Getting into Shape: An Empirical Comparison of Traditional Truss-Based Morphometric Methods with a Newer Geometric Method Applied to New World Cichlids

Body shape is a difficult, but important, trait to quantify. Researchers have traditionally used multivariate analysis of several linear measures ('trusses') across the body form to quantify shape. Newer geometric morphometric methods claim to better estimate shape because they analyze the geometry among the locations of all landmarks simultaneously rather than the linear distances between pairs of landmarks. We tested this claim by comparing the results of several traditional morphometric analyses against a newer geometric analysis involving thin-plate splines (TPS), all applied to a common data set of morphologically variable new world cichlids Amphilophus citrinellus and A. zaliosus. The TPS method yielded slightly stronger evidence of morphological differences among forms, although traditional methods also distinguished the two species. Perhaps our most important result was the idiosyncratic interpretation of shape variation among the traditional truss-based methods, whereas the generation of deformation grids using the TPS approach yielded clear and visually interpretable figures. Our results indicate that geometric morphometrics can be a more effective way to analyze and interpret body form, but also that traditional methods can be relied upon to provide statistical evidence of shape differences, although not necessarily accurate information about the nature of variation in shape.     

An Integrated Approach for Landmark-Based Resistant Shape Analysis in 3D

The study of shape changes in morphology has seen a significant renovation in the last 20 years, particularly as a consequence of the development of geometric morphometric methods based on Cartesian coordinates of points. In order to extract information about shape differences when Cartesian coordinates are used, it is necessary to establish a common reference frame or system for all specimens to be compared. Therefore, a central issue in coordinate-based methods is which criterion should be used to align these configurations of points, since shape differences highly depend on those alignments. This is usually accomplished by aligning the configurations in a way that the sum of squared distances between coordinates of homologous points (landmarks) is minimized: the least-squares superimposition method. However, it is widely recognized that this method has some limitations when shape differences are not homogeneous across landmarks. Here we present an integrated approach for the resistant shape comparison of 3D landmark sets. It includes a new ordinary resistant Procrustes superimposition and its corresponding generalized resistant Procrustes version. In addition, they are combined with existing resistant multivariate statistical techniques for depicting the results. We demonstrate, by using both simulated and real datasets, that resistant Procrustes better detects and measures localized shape variation whenever present in up to half but one of the landmarks. The resistant Procrustes results are highly concordant with a priori biological information, and might dramatically improve the quality of inferences on patterns of shape variation.     

The pH-related morphological variations of two acidophilic species of Desmidiales (Viridiplantae) isolated from a lowland peat bog,Czech Republic

Morphological variation related to pH was investigated in two acidophilic desmid species (Euastrum binale var. gutwinskii and Staurastrum hirsutum) utilizing geometric morphometric methods. Clones isolated from acidic habitats were cultured using a range of pH values from 3.5 to 6.5. The plasticity of ensuing populations was quantified and illustrated by the general Procrustes superimposition of landmarks placed along the outline of cells and subsequent statistical analyses of shape data. In both species, there was a significant effect of pH on the morphology of cells. In Staurastrum hirsutum, the pH-related morphological change was accompanied by a decrease in the size of cells cultured at a higher pH. However, in Euastrum binale, cell size did not differ in relation to pH, but cell shape was characterized by a deepening of the incisions between cell lobes at higher pH. In both species, cell complexity based on surface-to-volume ratio was positively correlated with increasing pH. We conclude that by manipulating their surface-to-volume ratios, these desmid species can respond to pH variations in their environment.     

Cranial morphological variation of Dromiciops gliroides (Microbiotheria) along its geographical distribution in south-central Chile: A three-dimensional analysis

We analyzed the variation in cranial morphology of the marsupial Dromiciops gliroides along its distribution in south-central Chile. We evaluated whether the cranial morphological variation is congruent with the phylogeographic structure previously observed in this species. We built three-dimensional models of 69 crania on which we digitized 30 landmarks. We used standard geometric morphometric methods to extract and analyze the shape and size components of the crania. Our data showed a subtle but consistent cranial size and shape variation along the studied distributional range, suggesting a geographic variation pattern rather than a phylogeographic structuring. Indeed, our multivariate analyses recovered a subtle morphological differentiation between island and mainland populations, contrary to what is suggested by a former phylogeographic study. We detected that either the cranial size variation, as well as the insularity and the latitude could be important factors underlying the cranial shape changes. We suggest that an interplay of historical and contemporary processes could be shaping the morphological pattern observed in this marsupial.     

