Material and methods
Sample collectingnext section
Samples were collected from six populations along the Iberian coast (Fig. 1) from October 2003 to October 2004. All sites are wave-exposed rocky cliffs where Carcinus maenas (Linnaeus, 1758), a predator with a reported impact on gastropod shell morphology (e.g. Palmer, 1990), was not detected during sampling, and for which there are no records of occurrence. Another crab species, Pachygrapsus marmoratus (Fabricius, 1787), is a very common inhabitant of rocky shores around the Iberian Peninsula and of the sampled sites (Zariquiey-Alvarez, 1968). Effects on gastropod shell morphology from predation by this crab have not been reported. Although this effect cannot be totally excluded, P. marmoratus is an omnivorous species with a relatively soft shell and flat chaela tips, which should have a much lower predatorial impact on gastropods. Each site was visited once by 2 to 3 collectors that explored a 10 to 50 m stretch of coast during approximately 15 min per collector, for each species. In order to minimize shape differences due to different ecotypes, which are a characteristic feature of Littorina saxatilis and other littorinid species, sampling was conducted within the barnacle belt for L. saxatilis and above this belt for Melarhaphe neritoides. Littorina saxatilis is a highly polymorphic species displaying a range of ecotypes that differ in size, shape, ornamentation and colour (Reid, 1996). In Galician shores (Carballo et al., 2005), two main ecotypes have been described, a ridged and banded morph found among barnacles in the upper intertidal and a small-sized, smooth and unbanded form found among mussels in the lower intertidal. In the transition zone where mussel density increases towards the typical dominance in the lower intertidal, a hybrid between the two ecotypes has been described. In order to minimize shape differences due to different ecotypes of L. saxatilis, sampling for this species was conducted exclusively within the barnacle belt, above the level of the first mussels. Melarhaphe neritoides is a typical high shore species with abundance maxima above the barnacle zone and sampling was conducted above the barnacle zone. Sampled gastropods were frozen at -20° C upon arrival at the laboratory and later transferred to 95% ethanol for 24h to facilitate the removal of soft parts.
Morphometric data acquisitionA subsample of 16 individuals from each population and species was randomly selected. A photograph of each specimen and of a scale was taken using a digital camera equipped with a 105 mm macro lens. Gastropod shells grow by spiral accretion of calcium carbonate starting at the larval protoconch and ending at the labrum of the adult teleoconch (Fretter and Graham, 1994). Because the protoconch at the apex and the apex itself are the most delicate parts of the shell and are usually eroded in larger juveniles and adults, implicating that the starting point of ontogeny is normally unknown, the determination of homologous points of the gastropod shell anatomy is often impossible (Guralnick and Kurpius, 2001). Moreover, since new morphology is continuously being added as the shell grows, older individuals do not share homologous landmarks in the new part of the shell with younger individuals. To minimize this problem, shells were mounted with the columella axis aligned with the horizontal and the shell rotated around this axis so that the aperture presented a frontal view to the camera (ventral view). Landmarks corresponding to 8 anatomical features (Fig. 2) were digitised using tpsDig software (Rohlf, 2006). These landmarks were selected because they: i) can be recognised in both species; ii) retrieve significant information related to the shape of the last whorl; iii) retrieve significant information relative to the elongation of the shell, given that erosion of the apex is not very pronounced in the two species; and iv) convey information related to the size and shape of the aperture. Landmarks 1 and 7 are Type I, 2 and 4 Type II and 3, 5, 6 and 8 Type III landmarks (Bookstein, 1991). Landmark data were used to estimate individual size, which was calculated as centroid size, i.e. the square root of the sum of the squared distances between the centroid and each landmark. In the absence of allometry, centroid size is uncorrelated with measures of shape (Tang and Pantel, 2005).
Fig. 2. Location of the 8 landmarks used to describe shell shape, on an illustration of a Melaraphe neritoides shell.
Statistical analysis of shape variation
We used Procrustes superimposition to compare shape, which minimises the sum of squared distances between pairs of landmarks on two different samples by adjusting size, rotation and translation. This squared distance is known as the Procrustes distance. Claude (2008) defines a number of functions to remove the effects of size, location (e.g. the transl() function on p 149), and orientation. The comparison of several samples (or configurations) is non-trivial because it entails a generalised procedure for the superimposition of all these samples and requires the definition of a single objective reference known as the mean shape. Shape variation is then compared in reference to this mean shape. In the present study, we use Generalised Procrustes Analysis (GPA), which determines the mean shape as the shape where the sum of pairwise squared coordinates with other rotated samples is minimised (Claude, 2008). A number of iterative algorithms have been described to obtain the best fit (Gower, 1975; Rohlf and Slice, 1990). In addition to this, full GPA entails posterior scaling between samples and mean shape to improve fit, while partial GPA maintains all samples at unit size. In the present study, we used the procGPA() function in the shapes library, which performs a full GPA. The default arguments were used, which included leaving the scale and tangentresiduals arguments as TRUE. In the results, we present Principal Components Analysis (PCA) ordinations using raw scores obtained with the procGPA() function. In addition to this, we use the shapepca() function in the shapes package to provide graphical summaries for PC’s of shape. Summaries are provided whereby vectors are drawn from the mean to +1 sd along the first 3 PC axes and a Thin-plate spline (TPS) grid from the mean to +1 sd along the first 3 PC axes. TPS’s are a means of interpolating how shape change affects the whole shape of an organism and mathematically express D’Arcy Thompson’s deformation grids (cited in Claude, 2008). The mathematics involved in TPS analysis were imported from continuum mechanics, where they were used to study the bending of thin metal plates under physical strains (Bookstein, 1989).
We tested for significant multivariate variation in shape among different populations of both snail species using a modified Hotelling-Lawley trace statistic and F-approximation in a function taken from Claude (2008). Importantly, when working with superimposed data, the shape space dimensions are not equal to the number of variables analysed. The transformations, namely, reduce the rank number of the original data leading to four lost dimensions in 2D and seven in 3D data respectively. Thus when working with Procrustes data, one needs to adapt the normal tests. To begin with, the amount of variables in the transformation of the multivariate statistic to its F approximation needs to be replaced by the number of space dimensions. A Moore-Penrose generalised inversion also needs to be applied instead of classic algorithms due to problems in inverting nonsingular matrices as opposed to normal covariance matrices.
We analysed the relationship between shape and allometry following the procedure outlined by Claude (2008). In summary, this entails first generating a linear model between shape and allometry using the lm() function in R and subsequently using the modified Hotelling-Lawley trace statistic to test for significance. In addition to the above multivariate test, we also tested for significant variation in centroid size among populations with the lm() function in R after controlling for deviations from normality with the shapiro.test() function in R (there were no significant deviations, i.e. P > 0.05, for both species) and an effect of allometry on shape using linear regression of PC scores versus centroid size. Examination of the residuals of these regressions, however, revealed both long and short tailed distributions in addition to the presence of outliers. Although square root transformation of the response variable improved the behaviour of the residuals, the fit was still less than perfect. We therefore decided to analyse the data using robust regression (Venables and Ripley, 2002). Robust or resistant regression methods dampen the effect of outliers on model fit. There are a large number of different methods with advantages and disadvantages. In the present study we used MM-estimation as proposed by Yohai et al. (1991) and implemented in the MASS library in R. MM-estimation combines the resistance of resistant regression methods with the efficiency of M-estimation (Venables and Ripley, 2002).