scholarly journals A method for quantifying, visualising, and analysing gastropod shell form

2014 ◽  
Author(s):  
Thor-Seng Liew ◽  
Menno Schilthuizen
Keyword(s):  
Evolutionary Biology ◽  
Growth Trajectory ◽  
Theoretical Modelling ◽  
Linear Measurements ◽  
Gastropod Shell ◽  
Qualitative Comparison ◽  
Shell Form ◽  
Potential Applications ◽  
Curvature And Torsion ◽  
Measurable Structure

Quantitative analysis of organismal form is an important component for almost every branch of biology. Although generally considered an easily-measurable structure, the quantification of gastropod shell form is still a challenge because shells lack homologous structures and have a spiral form that is difficult to capture with linear measurements. In view of this, we adopt the idea of theoretical modelling of shell form, in which the shell form is the product of aperture ontogeny profiles in terms of aperture growth trajectory that is quantified as curvature and torsion, and of aperture form that is represented by size and shape. We develop a workflow for the analysis of shell forms based on the aperture ontogeny profile, starting from the procedure of data preparation (retopologising the shell model), via data acquisition (calculation of aperture growth trajectory, aperture form and ontogeny axis), and data presentation (qualitative comparison between shell forms) and ending with data analysis (quantitative comparison between shell forms). We evaluate our methods on representative shells of the genus Opisthostoma, which exhibit great variability in shell form. The outcome suggests that our method is a robust, reproducible, and versatile approach for the analysis of shell form. Finally, we propose several potential applications of our methods in functional morphology, theoretical modelling, taxonomy, and evolutionary biology.

scholarly journals A method for quantifying, visualising, and analysing gastropod shell form

2014 ◽  
Author(s):  
Thor-Seng Liew ◽  
Menno Schilthuizen
Keyword(s):  
Evolutionary Biology ◽  
Growth Trajectory ◽  
Theoretical Modelling ◽  
Linear Measurements ◽  
Gastropod Shell ◽  
Qualitative Comparison ◽  
Shell Form ◽  
Potential Applications ◽  
Curvature And Torsion ◽  
Measurable Structure

Quantitative analysis of organismal form is an important component for almost every branch of biology. Although generally considered an easily-measurable structure, the quantification of gastropod shell form is still a challenge because shells lack homologous structures and have a spiral form that is difficult to capture with linear measurements. In view of this, we adopt the idea of theoretical modelling of shell form, in which the shell form is the product of aperture ontogeny profiles in terms of aperture growth trajectory that is quantified as curvature and torsion, and of aperture form that is represented by size and shape. We develop a workflow for the analysis of shell forms based on the aperture ontogeny profile, starting from the procedure of data preparation (retopologising the shell model), via data acquisition (calculation of aperture growth trajectory, aperture form and ontogeny axis), and data presentation (qualitative comparison between shell forms) and ending with data analysis (quantitative comparison between shell forms). We evaluate our methods on representative shells of the genus Opisthostoma, which exhibit great variability in shell form. The outcome suggests that our method is a robust, reproducible, and versatile approach for the analysis of shell form. Finally, we propose several potential applications of our methods in functional morphology, theoretical modelling, taxonomy, and evolutionary biology.

scholarly journals A method for quantifying, visualising, and analysing gastropod shell form

2014 ◽  
Author(s):  
Thor-Seng Liew ◽  
Menno Schilthuizen
Keyword(s):  
Evolutionary Biology ◽  
Growth Trajectory ◽  
Theoretical Modelling ◽  
Linear Measurements ◽  
Gastropod Shell ◽  
Qualitative Comparison ◽  
Shell Form ◽  
Potential Applications ◽  
Curvature And Torsion ◽  
Measurable Structure

