A Biogeometrical Model for Corolla Fusion in Asclepiad Flowers

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Modeling in Mathematics

Part of the book series: Atlantis Transactions in Geometry ((ATLANTIS,volume 2))

Abstract

The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization.

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Authors and Affiliations

  1. Department of Biosciences Engineering, University of Antwerp, Groenenborgerlaan 171, 2020, Antwerpen, Belgium

    Johan Gielis

  2. The Antenna Company Nederland B.V., High Tech Campus 41, Eindhoven, The Netherlands

    Diego Caratelli

  3. Tomsk Polytechnic University, 84/3 Sovetskaya Street, 634050, Tomsk, Russia

    Diego Caratelli

  4. LE2I FRE2005, CNRS, Arts et Métiers, Université Bourgogne Franche-Comté, 21000, Dijon, France

    Yohan Fougerolle

  5. International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186, Roma, Italia

    Paolo Emilio Ricci

  6. Radboud University Nijmegen, Section Plant Genetics, Institute for Wetland and Water Research, Faculty of Science, Nijmegen, The Netherlands

    Tom Gerats

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  1. Johan Gielis
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  2. Diego Caratelli
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  3. Yohan Fougerolle
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  4. Paolo Emilio Ricci
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  5. Tom Gerats
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Correspondence to Johan Gielis .

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Editors and Affiliations

  1. Bio-Engineering Sciences, University of Antwerp, Antwerp, Belgium

    Johan Gielis

  2. International Telematic University UniNettuno, Roma, Italy

    Paolo Emilio Ricci

  3. Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Ilia Tavkhelidze

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Gielis, J., Caratelli, D., Fougerolle, Y., Ricci, P.E., Gerats, T. (2017). A Biogeometrical Model for Corolla Fusion in Asclepiad Flowers. In: Gielis, J., Ricci , P., Tavkhelidze, I. (eds) Modeling in Mathematics . Atlantis Transactions in Geometry, vol 2. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-261-8_7

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