Landmark superimposition for taxonomic identification

The identification of organisms is a time-consuming task even for highly specialized researchers. Many ways to accelerate the identification process have been devised – from pictorial keys to automatic, machine identification – with different degrees of success. This paper explores landmark configurations as an aid to taxonomic identification. The basic hypothesis rests on the analogy between human fingerprints and organism landmark configuration. Translated into biological terms, it asks whether individual landmark configurations can be used as diagnostic characteristics for species identification. Water mites of the genus Torrenticola were used as test organisms. The results show that identification can be made simpler through the use of landmark configurations.  © 2004 The Linnean Society of London, Biological Journal of the Linnean Society , 2004, 81 , 267–274.     

Geometric morphometries and the analysis of higher taxa: a case study based on the metendosternite of the Scarabaeoidea (Coleoptera)

A geometric morphometric analysis of families belonging to the Scarabaeoidea, using landmarks from three two-dimensional views (frontal, dorsal and lateral) of an internally situated rigid structure, the metendosternite, was carried out. Procrustes distances matrices were obtained to produce phenograms from the three analyses. Relative warp analyses were also performed and the first two relative warps for the three data sets plotted against each other. The metendosternite is an internally situated anatomical structure that has largely been neglected in past studies. However, it proved to be useful in geometric morphometric studies, because it is rigid and landmarks can be easily identified. Geometric morphometries is shown to be a powerful tool to identify phenetic relationships between higher level taxa, and the metendosternite is a new structure available for beetle systematisists.     

Statistical analysis of unlabeled point sets: comparing molecules in chemoinformatics

We consider Bayesian methodology for comparing two or more unlabeled point sets. Application of the technique to a set of steroid molecules illustrates its potential utility involving the comparison of molecules in chemoinformatics and bioinformatics. We initially match a pair of molecules, where one molecule is regarded as random and the other fixed. A type of mixture model is proposed for the point set coordinates, and the parameters of the distribution are a labeling matrix (indicating which pairs of points match) and a concentration parameter. An important property of the likelihood is that it is invariant under rotations and translations of the data. Bayesian inference for the parameters is carried out using Markov chain Monte Carlo simulation, and it is demonstrated that the procedure works well on the steroid data. The posterior distribution is difficult to simulate from, due to multiple local modes, and we also use additional data (partial charges on atoms) to help with this task. An approximation is considered for speeding up the simulation algorithm, and the approximating fast algorithm leads to essentially identical inference to that under the exact method for our data. Extensions to multiple molecule alignment are also introduced, and an algorithm is described which also works well on the steroid data set. After all the steroid molecules have been matched, exploratory data analysis is carried out to examine which molecules are similar. Also, further Bayesian inference for the multiple alignment problem is considered.     

Diet and body shape changes of pāroko Kelloggella disalvoi (Gobiidae) from intertidal pools of Easter Island

This study assesses seasonal variation in the morphology and diet of juveniles and adults of the Easter Island endemic goby Kelloggella disalvoi from intertidal pools during September–October 2015 (spring) and June–July 2016 (winter), utilizing geometric morphometric and gut‐content analyses. A set of 16 landmarks was digitized in 128 individuals. Shape changes related to size changes (i.e. allometry) were low (18·6%) and were seasonally similar. Body shape changes were mainly dorsoventral (44·2% of variance) and comprised posteroventral displacement of the premaxilla and bending of the body. The latter included vertical displacement of the anterior portion of the first and second dorsal fins and the entire base of the caudal fin. Diets mainly comprised developmental stages of harpacticoid copepods (from eggs to adults), ostracods, isopods, gastropods and bivalves. Also, trophic niche breadth remained constant throughout development and did not vary between seasons. Nonetheless, significant dietary differences were detected in specimens collected during spring (main prey items: harpacticoid copepods and copepod eggs) and winter (harpacticoid copepods and copepod nauplii). Finally, there was weak but significant covariation between diet and morphology: molluscivores were characterized by having an inferior mouth gape, whereas planktivores had an anteriorly directed premaxilla.     