Quantitative analysis of organismal form is an important component for almost every branch of biology. Although generally considered an easily-measurable structure, the quantification of gastropod shell form is still a challenge because shells lack homologous structures and have a spiral form that is difficult to capture with linear measurements. In view of this, we adopt the idea of theoretical modelling of shell form, in which the shell form is the product of aperture ontogeny profiles in terms of aperture growth trajectory that is quantified as curvature and torsion, and of aperture form that is represented by size and shape. We develop a workflow for the analysis of shell forms based on the aperture ontogeny profile, starting from the procedure of data preparation (retopologising the shell model), via data acquisition (calculation of aperture growth trajectory, aperture form and ontogeny axis), and data presentation (qualitative comparison between shell forms) and ending with data analysis (quantitative comparison between shell forms). We evaluate our methods on representative shells of the genus Opisthostoma, which exhibit great variability in shell form. The outcome suggests that our method is a robust, reproducible, and versatile approach for the analysis of shell form. Finally, we propose several potential applications of our methods in functional morphology, theoretical modelling, taxonomy, and evolutionary biology.

scholarly journals A method for quantifying, visualising, and analysing gastropod shell form

2013 ◽  
Author(s):  
Thor-Seng Liew ◽  
Menno Schilthuizen
Keyword(s):  
Evolutionary Biology ◽  
Growth Trajectory ◽  
Theoretical Modelling ◽  
Linear Measurements ◽  
Gastropod Shell ◽  
Qualitative Comparison ◽  
Geometric Morphometric ◽  
Shell Form ◽  
Curvature And Torsion ◽  
Measurable Structure

Quantitative analysis of organismal form is an important component for almost every branch of biology. Although generally considered an easily-measurable structure, the quantification of gastropod shell form is still a challenge because shells lack homologous structures and have a spiral form that is difficult to capture with linear measurements. In view of this, we adopt the idea of theoretical modelling of shell form, in which the shell form is the product of aperture ontogeny profiles in terms of aperture growth trajectory that is quantified as curvature and torsion, and of aperture form that is represented by size and shape. We develop a workflow for the analysis of shell forms based on the aperture ontogeny profile, starting from the procedure of data preparation (retopologising the shell model), via data acquisition (calculation of aperture growth trajectory, aperture form and ontogeny axis), and data presentation (qualitative comparison between shell forms) and ending with data analysis (quantitative comparison between shell forms). We evaluate our methods on representative shells of the genus Opisthostoma, which exhibit great variability in shell form. The outcome suggests that our method is more robust, reproducible, and versatile than the conventional traditional and geometric morphometric approaches for the analysis of shell form. Finally, we propose several potential applications of our methods in functional morphology, theoretical modelling, taxonomy, and evolutionary biology.

scholarly journals Further twists in gastropod shell evolution

2008 ◽  
Vol 4 (2) ◽  
pp. 179-182 ◽  
Author(s):  
Reuben Clements ◽  
Thor-Seng Liew ◽  
Jaap Jan Vermeulen ◽  
Menno Schilthuizen
Keyword(s):  
Evolutionary Biology ◽  
Logarithmic Spiral ◽  
Spiral Growth ◽  
Evolutionary Perspective ◽  
Gastropod Shell ◽  
Form And Function ◽  
Evolutionary Origins ◽  
Taxonomic Groups ◽  
And Function ◽  
Shell Coiling

The manner in which a gastropod shell coils has long intrigued laypersons and scientists alike. In evolutionary biology, gastropod shells are among the best-studied palaeontological and neontological objects. A gastropod shell generally exhibits logarithmic spiral growth, right-handedness and coils tightly around a single axis. Atypical shell-coiling patterns (e.g. sinistroid growth, uncoiled whorls and multiple coiling axes), however, continue to be uncovered in nature. Here, we report another coiling strategy that is not only puzzling from an evolutionary perspective, but also hitherto unknown among shelled gastropods. The terrestrial gastropod Opisthostoma vermiculum sp. nov. generates a shell with: (i) four discernable coiling axes, (ii) body whorls that thrice detach and twice reattach to preceding whorls without any reference support, and (iii) detached whorls that coil around three secondary axes in addition to their primary teleoconch axis. As the coiling strategies of individuals were found to be generally consistent throughout, this species appears to possess an unorthodox but rigorously defined set of developmental instructions. Although the evolutionary origins of O. vermiculum and its shell's functional significance can be elucidated only once fossil intermediates and live individuals are found, its bewildering morphology suggests that we still lack an understanding of relationships between form and function in certain taxonomic groups.

