Elliptic Fourier Analysis Research Articles

A study of Late Woodland projectile point typology in New York using elliptical Fourier outline analysis

A sample of Late Woodland triangle points from the Mohawk Valley, New York, is studied using 2D elliptical Fourier analysis (EFA) in order to assess the applicability of formal tool typologies for the region. Lithic analysts have questioned two types of triangle, Levanna and Madison, as valid analytic units as they are quantifiably indeterminate when measured using caliper methods such as length and width. The geometric morphometric analysis here takes outline data from a previously studied collection of projectile points and uses elliptical Fourier harmonics analysis combined with principal components and discriminant functions tests to objectively define and separate the two types of projectile point. The result is a bimodal distribution of types that conforms to the traditional typological classification system for the region, in contrast to recent scholarship that conflates the two types into one. This study describes a high-resolution technique that offsets the inherent drawbacks of subjective, coarse-grained measurement approaches to projectile point characterization and comments on the study of typology as a whole.

Geometric Morphometrics on Gene Expression Patterns Within Phenotypes: A Case Example on Limb Development.

How the genotype translates into the phenotype through development is critical to fully understand the evolution of phenotypes. We propose a novel approach to directly assess how changes in gene expression patterns are associated with changes in morphology using the limb as a case example. Our method combines molecular biology techniques, such as whole-mount in situ hybridization, with image and shape analysis, extending the use of Geometric Morphometrics to the analysis of nonanatomical shapes, such as gene expression domains. Elliptical Fourier and Procrustes-based semilandmark analyses were used to analyze the variation and covariation patterns of the limb bud shape with the expression patterns of two relevant genes for limb morphogenesis, Hoxa11 and Hoxa13. We devised a multiple thresholding method to semiautomatically segment gene domains at several expression levels in large samples of limb buds from C57Bl6 mouse embryos between 10 and 12 postfertilization days. Besides providing an accurate phenotyping tool to quantify the spatiotemporal dynamics of gene expression patterns within developing structures, our morphometric analyses revealed high, non-random, and gene-specific variation undergoing canalization during limb development. Our results demonstrate that Hoxa11 and Hoxa13, despite being paralogs with analogous functions in limb patterning, show clearly distinct dynamic patterns, both in shape and size, and are associated differently with the limb bud shape. The correspondence between our results and already well-established molecular processes underlying limb development confirms that this morphometric approach is a powerful tool to extract features of development regulating morphogenesis. Such multilevel analyses are promising in systems where not so much molecular information is available and will advance our understanding of the genotype–phenotype map. In systematics, this knowledge will increase our ability to infer how evolution modified a common developmental pattern to generate a wide diversity of morphologies, as in the vertebrate limb.

Form changes inAmiantis purpurata(Bivalvia, Veneridae) shells over the past 100,000 years in North Patagonia (Argentina)

Amiantis purpuratashells from the San Matías Gulf (SMG) were analysed in order to compare both morphology and size throughout the late Quaternary in relation to environmental changes. Shells from modern beaches, Holocene marine assemblages (late Holocene, 3630 ± 100 yearsbp) and interglacial Pleistocene marine assemblages (MIS 5, 100 ka yearsbp) were studied by measuring the height and length, and using the elliptic Fourier analysis (EFA) to take an outline contour. The Pleistocene shells were smaller, more elliptical and with a deeper lunule than the Holocene and modern ones. No significant differences were recorded in the allometry index throughout the late Quaternary. The variation in size and shape of theA. purpuratashells could be related to the phenotypic plasticity of this species as a response to the environmental changes registered in the SMG during the Quaternary. These changes include variations in sea surface temperatures, salinities and substrates, and also water circulation changes, which would have modified nutrient availability. Morphological changes imply burrowing activity, mechanical stability, nutrient uptake and defence response to predation.

Human Identification via Lateral Patella Radiographs: A Validation Study.

