A Simple Mathematical Model for Chamber Arrangement of Planktic Foraminifera

Takashi Yoshino¹*, Katsunori Kimoto², Naoko Kishimoto³, Atsushi Matsuoka⁴, Toshiyuki Kurihara⁵, Naoto Ishida⁵ and Shu Matsuura⁶

¹Department of Mechanical Engineering, Toyo University, Kujirai 2100, Kawagoe, Saitama 350-8585, Japan
²Research Institute for Global Change (RIGC), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Japan
³Graduate School of Engineering, Kyoto Univiersity, Japan
⁴Department of Geology, Faculty of Science, Niigata University, Japan
⁵Graduate School of Science and Technology, Niigata University, Japan
⁶Faculty of Education, Tokyo Gakugei University, Japan
*E-mail address: tyoshino@toyonet.toyo.ac.jp

(Received March 16, 2009; Accepted January 12, 2010)

Abstract. We propose a simple mathematical model for chamber arrangement of planktic foraminifera. The arrangement is approximated using connection of spheres. It is represented by combination of four sequences: they correspond to radius of chamber, horizontal/vertical distance of connected chambers, and angle of horizontally projected two lines constructed by connection of centers of adjacent spheres. We assumed that the sequences of the radius and horizontal/vertical distances are geometric series and that of the angle is constant. We succeeded in reproducing the chamber configuration of all recent planktic foraminifera at the level of family in taxonomy. We also point out that some other parameters are required in order to classify the chamber arrangement in detail. The model enables us to consider an optimization problem of the volume-surface area ratio which corresponds to the cost of chamber forming materials. Using the simplest case of our models, we obtain an optimized radius-distance relation.

Keywords: Planktic Foraminifera, Chamber Arrangement, Mathematical Model