A geometric analysis of growth in gastropod shells, with particular reference to turbinate forms

1983 ◽  
Vol 63 (4) ◽  
pp. 777-797 ◽  
Author(s):  
S. U. K. Ekaratne ◽  
D. J. Crisp
Keyword(s):  
Conversion Factor ◽  
Shell Height ◽  
Geometric Analysis ◽  
Logarithmic Spiral ◽  
Maximum Growth ◽  
Relative Magnitude ◽  
Shell Shape ◽  
Growth Band ◽  
Apical Angle ◽  
Image Position

Nucella lapillus and Littorina littorea afford examples of turbinately coiled shells with no space between the columella and the inner face of the whorls. Three constants are sufficient to determine the form of such shells: λ, the ratio between diameters of successive whorls; β, the semi-apical angle and ρ, the ratio of aperture length and breadth in the apertural plane passing through the axis. The variation of these three constants with size was examined and shown to be relatively small and insignificant in Nucella, but in Littorina it was significant.For Nucella and Littorina these shell characteristics were used to relate for the nth whorl, the length along the shell spiral (ln) to the shell height (Hn), the latter being the measure usually employed in growth studies. This relation was derived mathematically and confirmed empirically aswhere α is the angle of the logarithmic spiral given by α = tan−1 2π sin β/loge λ. The increased resolution of the micro-growth band increments, which are measured along the shell spiral was directly related to the ln:Hn ratios.Since the formula for the ln/Hn ratio (= shell conversion factor) includes λ, β and ρ, the three constants necessary to determine shell form in turbinately coiled shells of the type described, the shell conversion factor may be a better index of shell shape than indices based on a single constant. In species where the shell grows isometrically this ratio will remain constant, whereas changes in shell shape with size will influence this ratio. Such changes in shell shape during growth can be quantified in terms of the shell constants and when included in calculating the shell conversion factor, will show the relative magnitude of shell shape changes brought about by growth. The shell conversion factor may also be used to study the effects of ecological variations on the geometry of the shell.The conical shell of the limpet, Patella vulgata, is geometrically a much simpler system in which direct shell measurements were used to relate length along the direction of maximum growth to the antero-posterior diameter of aperture.

scholarly journals CO2-induced low pH in an eastern oyster (Crassostrea virginica) hatchery positively affects reproductive development and larval survival but negatively affects larval shape and size, with no intergenerational linkages

2020 ◽  
Author(s):  
Jeff C Clements ◽  
Claire E Carver ◽  
Martin A Mallet ◽  
Luc A Comeau ◽  
André L Mallet
Keyword(s):  
Crassostrea Virginica ◽  
Shell Height ◽  
Reproductive Development ◽  
Eastern Oyster ◽  
Larval Survival ◽  
Low Ph ◽  
Shell Shape ◽  
Biological Sex ◽  
Positive Effects ◽  
Ph Conditions

Abstract In North America, studies regarding effects of CO2-induced low pH in bivalve aquaculture are largely restricted to the US Pacific coast. Studies on species from the northwest Atlantic are lacking. Furthermore, information on the roles of intergenerational exposure and biological sex in bivalve responses to low pH, particularly in an aquaculture-specific context, is scant. We tested if short-term (1 month) exposure to CO2-induced reductions in pHNBS affected the reproductive development of male and female eastern oysters (Crassostrea virginica) during hatchery-specific reproductive conditioning and whether maternal and/or paternal exposure influenced larval responses. Reduced pH (7.5–7.7) increased the rate of reproductive development in both males and females. There was no indication of intergenerational effects; adult pH conditions did not affect early larval development. In contrast, low pH conditions experienced by gametes during spawning, fertilization, and embryo incubation (48 h) resulted in higher larval survival (+6–8% from control), reduced shell height (−2 to 3 µm), and increased deformities (abnormal shell shape; +3–5%). We suggest that local adaptation to acidic land runoff may account for the positive effects of low pH observed in this study. Bioeconomic assessments are now needed to understand the implications of reduced pH on aquaculture operations in these regions of Atlantic Canada.

scholarly journals Performance Surface Analysis Identifies Consistent Functional Patterns across 10 Morphologically Divergent Terrestrial Turtle Lineages

2019 ◽  
Vol 59 (2) ◽  
pp. 346-357 ◽  
Author(s):  
C Tristan Stayton
Keyword(s):  
Functional Performance ◽  
Morphological Changes ◽  
Shell Height ◽  
Model Systems ◽  
Hydrodynamic Performance ◽  
Shell Shape ◽  
Test Case ◽  
Evolutionary Diversification ◽  
And Performance ◽  
Performance Surface