scholarly journals The evolution of gastropod shell form: a developmental model illustrating the roles of heterochrony and non-heterochronic changes

1992 ◽  
Vol 6 ◽  
pp. 245-245
Author(s):  
Sean H. Rice
Keyword(s):  
Growth Rate ◽  
Specific Pattern ◽  
Apex Angle ◽  
Developmental Model ◽  
Gastropod Shell ◽  
Shell Form ◽  
Marine Snails ◽  
Highly Sensitive ◽  
Highly Correlated ◽  
Shell Production

The shape of an isometric gastropod shell can be described completely by specifying the pattern of shell secretion around the aperture (relative to aperture size) and the growth rate of the aperture itself. These descriptors provide a “natural” morphometric in that they correspond to the specific biological processes involved in constructing the shell.Describing shell form in this way allows us to specify what developmental changes must occur during the transition of one shell form to another. In particular, we can distinguish between transitions that can occur through purely heterochronic processes (changes in growth rate) and those that require a change in the specific pattern in which cells of the mantle lay down shell. We can also investigate just what changes occur during the ontogeny of non-isometric shells.Any change in either the pattern of shell secretion or the growth rate of the animal leads to changes in a number of classical morphometric measures, such as apex angle and whorl expansion rate. Those transformations resulting from changes in growth rate, however, are much more predictable than those resulting from changes in the pattern of shell production. A slight increase in the growth rate of the animal, for instance, produces a correspondingly slight increase in the apex angle and the rate of whorl expansion. By contrast, the consequences of a slight change in the pattern of shell production are highly sensitive to just how that change was achieved.Data from 8 genera of marine snails show that the variance within each genus, relative to the variance among all genera, is smaller for measures of aperture shape (which can only be altered through a change in the pattern of secretion of shell material) than for characters that can change through heterochronic transformations (such as apex angle). Furthermore, the shell forms of a number of non isometric shells can be described by a constant pattern of shell production and a variable growth rate.Heterochronic changes thus appear to be the preferred mechanism for changing phenotype in gastropod shells. Those characters that can only be altered by changing the pattern of shell production around the mantle, such as aperture shape, appear to be more conservative than those that can be changed through purely heterochronic transitions. This is consistent with the idea that mutations which alter many characters in a highly correlated manner have a higher probability of being favored by selection than those with relatively unpredictable consequences.

Some “laws” of gastropod shell form

Paleobiology ◽  
1977 ◽  
Vol 3 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Robert M. Linsley
Keyword(s):  
Center Of Mass ◽  
Mantle Cavity ◽  
Center Of Gravity ◽  
The Body ◽  
Water Current ◽  
Gastropod Shell ◽  
Shell Form ◽  
Body Whorl ◽  
Anterior Posterior ◽  
Anterior Posterior Axis

Five generalizations derived from the shell form of prosobranch gastropods are developed. (1) A univalve of more than one volution whose aperture lies in a plane that passes through the axis of coiling does not live with the aperture parallel to the substrate. (2) A univalve of more than one volution whose aperture lies in a plane that is tangential to the body whorl does live with the plane of the aperture parallel to the substrate. (3) Gastropods with tangential apertures, when extended, support the shell so that the center of mass of the shell and its contents is over the midline of the cephalopedal mass; this balancing of the shell may be accomplished either by regulatory detorsion, by inclination or by a combination thereof, to keep the center of gravity of the shell as low as possible. (4) Angulations or re-entrants in the gastropod aperture are usually indicative of inhalent or exhalent areas; inhalent areas are directed as far anteriorly as possible. (5) Gastropods having elongated apertures possess only a single gill and develop a water current through the mantle cavity from anterior to posterior along the long axis of the aperture; this axis is subparallel to the anterior-posterior axis of the foot.These generalizations are then used as the basis for some deductive interpretations of behavioral modes of Paleozoic Gastropoda.