Genetic architecture of mandible shape in mice: effects of quantitative trait loci analyzed by geometric morphometrics

This study introduces a new multivariate approach for analyzing the effects of quantitative trait loci (QTL) on shape and demonstrates this method for the mouse mandible. We quantified size and shape with the methods of geometric morphometrics, based on Procrustes superimposition of five morphological landmarks recorded on each mandible. Interval mapping for F(2) mice originating from an intercross of the LG/J and SM/J inbred strains revealed 12 QTL for size, 25 QTL for shape, and 5 QTL for left-right asymmetry. Multivariate ordination of QTL effects by principal component analysis identified two recurrent features of shape variation, which involved the positions of the coronoid and angular processes relative to each other and to the rest of the mandible. These patterns are reminiscent of the knockout phenotypes of a number of genes involved in mandible development, although only a few of these are possible candidates for QTL in our study. The variation of shape effects among the QTL showed no evidence of clustering into distinct groups, as would be expected from theories of morphological integration. Further, for most QTL, additive and dominance effects on shape were markedly different, implying overdominance for specific features of shape. We conclude that geometric morphometrics offers a promising new approach to address problems at the interface of evolutionary and developmental genetics.     

Principles for the virtual reconstruction of hominin crania

Fossils are usually discovered broken or distorted, therefore reconstruction is inevitably the first step towards any comparative analysis. We outline a general methodological framework by which missing information about biological specimens can be estimated using geometric morphometric methods and discuss how this relates to effective paleoanthropological use of incomplete and distorted crania.Combining digital data resources with geometric morphometrics, we go beyond the assembly of fragments on the computer. As in a three-dimensional jigsaw puzzle, we first assemble the virtual pieces manually. Then we use landmarks, several hundred semilandmarks, and information from complete specimens to estimate missing coordinates and correct for distortion simultaneously. One can thus incorporate information from incomplete specimens in a comparative morphometric analysis while keeping track of the uncertainties that result from partial preservation or deformation. We exemplify our approach by reconstructing the fossil crania Arago XXI, Taung, and KNM-WT 15000. As different assumptions and algorithms lead to different estimations, there exists no “all-purpose” reconstruction. Instead one creates multiple reconstructions—a posterior distribution in a Bayesian sense. This distribution reflects uncertainty due to missing data values and sensitivity to prior assumptions. While there will typically be shape differences among equally plausible reconstructions, these different estimates might still support a single conclusion.     

Morpho-Functional Analysis Using Procrustes Superimposition by Static Reference

In conventional geometric morphometric analyses of limb long bones, differences in the evolutionary capacity of articular surfaces and non-articular structures often remain unrecognised. It can be shown that areas of high spatial variance dominate shape data, which is problematic for the functional interpretation of limb long bone shape. We herein introduce Procrustes superimposition by static reference (PSSR), a novel analysis strategy that aims to facilitate morpho-functional inference. This procedure exploits the spatial constraint of some reference structures (in our case, articular surfaces) for the superimposition of other subareas (e.g. muscle attachment sites) in relation to that static reference. PSSR allows for the transformation of raw scan data, enabling researchers to extract geometric models of two- and three-dimensional substructures that cannot effectively be integrated with landmarks. As we demonstrate by a simple model analysis for one muscle attachment site, this procedure can yield measures of direct functional relevance. Multivariate analysis of an extensive set of subareas indicates how this type of data relates to conventional shape coordinates. The shape evolution of xenarthran humeri, which has previously been subject to a detailed study (Milne et al., J Zool 278(1):48–56, 2009), serves as a test case. The concept of a variance-based separation of landmark subsets expands mathematical methods by incorporating knowledge about evolutionary constraints. PSSR could therefore find application far beyond the intuitive case study of long bone shape.     

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.     

Geometric morphometrics of the skull of various murid rodents (Mammalia, Rodentia): relation of the skull shape to the trophic specialization

Presented is a brief overview of basic principles and notions of geometric morphometrics, a new approach to quantitative analysis of shape variations. This approach is applied to analysis of variation of the skull shape in the sample of 18 muroid genera belonging to the families Cricetidae, Arvicolidae and Gerbillidae. The skull shape is described by landmarks, and skulls are compared by resistant fit and superimposition methods. Under consideration is relation of skull shape to the trophic specialization, to family belonging, and to body size. Axial skull reveals more conspicuous relation to each of the factor analyzed as compared to mandible. Zygomatic region and tooth raw are most differentiable, while change of auditory bulla is of secondary effect. Transition from omnivorous through granivorous to grass-eating specialization involves the same trend in each of the family studied in the case of axial skull but not of mandible. Most dependent of trophic specialization appeared to be shape of axial skull rather then of mandible. Arvicolines are most specific in respect to the skull shape. Shape to size relation, although rather slight, also involves the same zygomatic-dental region. The results obtained indicate probably that geometric morphometrics does reveal variations in the skull shape that are free of the size effect.     