Abstract Newly-developed methods for utilizing performance surfaces—multivariate representations of the relationship between phenotype and functional performance—allow researchers to test hypotheses about adaptive landscapes and evolutionary diversification with explicit attention to functional factors. Here, information from performance surfaces of three turtle shell functions—shell strength, hydrodynamics, and self-righting—is used to test the hypothesis that turtle lineages transitioning from aquatic to terrestrial habitats show patterns of shell shape evolution consistent with decreased importance of hydrodynamic performance. Turtle shells are excellent model systems for evolutionary functional analysis. The evolution of terrestriality is an interesting test case for the efficacy of these methods because terrestrial turtles do not show a straightforward pattern of morphological convergence in shell shape: many terrestrial lineages show increased shell height, typically assumed to decrease hydrodynamic performance, but there are also several lineages where the evolution of terrestriality was accompanied by shell flattening. Performance surface analyses allow exploration of these complex patterns and explicit quantitative analysis of the functional implications of changes in shell shape. Ten lineages were examined. Nearly all terrestrial lineages, including those which experienced decreased shell height, are associated with morphological changes consistent with a decrease in the importance of shell hydrodynamics. This implies a common selective pattern across lineages showing divergent morphological patterns. Performance studies such as these hold great potential for integrating adaptive and performance data in macroevolutionary studies.

Factors Influencing Shell Shape in the Mussel Mytilus Edulis

1968 ◽  
Vol 48 (3) ◽  
pp. 561-584 ◽  
Author(s):  
R. Seed
Keyword(s):  
Mytilus Edulis ◽  
Slow Growth ◽  
Shell Height ◽  
Shell Morphology ◽  
Population Variation ◽  
Shell Shape ◽  
Factors Influencing ◽  
High Incidence ◽  
Local Variability ◽  
Transplantation Experiments

An attempt is made to explain the great variations in gross shell morphology noted in field populations of Mytilus edulis.In any one mussel population, variation in shell form can be attributed to differences in age, old mussels having proportionately heavier shells where width often exceeds shell height. This is invariably accompanied by down-turned, divergent umbones and varying degrees of incurvature of the ventral shell margin.Variations in the age structure of mussel populations from different habitats can also account for local variability in shell morphology. Localities where the life expectancy of mussels is increased due to absence of predators (especially in the upper shore) reveal a high incidence of old ‘ungulate’ individuals, whereas populations in which the mussel turnover is more rapid show a preponderance of relatively young mussels.Shell morphology is greatly influenced by growth rate and density. These probably exert their effect through physical compression which is maximum in localities of fast growth and high density and least in areas of slow growth and low density. High compression leads to an elongate form whereas low compression results in higher, more triangular shaped shells. Growth rates and densities, even within the same habitat, are, however, exceedingly variable.Since all environmental conditions vary in both time and space, wide variation in shell morphology is to be expected, even in animals from the same locality.Transplantation experiments indicate that variation in shell morphology is essentially phenotypic, older animals being more likely to exhibit a form which is characteristic of their particular habitat. Smaller mussels from widely different habitats show remarkable similarity in shell morphology.

On the asymptotic behaviour of sample spacings

1981 ◽  
Vol 90 (2) ◽  
pp. 293-303 ◽  
Author(s):  
John Hawkes
Keyword(s):  
Growth Rate ◽  
Asymptotic Behaviour ◽  
Growth Rates ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Unit Interval ◽  
Sample Spacing ◽  
Image Position ◽  
Almost All ◽  
Sample Spacings

SummarySuppose that we are given a random sample of size n chosen according to the uniform distribution on the unit interval. Let Zn(x) = Zn(x, ω) be the length of the unique left-closed and right-open sample spacing that contains x. The purpose of this paper is to examine the almost sure, and exceptional, growth rates of the process {Zn}. The typical maximum growth rate and the growth rate of the maximum can be of quite different orders of magnitude as is shown by the following two results.Theorem 2. With probability one we havefor almost all x.Theorem 3. With probability one we have

Growth and reproduction of Macoma balthica (L.) on a mud flat in the Fraser River estuary, British Columbia

1983 ◽  
Vol 61 (4) ◽  
pp. 887-894 ◽  
Author(s):  
E. R. McGreer
Keyword(s):  
Growth Rate ◽  
British Columbia ◽  
Shell Height ◽  
Macoma Balthica ◽  
River Estuary ◽  
Dry Weight ◽  
Maximum Growth ◽  
Fraser River ◽  
Mud Flat ◽  
Growth And Reproduction

