Going round the twist—an empirical analysis of shell coiling in helicospiral gastropods

The logarithmic helicospiral has been the most widely accepted model of regularly coiled molluscan form since it was proposed by Moseley and popularized by Thompson and Raup. It is based on an explicit assumption that shells are isometric and grow exponentially, and an implicit assumption that the external form of the shell follows the internal shape, which implies that the parameters of the spiral could be reconstructed from the external whorl profile. In this contribution, we show that these assumptions fail on all 25 gastropod species we examine. Using a dataset of 176 fossil and modern gastropod shells, we construct an empirical morphospace of coiling using the parameters of whorl expansion rate, translation rate, and rate of increasing distance from coiling axis, plus rate of aperture shape change, from their best-fit models. We present a case study of change in shell form through geologic time in the austral family Struthiolariidae to demonstrate the utility of our approach for evolutionary paleobiology. We fit various functions to the shell-coiling parameters to demonstrate that the best morphological model is not the same for each parameter. We present a set of R routines that will calculate helicospiral parameters from sagittal sections through coiled shells and allow workers to compare models and choose appropriate sets of parameters for their own datasets. Shell-form parameters in the Struthiolariidae highlight a hitherto neglected hypothesis of relationship between Antarctic Perissodonta and the enigmatic Australian genus Tylospira that fits the biogeographic and stratigraphic distribution of both genera.

Change of information by positive frequency-dependent selection in two very different models (laser-like and chirality of shell-coiling in the snail Partula suturalis)

Although according to the second law of thermodynamics the world tends toward maximum disorder, over millions of years evolution has given rise to an enormous variety of complex organisms. To explain this, one must assume that natural selection is a process of information acquisition. Since some years an information theory of selection exists that can quantify this change and thus helps to understand the apparent contradiction between the existence of biological complexity and the tendency toward disorder that generally prevails in nature. Here I apply this theory to examples of frequency-dependent selection (this means: in which phenotype frequency determines its fitness).The snail Partula suturalis gave an evolutionary and ecologically unique and hence very valuable example of this type of selection before it became extinct about thirty years ago on its native island. Spatially separated populations with left- and right-coiled shells occurred on Moorea, but also hybridization zones. Since both types of shells were the same except for chirality, the question is whether selection happened at all. The inheritance of this character is monogenic and in this respect simple, but is complicated by the fact that it is the maternal genotype, not the own, that determines the phenotype. This causes that for the calculation of the information change by selection not the genotype or phenotype frequencies are sufficient, but one must consider their combination. The simulation shows that frequency-dependent selection in P. suturalis indeed increased information.It has already been shown that selection can also be important outside animate nature, for example in the generation of laser light, which has extraordinary properties: it is monochromatic, monoaxial and monophasic. Phase selection is frequency(=density)-dependent and therefore of interest here. In selection theory the mean fitness ω is of special significance. In a laser-like model, in modeling phase selection, we find that ω=1+A2, where A2 is the the light intensity or the square of the amplitude, respectively. During selection, ω increases and, in parallel, since selection is a process of information acquisition, so does the information. Because of the connection between ω and A2 this also means for the laser-like model that – assuming a constant number of photons – a larger amplitude always means more information (less entropy).

The pond snail Lymnaea stagnalis

The freshwater snail Lymnaea stagnalis has a long research history, but only relatively recently has it emerged as an attractive model organism to study molecular mechanisms in the areas of developmental biology and translational medicine such as learning/memory and neurodegenerative diseases. The species has the advantage of being a hermaphrodite and can both cross- and self-mate, which greatly facilitates genetic approaches. The establishment of body-handedness, or chiromorphogenesis, is a major topic of study, since chirality is evident in the shell coiling. Chirality is maternally inherited, and only recently a gene-editing approach identified the actin-related gene Lsdia1 as the key handedness determinant. This short article reviews the natural habitat, life cycle, major research questions and interests, and experimental approaches.

Internet ‘shellebrity' reflects on origin of rare mirror-image snails

While animal bodies are typically bilaterally symmetric on the outside, the internal organs nearly always show an invariant left–right (LR) asymmetry. In comparison, snails are both internally and externally LR asymmetric, outwardly obvious in the shell coiling direction, or chirality. Although some species of snail are naturally variable for chirality, sinistral individuals occur very rarely in most species. The developmental and genetic basis of these rare mirror-imaged individuals remains mysterious. To resolve this issue, the finding of a ‘one in a million' sinistral garden snail called ‘Jeremy' was used to recruit citizen scientists to find further sinistral snails. These snails were then bred together to understand whether their occurrence is due an inherited condition. The combined evidence shows that rare sinistral garden snails are not usually produced due to a major effect maternal Mendelian locus. Instead, they are likely mainly produced by a developmental accident. This finding has relevance to understanding the common factors that define cellular and organismal LR asymmetry, and the origin of rare reversed individuals in other animal groups that exhibit nearly invariant LR asymmetry.

PATTERNS AND PROCESSES IN MORPHOSPACE: GEOMETRIC MORPHOMETRICS OF THREE-DIMENSIONAL OBJECTS

Focusing on geometric morphometrics (GMM), we review methods for acquiring morphometric data from 3-D objects (including fossils), algorithms for producing shape variables and morphospaces, the mathematical properties of shape space, especially how they relate to morphogenetic and evolutionary factors, and issues posed by working with fossil objects. We use the Raupian shell-coiling equations to illustrate the complexity of the relationship between such factors and GMM morphospaces. The complexity of these issues re-emphasize what are arguably the two most important recommendations for GMM studies: 1) always use multivariate methods and all of the morphospace axes in an analysis; and 2) always anticipate the possibility that the factors of interest can have complex, nonlinear relationships with shape.

Further twists in gastropod shell evolution

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.