This research examines the utility of patella outline shape for matching 3D scans of patellae to knee radiographs using elliptical Fourier analysis and subjective methods of human visual comparison of patellae across radiographs for identification purposes. Repeat radiographs were captured of cadaver's knees for visual comparison before patellae were extracted and skeletonized for quantitative comparisons. Quantitative methods provided significant narrowing down of the candidate pool to just a few potential matches (<5% of original sample), while the human analysts showed high capacity for correctly matching radiographs, irrespective of educational level (positive predictive value = 99.8%). The successful computerized matching based on a single quantified patella trait (outline shape) helps explain the potency achieved by subjective visual examination. This work adds to a growing body of studies demonstrating the value of single isolated infracranial bones for human identification via radiographic comparison.

Genome-Wide Association Study on Male Genital Shape and Size in Drosophila melanogaster.

Male genital morphology of animals with internal fertilization and promiscuous mating systems have been one of the most diverse and rapidly evolving morphological traits. The male genital morphology in general is known to have low phenotypic and genetic variations, but the genetic basis of the male genital variation remains unclear. Drosophila melanogaster and its closely related species are morphologically very similar, but the shapes of the posterior lobe, a cuticular projection on the male genital arch are distinct from each other, representing a model system for studying the genetic basis of male genital morphology. In this study, we used highly inbred whole genome sequenced strains of D. melanogaster to perform genome wide association analysis on posterior lobe morphology. We quantified the outline shape of posterior lobes with Fourier coefficients obtained from elliptic Fourier analysis and performed principal component analysis, and posterior lobe size. The first and second principal components (PC1 and PC2) explained approximately 88% of the total variation of the posterior lobe shape. We then examined the association between the principal component scores and posterior lobe size and 1902142 single nucleotide polymorphisms (SNPs). As a result, we obtained 15, 14 and 15 SNPs for PC1, PC2 and posterior lobe size with P-values smaller than 10-5. Based on the location of the SNPs, 13, 13 and six protein coding genes were identified as potential candidates for PC1, PC2 and posterior lobe size, respectively. In addition to the previous findings showing that the intraspecific posterior shape variation are regulated by multiple QTL with strong effects, the present study suggests that the intraspecific variation may be under polygenic regulation with a number of loci with small effects. Further studies are required for investigating whether these candidate genes are responsible for the intraspecific posterior lobe shape variation.

Unsupervised model-based clustering for typological classification of Middle Bronze Age flanged axes

The classification of Western European flanged axes dating to the Middle Bronze Age (1650–1350 BC) is very complex. Many types of axe have been identified, some of which have numerous variant forms. In the current French terminology, all axes are divided into two generic groups: namely “Atlantic” (Atlantique) and “Eastern” (Orientale). Each of these generic groups, however, is highly polymorphic, so that it is often very difficult for the operator to classify individual axes with absolute confidence and certainty. In order to overcome such problems, a new shape classification is proposed, using morphometric analysis (Elliptic Fourier Analysis) followed by unsupervised model-based clustering and discriminant analysis, both based on Gaussian mixture modelling. Together, these methods produce a clearer pattern, which is independently validated by the spatial distribution of the findings, and multinomial scan statistics. This approach is fast, reproducible, and operator-independent, allowing artefacts of unknown membership to be classified rapidly. The method is designed to be amendable by the introduction of new artefacts, in the light of future discoveries. This method can be adapted to suit many other archaeological artefacts, providing information about the material, social and cultural relations of ancient populations.

Toward a Better Understanding of the Native–Nonnative Status ofMytilusMussels in the Southwestern Atlantic: Comparing Pre-European Middens and Modern Populations

ABSTRACT Savoya, V.; Gomez Otero, J., and Schwindt, E., 2015. Toward a better understanding of the native–nonnative status of Mytilus mussels in the southwestern Atlantic: comparing pre-European middens and modern populations. The aim of this study is to determine the degree of similarity of the Mytilus mussels currently found along the Patagonian coast of Argentina to those found in pre-European colonization middens, in order to approach an understanding of whether the former are native or not. An elliptic Fourier analysis between pre-European archaeological (native) and modern mussels (cryptogenic) was performed, and the resulting data were analyzed with multivariate approaches (principal component analysis, discriminant function analysis, and cluster analysis). Our results showed that when all samples belonging to the Patagonian coast were included on a single analysis, modern and archaeological mussels were clustered in two major groups, matching the macroregional marine biogeographic scheme. In addit...