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.     

Geographic and stratigraphic change in the morphology of Triarthrus beckii (Green) (Trilobita): a test of the Plus ça change model of evolution

The Plus ça change model predicts that deepwater trilobite species such as Triarthrus should exhibit gradual phyletic evolution. A detailed stratigraphic sequence of Triarthrus beckii specimens considered together with geographically separated samples from a single time interval provide a test of the Plus ça change model. We examined geographic patterns of variation in cranidial shape based on specimens from four approximately synchronous levels within the Upper Ordovician (lower Edenian) strata of New York, Québec, Kentucky and Pennsylvania. All geographic populations differ in mean size, except for New York and Pennsylvania. Because allometry is present in both meraspid and holaspid phases of the trilobite, size effects on shape were removed by ontogenetic standardization. Cranidial shapes were then compared among the four study sites and eight stratophenetic samples from New York, obtained by subdividing our Mohawkian Composite Standard Section into 20-m-thick intervals. Goodall's F-test of pairwise comparisons of cranidial shape between eight subintervals in New York and the other three populations are all significant. Geographic variation in cranidial size and shape in T . beckii appears to display a gradient or cline-like pattern that is related to paleogeography. Although cranidial shape is not entirely static within the New York stratophenetic series, it is in all cases different from that sampled elsewhere in the region. Thus, there is no evidence of wholesale immigration and emigration among the geographic areas. Instead, the geographic gradient of T . beckii shape variation may have remained fairly stable over ca. 3 million years during the mid-Chatfieldian to early Edenian interval. This result is indicative of stasis. Consequently, the evolutionary history of T . beckii contradicts the Plus ça change model.     

Ontogenetic allometry, heterochrony, and interspecific differences in the skull of African apes, using tridimensional Procrustes analysis

Ontogenetic studies of African ape skulls lead to an analysis of morphological differences in terms of allometry, heterochrony, and sexual dimorphism. The use of geometric morphometrics allows us 1) to define size and shape variations as independent factors (an essential but seldom respected condition for heterochrony), and 2) to calculate in percentage of shape changes and to graphically represent the parts of shape variation which are related to various biological phenomena: common allometry, intraspecific allometry, and allometric and nonallometric shape discrimination. Three tridimensional Procrustes analyses and the calculation of multivariate allometries, discriminant functions, and statistical tests are used to compare the skulls of 50 Pan troglodytes, and 50 Gorilla gorilla of different dental stages. The results both complement and modify classical results obtained from similar material but with different methods. Size and Scaling in Primate Morphology, New York: Plenum, p. 175-205). As previously described by Shea, the common growth allometric pattern is very important (64% of total shape variation). It corresponds to a larger increase of facial volume than of neurocranial volume, a more obliquely oriented foramen magnum, and a noticeable reshaping of the nuchal region (higher inion). However, the heterochronic interpretation based on common allometry is rather different from Shea. Gorillas differ from chimpanzees not only with a larger magnitude of allometric change (rate peramorphosis), as is classically said, but also grow more in size than in shape (size acceleration). In other words, for a similar stage of growth, gorillas have the size and shape corresponding to older chimpanzees, and for a similar shape, gorillas have a larger size than chimpanzees. In contrast, sexual dimorphism actually corresponds to allometric changes only, as classically demonstrated (time hypermorphosis). Sexual dimorphism is here significant in adult gorillas alone, and solely in terms of allometry (size-related shape and size, given that sagittal and nuchal crests are not taken into account). The study also permits us to differentiate two different shape variations that are classically confused in ontogenetic studies: a very small part of allometric shape change which is specific to each species (1% of the total shape variation), and nonallometric species-specific traits independent of growth (8% of total shape change). When calculated in terms of intraspecific allometries (including common allometry and noncommon allometry), shape changes are more extensive in gorillas (36% of total shape change) than in chimpanzees (29% of total shape change). The allometric differences mainly concern the inion, which becomes higher; the position of the foramen magnum, more dorsally oriented; and the palate, more tilted in adult gorillas than in adult chimpanzees. In contrast, nonallometric species-specific traits in gorillas are the long and flat vault characterized by a prominent occipital region, the higher and displaced backward glabella, and the protrusive nose. Biomechanical schemes built from shape partition suggest that the increased out-of-plumb position of the head during growth is partially compensated in gorillas by a powerful nuchal musculature due to the peculiar shape of the occipital region.     

Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry

Abstract.— Morphometric studies often consider parts with internal left-right symmetry, for instance, the vertebrate skull. This type of symmetry is called object symmetry and is distinguished from matching symmetry, in which two separate structures exist as mirror images of each other, one on each body side. We explain a method for partitioning the total shape variation of landmark configurations with object symmetry into components of symmetric variation among individuals and asymmetry. This method is based on the Procrustes superimposition of the original and a reflected copy of each landmark configuration and is compatible with the two-factor ANOVA model customary in studies of fluctuating asymmetry. We show a fully multivariate framework for testing the effects in the two-factor model with MANOVA statistics, which also applies to shapes with matching symmetry. We apply the new methods in a small case study of pharyngeal jaws of the Neotropical cichlid fish Amphilophus citrinellus . The analysis revealed that the symmetric component of variation in the pharyngeal jaws is dominated by the contrast between two alternative trophic morphs in this species and that there is subtle but statistically significant directional asymmetry. Finally, we provide some general recommendations for morphometric studies of symmetric shapes.     

Ontogenetic study of the skull in modern humans and the common chimpanzees: neotenic hypothesis reconsidered with a tridimensional Procrustes analysis

Heterochronic studies compare ontogenetic trajectories of an organ in different species: here, the skulls of common chimpanzees and modern humans. A growth trajectory requires three parameters: size, shape, and ontogenetic age. One of the great advantages of the Procrustes method is the precise definition of size and shape for whole organs such as the skull. The estimated ontogenetic age (dental stages) is added to the plot to give a graphical representation to compare growth trajectories. We used the skulls of 41 Homo sapiens and 50 Pan troglodytes at various stages of growth. The Procrustes superimposition of all specimens was completed by statistical procedures (principal component analysis, multivariate regression, and discriminant function) to calculate separately size-related shape changes (allometry common to chimpanzees and humans), and interspecific shape differences (discriminant function). The results confirm the neotenic theory of the human skull (sensu Gould [1977] Ontogeny and Phylogeny, Cambridge: Harvard University Press; Alberch et al. [1979] Paleobiology 5:296-317), but modify it slightly. Human growth is clearly retarded in terms of both the magnitude of changes (size-shape covariation) and shape alone (size-shape dissociation) with respect to the chimpanzees. At the end of growth, the adult skull in humans reaches an allometric shape (size-related shape) which is equivalent to that of juvenile chimpanzees with no permanent teeth, and a size which is equivalent to that of adult chimpanzees. Our results show that human neoteny involves not only shape retardation (paedomorphosis), but also changes in relative growth velocity. Before the eruption of the first molar, human growth is accelerated, and then strongly decelerated, relative to the growth of the chimpanzee as a reference. This entails a complex process, which explains why these species reach the same overall (i.e., brain + face) size in adult stage. The neotenic traits seem to concern primarily the function of encephalization, but less so other parts of the skull. Our results, based on the discriminant function, reveal that additional structural traits (corresponding to the nonallometric part of the shape which is specific to humans) are rather situated in the other part of the skull. They mainly concern the equilibrium of the head related to bipedalism, and the respiratory and masticatory functions. Thus, the reduced prognathism, the flexed cranial base (forward position of the foramen magnum which is brought closer to the palate), the reduced anterior portion of the face, the reduced glabella, and the prominent nose mainly correspond to functional innovations which have nothing to do with a neotenic process in human evolution. The statistical analysis used here gives us the possibility to point out that some traits, which have been classically described as paedomorphic because they superficially resemble juvenile traits, are in reality independent of growth.