Growth and reproduction of the bivalve, Macoma balthica (Linnaeus, 1758) was studied for one year (April 1977 – March 1978) on an intertidal mud flat in the Fraser River estuary, British Columbia. The maximum number of individuals (1830/m2) occurred in April, then steadily declined throughout the year. Spawning occurred between mid-June and late July but recruitment was slow and prolonged. Peak spatfall (age 0+ individuals) did not occur until the following March when a maximum density of only 410/m2 for newly settled spat was observed. The oldest animals found were 5+ years of age. Maximum growth took place from April through July. The growth rate measured was one of the highest recorded for any M. balthica population. A direct relationship between high water temperatures, a fast growth rate, and reduced longevity was apparent. A regression of body weight on shell height was used to calculate a condition factor (CF), which reached its highest value during growth and its lowest value immediately after spawning. The mean annual biomass measured was 2.96 g dry weight per square metre.

The shape of the Upper Carboniferous non-marine bivalve Anthraconaia in relation to the organic carbon content of the host sediment

1987 ◽  
Vol 78 (3) ◽  
pp. 177-195 ◽  
Author(s):  
R. M. C. Eagar
Keyword(s):  
Organic Carbon ◽  
Regional Distribution ◽  
Maximum Growth ◽  
Shell Shape ◽  
Marine Bivalve ◽  
Organic Carbon Content ◽  
Maximum Width ◽  
Upper Carboniferous ◽  
The Relationship ◽  
Host Sediment

ABSTRACTAnthraconaia lived on clay grade sediments. In highly variable life assemblages of the A.prolifera group of the E German Wettin Shales (Stephanian C) organic carbon percentage of the host sediment correlates with wu/m and A/L ratios of the shell (where wu is the maximum width ventral to the line of maximum growth, m, L the maximum length measured parallel to the line of the hinge, and A the length anterior to the umbo). Decrease in the organic carbon of the sediment is associated with decrease in umbonal development, elongation of the shell along the m axis, and straightening and reflection of the ventral margin; the latter becomes subparallel to the dorsum or to the m axis with a concomitant decrease in size. These results confirm and amplify earlier work on Anthraconaia in the Appalachian coalfields. The same morphological trends in relation to organic carbon characterise the Anthraconaia modiolaris group of Britain, both within a single succession in upper Westphalian A sediments in Yorkshire, and also in three shell bands of Lower Westphalian B age in S Wales, Yorkshire and central Scotland. In the last named, above the Musselband Coal, statistical formulae (of Leitch 1940) for the species A.salteri are shown to define neither the type assemblage nor its stratigraphical position. The shell-shape/organic carbon relationship has been broadly confirmed on other horizons of lower Westphalian B age in the Scottish and Pennine coalfields. Far from embarrassing the stratigrapher, the relationship, which reflects ultimately trophic level of deltaic palaeoenvironments, contributes to our understanding of non-marine bivalve faunas, especially of the apparent regional distribution of ‘species’ of Anthraconaia.

Shell shape, dysodont tooth morphology, and hinge-ligament thickness in the bay mussel Mytilus trossulus correlate with wave exposure

2000 ◽  
Vol 78 (2) ◽  
pp. 240-253 ◽  
Author(s):  
Robert J Akester ◽  
André L Martel
Keyword(s):  
Shell Length ◽  
Shell Height ◽  
Wave Exposure ◽  
Shell Morphology ◽  
Shell Shape ◽  
Width Ratio ◽  
Mytilus Trossulus ◽  
Barkley Sound ◽  
High Wave Energy ◽  
Mussel Mytilus Trossulus

We examined the shell morphology of the bay mussel Mytilus trossulus (Gould) at six locations with various levels of wave exposure in Barkley Sound on the west coast of Vancouver Island, British Columbia, Canada. Young adult M. trossulus (29-35 mm shell length) collected from wave-exposed sites displayed striking differences in shell morphology from M. trossulus from sheltered sites. Mytilus trossulus from wave-exposed habitats had a lower shell height / shell width ratio and a thicker shell; they also had higher, more robust dysodont teeth, as well as a thicker hinge ligament. Examination of juveniles (12-14 mm shell length) collected from a wave-exposed shore and a sheltered shore separated by only a few hundred metres displayed similar differences in shell morphology and ligament thickness. These observations suggest that wave exposure is the cause of the observed differences in shell morphology and ligament thickness in M. trossulus. This is the first report of a correlation between wave exposure and morphology of the dysodont teeth and ligament in a bivalve. We discuss potential selective pressures that may favor characteristics of wave-exposed shells, including the probability of dislodgment and misalignment of valves in high wave energy areas.

scholarly journals Deformation Behavior of Press Formed Shell by Indentation and Its Numerical Simulation