Deconstructing cartilage shape and size into contributions from embryogenesis, metamorphosis, and tadpole and frog growth.

Understanding skeletal diversification involves knowing not only how skeletal rudiments are shaped embryonically, but also how skeletal shape changes throughout life. The pharyngeal arch (PA) skeleton of metamorphosing amphibians persists largely as cartilage and undergoes two phases of development (embryogenesis and metamorphosis) and two phases of growth (larval and post-metamorphic). Though embryogenesis and metamorphosis produce species-specific features of PA cartilage shape, the extents to which shape and size change during growth and metamorphosis remain unaddressed. This study uses allometric equations and thin-plate spline, relative warp and elliptic Fourier analyses to describe shape and size trajectories for the ventral PA cartilages of the frog Xenopus laevis in tadpole and frog growth and metamorphosis. Cartilage sizes scale negatively with body size in both growth phases and cartilage shapes scale isometrically or close to it. This implies that most species-specific aspects of cartilage shape arise in embryogenesis and metamorphosis. Contributions from growth are limited to minor changes in lower jaw (LJ) curvature that produce relative gape narrowing and widening in tadpoles and frogs, respectively, and most cartilages becoming relatively thinner. Metamorphosis involves previously unreported decreases in cartilage size as well as changes in cartilage shape. The LJ becomes slightly longer, narrower and more curved, and the adult ceratohyal emerges from deep within the resorbing tadpole ceratohyal. This contrast in shape and size changes suggests a fundamental difference in the underlying cellular pathways. The observation that variation in PA cartilage shape decreases with tadpole growth supports the hypothesis that isometric growth is required for the metamorphic remodeling of PA cartilages. It also supports the existence of shape-regulating mechanisms that are specific to PA cartilages and that resist local adaptation and phenotypic plasticity.

Reading shell shape: implications for palaeoenvironmental reconstructions. A case study for bivalves from the marine Quaternary of Argentina (south-western Atlantic)

Most research on bivalves from the south-western Atlantic used morphological (shell) characters for taxonomic discriminations. Dominant Veneroids from Argentinian Quaternary coastal deposits exhibit wide morphological variation – often making objective discriminations difficult/impossible, which could be objectively described and compared through geometric morphometrics techniques. This work focuses on comparison of geometric morphometrics methods applied to fossil and modern shells, to assess inter- and intra-generic variations. Three approaches were considered: landmarks (L), semi-landmarks (SL) and outlines. Shell shape analyses for different time spans (Pleistocene, fossil Holocene and modern) and areas (Patagonia and Bonaerensian) showed that Elliptic Fourier analysis (EFA), Landmarks and Landmarks plus Semilandmarks (L+SL) can discriminate at generic levels: Mactra, Mulinia (Mactridae) vs. Pitar, Protothaca, Eurhomalea, Clausinella (Veneridae). L and L+SL are powerful for inter/intraspecific distinctions of Mactra. Variability of Mactra isabelleana includes the remaining nominal ‘species’ (transitional morphs). Causal environmental factors of (phenotype) variation could be addressed for modern environments (substrate, salinity and energy). Subtrigonal-inflated shells predominate in muddy, quieter, shallow mixo-polyhaline waters; ovate-elongate-compressed in sandy, poly-euhaline, deeper habitats. Differential spatial distribution (and abundance) across time responds to Late Quaternary high sea-level stands: transgressive maxima allowed higher salinity in marginal-marine areas and optimal conditions for Mactra isabelleana contrasting with scarcer records in the Mar Argentino today.

