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Allometries and the morphogenesis of the molluscan shell: a quantitative and theoretical model


Urdy, S; Goudemand, N; Bucher, H; Chirat, R (2010). Allometries and the morphogenesis of the molluscan shell: a quantitative and theoretical model. Journal of Experimental Zoology. Part B: Molecular and Developmental Evolution:280-302.

Abstract

This article explores the close relationships between growth rate and allometries of molluscan shells. After reviewing the previous theoretical approaches devoted to the understanding of shell form and its morphogenesis, we present a free-form vector model which can simulate apertural shape changes and nonlinear allometries. Shell morphology is generated by iteratively adding a growth increment onto the last computed aperture. The first growth increment defines so-called growth vectors which are assumed to be constant in direction (relative to the last computed aperture position) during a simulation of a shell (ontogeny). These growth vectors are uniformly scaled at each time step according to various growth rate curves that are used to simulate the mantle growth over time. From the model, we derive morphometric variables that illustrate the ontogenetic trajectories in time-size-shape space. We investigate the effects of changing the growth curves types, growth rate parameters and growth vector maps on the direction, speed and patterns of ontogenetic allometries. Because this model focuses the issue on time, it highlights a plausible effect of growth rate on shell shape and illustrates some fundamental geometrical properties of the logarithmic spiral, in particular the close relationship between the size and the geometry of growth increments. This model could be used to develop a mathematically data-driven approach where experimentally obtained growth curves could be used as inputs in the model. More generally, our study recalls the role of growth rates in the generation of allometries.

Abstract

This article explores the close relationships between growth rate and allometries of molluscan shells. After reviewing the previous theoretical approaches devoted to the understanding of shell form and its morphogenesis, we present a free-form vector model which can simulate apertural shape changes and nonlinear allometries. Shell morphology is generated by iteratively adding a growth increment onto the last computed aperture. The first growth increment defines so-called growth vectors which are assumed to be constant in direction (relative to the last computed aperture position) during a simulation of a shell (ontogeny). These growth vectors are uniformly scaled at each time step according to various growth rate curves that are used to simulate the mantle growth over time. From the model, we derive morphometric variables that illustrate the ontogenetic trajectories in time-size-shape space. We investigate the effects of changing the growth curves types, growth rate parameters and growth vector maps on the direction, speed and patterns of ontogenetic allometries. Because this model focuses the issue on time, it highlights a plausible effect of growth rate on shell shape and illustrates some fundamental geometrical properties of the logarithmic spiral, in particular the close relationship between the size and the geometry of growth increments. This model could be used to develop a mathematically data-driven approach where experimentally obtained growth curves could be used as inputs in the model. More generally, our study recalls the role of growth rates in the generation of allometries.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Paleontological Institute and Museum
Dewey Decimal Classification:560 Fossils & prehistoric life
Language:English
Date:2010
Deposited On:28 Jan 2010 13:51
Last Modified:06 Dec 2017 23:55
Publisher:Wiley-Blackwell
ISSN:1552-5007
Publisher DOI:https://doi.org/10.1002/jez.b.21337
PubMed ID:20095030

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