A Mathematical Model for Mollusc Shells Based on Parametric Surfaces and the Construction of Theoretical Morphospaces
Por:
Contreras-Figueroa, Gabriela, Aragon, Jose L.
Publicada:
1 mar 2023
Resumen:
In this study, we propose a mathematical model based on parametric
surfaces for the shell morphology of the phylum Mollusca. Since David
Raup's pioneering works, many mathematical models have been proposed for
different contexts to describe general shell morphology; however, there
has been a gap in the practicality of models that allow the estimation
of their parameter values in real specimens. Our model collects ideas
from previous pioneering studies; it rests on the equation of the
logarithmic spiral, uses a fixed coordinate system (coiling axis), and
defines the position of the generating curve with a local moving system
using the Frenet frame. However, it improves upon previous models by
applying apex formation, rotations, and substantially different
parameter definitions. Furthermore, the most conspicuous improvement is
the development of a simple and standardized methodology to obtain the
six theoretical parameters from shell images from different mollusc
classes and to generate useful theoretical morphospaces. The model was
applied to reproduce the shape of real mollusc-shell specimens from
Gasteropoda, Cephaloda and Bivalvia, which represent important classes
in geological time. We propose a specific methodology to obtain the
parameters in four morphological groups: helicoidal, planispiral, conic,
and valve-like shells, thereby demonstrating that the model offers an
adequate representation of real shells. Finally, possible improvements
to the model are discussed along with further work. Based on the above
considerations, the capacity of the model to allow the construction of
theoretical morphospaces, the methodology to estimate parameters and
from the comparison between several existing models for shells, we
believe that our model can contribute to future research on the
development, diversity and evolutionary processes that generated the
diversity in mollusc shells.
Filiaciones:
Contreras-Figueroa, Gabriela:
Univ Nacl Autonoma Mexico, Inst Neurobiol, Blvd Juriquilla 3001, Queretaro 76230, Mexico
Univ Nacl Autonoma Mexico, Ctr Fis Aplicada & Tecnol Avanzada, Blvd Juriquilla 3001, Queretaro 76230, Mexico
Aragon, Jose L.:
Univ Nacl Autonoma Mexico, Ctr Fis Aplicada & Tecnol Avanzada, Blvd Juriquilla 3001, Queretaro 76230, Mexico
gold
|