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Minoru Yamashita ◽  
Zubair Bin Khalil
Keyword(s):  
Deformation Behavior ◽  
Kinematic Hardening ◽  
Shell Height ◽  
Mutual Effect ◽  
Material Model ◽  
Shell Shape ◽  
Indentation Force ◽  
Hemispherical Shell ◽  
Deformation Behaviors ◽  
Energy Absorbing

Deformation behavior and energy absorbing performance of the press formed aluminum alloy A5052 shells were investigated to obtain the basic information regarding the mutual effect of the shell shape and the indentor. Flat top and hemispherical shells were indented by the flat- or hemispherical-headed indentor. Indentation force in the rising stage was sharper for both shell shapes when the flat indentor was used. Remarkable force increase due to high in-plane compressive stress arisen by the appropriate tool constraint was observed in the early indentation stage, where the hemispherical shell was deformed with the flat-headed indentor. This aspect is preferable for energy absorption performance per unit mass. Less fluctuation in indentation force was achieved in the combination of the hemispherical shell and similar shaped indentor. The consumed energy in the travel length of the indentor equal to the shell height was evaluated. The increase ratio of the energy is prominent when the hemispherical indentor is replaced by a flat-headed one in both shell shapes. Finite element simulation was also conducted. Deformation behaviors were successfully predicted when the kinematic hardening plasticity was introduced in the material model.

scholarly journals The arboreal microsnail Pupisoma dioscoricola (C. B. Adams, 1845) from West Bengal, India: morphology, plant preferences and distribution

2021 ◽  
pp. 148-157
Author(s):  
Himangshu Barman ◽  
Pranesh Paul ◽  
Gautam Aditya
Keyword(s):  
Body Weight ◽  
Host Plant ◽  
West Bengal ◽  
Shell Height ◽  
Species Distribution Modelling ◽  
Influential Factors ◽  
Morphological Features ◽  
Shell Size ◽  
Apical Angle ◽  
Mango Tree

The microsnails (Mollusca: Gastropoda), featured by miniscule size (adult shell size < 5mm), are little explored among the Indian terrestrial malacofauna. In the present study, the morphological features, host plant preference and predicted distribution of the arboreal microsnail Pupisoma dioscoricola (C. B. Adams, 1845) (Gastropoda: Valloniidae) are characterized from West Bengal, India. The shell features were highly correlated and showed a positive correlation with body weight. The apical angle of the shell of P. dioscoricola was negatively correlated with shell height and body weight and revealed a typical value, indicative of the arboreal adaptations. The toothless pupa snail P. dioscoricola exhibited a greater preference for the mango tree over China rose, Bengal quince, Indian mahogany and coconut as a host plant. The results of the species distribution modelling suggested that cultivated or managed vegetation and annual precipitation might be the most influential factors for its distribution. Although the present study is a pioneer effort to describe the plant preferences and the morphological features of the microsnail P. dioscoricola, further studies should be carried out to decipher the functional roles and conservation management of such an apparently cryptic organism.

Sexual dimorphism in size and shell shape, and dichromatism of spotted turtles (Clemmys guttata) in Southwestern Michigan

2012 ◽  
Vol 33 (3-4) ◽  
pp. 443-450 ◽  
Author(s):  
John W. Rowe ◽  
Jessica R. Gradel ◽  
Charles F. Bunce ◽  
David L. Clark
Keyword(s):  
Body Size ◽  
Shell Height ◽  
Mate Recognition ◽  
Shell Shape ◽  
Sexually Dimorphic ◽  
Aquatic Habitats ◽  
Uv Spectrum ◽  
Full Spectrum ◽  
Cryptic Coloration ◽  
Clemmys Guttata

Differences in pigmentation, morphometry, and body size between sexes within populations can imply inter-sexual differences in reproductive biology. We assessed variation in body size, morphometrics, and pigmentation in Spotted Turtles (Clemmys guttata) in a southwestern Michigan population. Clemmys guttata was not sexually dimorphic in body size but when compared to males, positive allometric increases in shell height resulted in relatively domed shells in females. Integumental reflectance was mostly limited to the visual spectrum 400-700 nm with little to no reflectance in the UV spectrum (340-700 nm). We found no intersexual differences in the intensity (brightness) of yellow spots or black ground color of the head and carapace, perhaps suggesting that such markings are involved in cryptic coloration. The orange-red stripes of the head and forelimbs, that were similar in intensity between the sexes, would look conspicuous in the full spectrum light of the shallow aquatic habitats of C. guttata and thus could be involved in mate recognition. Chins of males were darker than those of females suggesting that chin color is a sexually selected trait.

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