Chondrocranial development in larval Rana sylvatica (Anura: Ranidae): morphometric analysis of cranial allometry and ontogenetic shape change

This study provides baseline quantitative data on the morphological development of the chondrocranium in a larval anuran. Both linear and geometric morphometric methods are used to quantitatively analyze size-related shape change in a complete developmental series of larvae of the wood frog, Rana sylvatica. The null hypothesis of isometry was rejected in all geometric morphometric and most linear morphometric analyses. Reduced major axis regressions of 11 linear chondrocranial measurements on size indicate a mixture of allometric and isometric scaling. Measurements in the otic and oral regions tend to scale with negative allometry and those associated with the palatoquadrate and muscular process scale with isometry or positive allometry. Geometric morphometric analyses, based on a set of 11 chondrocranial landmarks, include linear regression of relative warp scores and multivariate regression of partial warp scores and uniform components on log centroid size. Body size explains about one-quarter to one-third of the total shape variation found in the sample. Areas of regional shape transformation (e.g., palatoquadrate, otic region, trabecular horns) are identified by thin-plate spline deformation grids and are concordant with linear morphometric results. Thus, the anuran chondrocranium is not a static structure during premetamorphic stages and allometric patterns generally follow scaling predictions for tetrapod cranial development. Potential implications regarding larval functional morphology, cranial development, and chondrocranial evolution in anurans are discussed.     

Variation in scale shape among alternative sympatric phenotypes of Arctic charr Salvelinus alpinus from two lakes in Scotland

Landmark‐based geometric morphometric analysis was used to detect differences in scale shape between ecologically distinct phenotypes of Arctic charr Salvelinus alpinus coexisting in the same lake. Relative warp analysis and standard multivariate analyses of the partial warps, obtained after a Procrustes superimposition, showed that scale landmarks were efficient in discriminating among two closely related alternative phenotypes within each of the two lakes. In Loch Tay, S. alpinus exhibited a bimodal body size‐frequency distribution among sexually mature fish, whereas in Loch Awe, S. alpinus are unimodal in body size but segregated into two distinct spawning phenotypes. In both lakes, alternative phenotypes showed significant differences in foraging ecology, habitat use and life history. It is probable that differences in scale shape reflect differences in ecology of these forms.     

GEOMETRIC MORPHOMETRICS OF DEVELOPMENTAL INSTABILITY: ANALYZING PATTERNS OF FLUCTUATING ASYMMETRY WITH PROCRUSTES METHODS

Although fluctuating asymmetry has become popular as a measure of developmental instability, few studies have examined its developmental basis. We propose an approach to investigate the role of development for morphological asymmetry by means of morphometric methods. Our approach combines geometric morphometrics with the two-way ANOVA customary for conventional analyses of fluctuating asymmetry and can discover localized features of shape variation by examining the patterns of covariance among landmarks. This approach extends the notion of form used in studies of fluctuating asymmetry from collections of distances between morphological landmarks to an explicitly geometric concept of shape characterized by the configuration of landmarks. We demonstrate this approach with a study of asymmetry in the wings of tsetse flies (Glossina palpalis gambiensis). The analysis revealed significant fluctuating and directional asymmetry for shape as well as ample shape variation among individuals and between the offspring of young and old females. The morphological landmarks differed markedly in their degree of variability but multivariate patterns of landmark covariation identified by principal component analysis were generally similar between fluctuating asymmetry (within-individual variability) and variation among individuals. Therefore there is no evidence that special developmental processes control fluctuating asymmetry. We relate some of the morphometric patterns to processes known to be involved in the development of fly wings.     

On comparing biological shapes: detection of influential landmarks.

For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form consists of size and shape. Several approaches for comparing biological forms using landmark data are available. If the two biological forms are demonstrated to be different, the next important issue is to localize the differences by identifying those areas which differ most between the two objects. In this paper we suggest a technique to detect influential landmarks, those which contribute most to the difference between forms. We study the effectiveness of the technique using three-dimensional simulated data sets and two examples. Results suggest that the technique is useful in the study of biological form and its variation.     

LeafAnalyser: a computational method for rapid and large-scale analyses of leaf shape variation

A comprehensive understanding of leaf shape is important in many investigations in plant biology. Techniques to assess variation in leaf shape are often time-consuming, labour-intensive and prohibited by complex calculation of large data sets. We have developed LeafAnalyser, software that uses image-processing techniques to greatly simplify the measurement of leaf shape variation. LeafAnalyser places a large number of evenly distributed landmarks along leaf margins and records the position of each automatically. We used LeafAnalyser to analyse the variation in 3000 leaves from 400 plants of Antirrhinum majus . We were able to summarise the major trends in leaf shape variation using a principal components (PC) analysis and assess the changes in size, width and tip-to-base asymmetry within our leaf library. We demonstrate how this information can be used to develop a model that describes the range and variation of leaf shape within standard wild-type lines, and illustrate the shape transformations that occur between leaf nodes. We also show that information from LeafAnalyser can be used to identify novel trends in shape variation, as low-variance PCs that only affect a subset of position landmarks. These results provide a high-throughput method to calculate leaf shape variation that allows a large number of leaves to be visualised in higher-dimensional phenotypic space. To illustrate the applicability of LeafAnalyser we also calculated the leaf shape variation in 300 leaves from Arabidopsis thaliana .     