scholarly journals Conditional Distributions and Waiting Times in Multitype Branching Processes

2013 ◽  
Vol 45 (03) ◽  
pp. 692-718 ◽  
Author(s):  
H. K. Alexander
Keyword(s):  
Continuous Time ◽  
Evolutionary Biology ◽  
Branching Processes ◽  
Waiting Times ◽  
Escape Mutant ◽  
Conditional Distributions ◽  
Specific Population ◽  
Potential Applications ◽  
Population Sizes ◽  
Multitype Branching Processes

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

scholarly journals A Method for Quantifying, Visualising, and Analysing Gastropod Shell Form

PLoS ONE ◽  
2016 ◽  
Vol 11 (6) ◽  
pp. e0157069 ◽  
Author(s):  
Thor-Seng Liew ◽  
Menno Schilthuizen
Keyword(s):  
Gastropod Shell ◽  
Shell Form

scholarly journals Conditional Distributions and Waiting Times in Multitype Branching Processes

2013 ◽  
Vol 45 (3) ◽  
pp. 692-718 ◽  
Author(s):  
H. K. Alexander
Keyword(s):  
Continuous Time ◽  
Evolutionary Biology ◽  
Branching Processes ◽  
Waiting Times ◽  
Escape Mutant ◽  
Conditional Distributions ◽  
Specific Population ◽  
Potential Applications ◽  
Population Sizes ◽  
Multitype Branching Processes

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

Modeling Economic Growth Based on a One-Good Model Taking into Account Behavioral Factors

2021 ◽  
pp. 26-39
Author(s):  
Alexander A. Yeroshin
Keyword(s):  
Economic Growth ◽  
Resource Constraints ◽  
Functional Dependence ◽  
Labour Productivity ◽  
Optimal Number ◽  
Research Field ◽  
Growth Trajectory ◽  
Economic Research ◽  
Theoretical Modelling ◽  
Growth Theory

As part of theoretical study, a simple mathematical model of economic growth is developed by combining alternative methodological traditions. This article was prepared to put forward a new approach to the growth theory and to provide the scientific community with more information about the fundamental problems of economic dynamics. The main part of the study involves a multi-step analysis of the subject. The first step is building a discrete-time constant-rate growth model in the form of a functional dependence of the output rate on the labour stock growth for invariable technology. The growth function also includes the influence of behavioural factors – ​intertemporal preferences and the entrepreneur-employee consumption ratio. Macro- and microeconomic formulas are used to demonstrate how the deviation of the actual behavioural variable values from the formal optimum leads to disequilibrium growth. The second step is the microeconomic rationale for growth. Here, the author creates an effective entrepreneurship model for determining the optimal number of entrepreneurs at the intersection of the descending profit rate curve and the horizontal interest rate graphic. The third step involves theoretical modelling of the output dynamics along a changing trajectory. Two abstract examples of a changing growth trajectory are given: one due to changes in the labour stock, and the other – ​labour productivity. The transition to a new equilibrium trajectory (switching path) is accompanied by exogenous shocks – ​excess output and (or) underemployment. Economic shocks on the growth trajectory are associated with the force of habit in entrepreneurs’ behaviour, which slows down the adaptation of intertemporal consumption preferences to unexpected changes in resource constraints in a growing economy. The author suggests combining the growth theory with the business fluctuations theory and considering dynamic disequilibrium as a phenomenon of a related economic research field.

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