Evolutionary patterns of hind wing morphology in dung beetles (Coleoptera: Scarabaeinae)

The shape of wings can be a good predictor of adaptations to different selective pressures and the value of wing features in taxonomy and phylogeny has long been recognized. In our investigation of the hind wing evolution of dung beetles (Scarabaeinae) we use geometric morphometrics combined with a cladistic approach. The variations of entire hind wings and of three specific regions of 80 dung beetle species were investigated using 19 landmarks and outline data. Extensive evidence indicates that the wing as a whole and the three separate regions were under different selective pressures. The detailed evolutionary patterns of the three regions and the reconstruction of the ancestral forms were computed by mapping the geometric morphometrics data onto a tree based on a cladistic character analysis.     

A complete survey of normal pores on a smooth shell ostracod (Crustacea): Landmark‐based versus outline geometric morphometrics

Pores and sensilla on ostracod shell have often been used in studies of ontogeny, taxonomy, and phylogeny of the group. However, an analysis of sexual dimorphism and variation between valves in the number and distribution of pores is lacking. Also, such studies have never been done on a widely distributed, morphologically variable, and weakly ornamented freshwater ostracod. Here, we survey pores in one such species, Physocypria kraepelini . We choose 27 homologous pores as landmarks for 2D‐geometric morphometric analysis, with the aim to assess intersexual and between valves variation in size and shape relative to the Fourier outline analysis. This species has only simple (Type A) pores with and without a lip, and each pore carries an undivided sensory seta. Our results show that the total number of pores varies (from 270 to 296), but this is not associated with a specific valve. Males carry fewer pores than females, however no sex specific pores are found. Small intrapopulation divergence of the Cyt b molecular marker (1%) indicates that morphological variability is not species related. We found that P. kraepelini exhibits directional asymmetry of size and shape, sexual size dimorphism (SSD) but lacks sexual shape dimorphism (SShD). Two geometric morphometrics methods were congruent in the estimation of SSD, SShD, and directional asymmetry of shape but differ in the statistical evaluation of directional asymmetry of size. Contrary to other animal groups, our study suggests that ostracods have more pronounced directional asymmetry of shape compared to directional asymmetry of size.     

The influence of size on body shape diversification across Indo‐Pacific shore fishes*

Understanding the causes of body shape variability across the tree of life is one of the central issues surrounding the origins of biodiversity. One potential mechanism driving observed patterns of shape disparity is a strongly conserved relationship between size and shape. Conserved allometry has been shown to account for as much as 80% of shape variation in some vertebrate groups. Here, we quantify the amount of body shape disparity attributable to changes in body size across nearly 800 species of Indo‐Pacific shore fishes using a phylogenetic framework to analyze 17 geometric landmarks positioned to capture general body shape and functionally significant features. In marked contrast to other vertebrate lineages, we find that changes in body size only explain 2.9% of the body shape variation across fishes, ranging from 3% to 50% within our 11 sampled families. We also find a slight but significant trend of decreasing rates of shape evolution with increasing size. Our results suggest that the influence of size on fish shape has largely been overwhelmed by lineage‐specific patterns of diversification that have produced the modern landscape of highly diverse forms that we currently observe in nature.     

Quantitative-genetic analysis of wing form and bilateral asymmetry in isochromosomal lines ofDrosophila subobscura using Procrustes methods

Fluctuating asymmetry (FA) is often used as a measure of underlying developmental instability (DI), motivated by the idea that morphological variance is maladaptive. Whether or not DI has evolutionary potential is a highly disputed topic, marred by methodological problems and fuzzy prejudices. We report here some results from an ongoing study of the effects of karyotype, homozygosity and temperature on wing form and bilateral asymmetry using isochromosomal lines ofDrosophila subobscura. Our approach uses the recently developed methodologies in geometric morphometrics to analyse shape configurations of landmarks within the standard statistical framework employed in studies of bilateral asymmetries, and we have extended these methods to partition the individual variation and the variation in asymmetries into genetic and environmental causal components. The analyses revealed temperaturedependent expression of genetic variation for wing size and wing shape, directional asymmetry (DA) of wing size, increased asymmetries at suboptimal temperature, and a transition from FA to DA in males as a result of increase in the rearing temperature. No genetic variation was generally detected for FA in our samples, but these are preliminary results because no crosses between lines were carried out and, therefore, the contribution of dominance was not taken into account. In addition, only a subset of the standing genetic variation was represented in the experiments.