An evaluation of nasal bone and aperture shape among three South African populations

Reliable and valid population specific standards are necessary to accurately develop a biological profile, which includes an estimation of peer-reported social identification (Hefner, 2009). During the last 300 years, colonialism, slavery and apartheid created geographic, physical and social divisions of population groups in South Africa. The purpose of this study was to evaluate variation in nasal bone and aperture shape in a modern population of black, white, and coloured South Africans using standard craniometric variables and geometric morphometrics, namely general Procrustes and elliptical Fourier analyses.Fourteen standard landmarks were digitally recorded or computationally derived from 310 crania using a 3D coordinate digitizer for discriminant function, principal components and generalized Procrustes analyses. For elliptical Fourier analysis, outlines of the nasal aperture were generated from standardized photographs. All classification accuracies were better than chance; the lowest accuracies were for coloured and the highest accuracies were for white South Africans. Most difficulties arose in distinguishing coloured and black South African groups from each other. Generally, misclassifications were noted between the sexes within each group rather than among groups, which suggests that sex has less influence on nasal bone and aperture shape than ancestry. Quantifiable variation in shape of the nasal aperture region between white and non-white South African groups was observed.

Quantifying the Shape of the Greater Sciatic Notch using Elliptical Fourier Analysis

The greater sciatic notch of the coxa is well established as a sexually dimorphic feature in humans, with wider notches being more common in females. However, the size and shape of the notch can vary between populations, which can complicate the use of this feature as a sex determinant in forensic analyses. The current study investigates the relative contributions of variables that may influence the shape of the greater sciatic notch, including sex, ancestry, age at death, and environmental effects (secular change). As the notch is a complex curvilinear shape not easily quantified using standard linear measurements, a more sensitive morphometric approach was used. The study sample included 975 dry bone specimens obtained from three skeletal collections, including three ancestral groups from recent (1950‐present) and earlier (pre‐1950) time periods. Each coxa was photographed and the contour of the greater sciatic notch was outlined. These contours were uploaded into SHAPE v1.3 and subjected to elliptical Fourier analysis. Principle components generated eigenvalues that identified the variables contributing to the shape of the notch, and 97% of the observed variation could be described using four principle components. Notch shape varies systematically with each of the aforementioned variables, with sex having the greatest contribution. As expected, females display wider symmetrical notches, while those of males are narrow and asymmetrical. However, the final model was only able to explain 14.3% of the total variation in the shape of the notch, indicating that the growth and development of this feature is quite complex.

Genomic prediction of biological shape: elliptic Fourier analysis and kernel partial least squares (PLS) regression applied to grain shape prediction in rice (Oryza sativa L.).

Shape is an important morphological characteristic both in animals and plants. In the present study, we examined a method for predicting biological contour shapes based on genome-wide marker polymorphisms. The method is expected to contribute to the acceleration of genetic improvement of biological shape via genomic selection. Grain shape variation observed in rice (Oryza sativa L.) germplasms was delineated using elliptic Fourier descriptors (EFDs), and was predicted based on genome-wide single nucleotide polymorphism (SNP) genotypes. We applied four methods including kernel PLS (KPLS) regression for building a prediction model of grain shape, and compared the accuracy of the methods via cross-validation. We analyzed multiple datasets that differed in marker density and sample size. Datasets with larger sample size and higher marker density showed higher accuracy. Among the four methods, KPLS showed the highest accuracy. Although KPLS and ridge regression (RR) had equivalent accuracy in a single dataset, the result suggested the potential of KPLS for the prediction of high-dimensional EFDs. Ordinary PLS, however, was less accurate than RR in all datasets, suggesting that the use of a non-linear kernel was necessary for accurate prediction using the PLS method. Rice grain shape can be predicted accurately based on genome-wide SNP genotypes. The proposed method is expected to be useful for genomic selection in biological shape.

Natural growth, otolith shape and diet analyses of Odontesthes nigricans Richardson (Atherinopsidae) from southern Patagonia

Age and growth, otolith shape and diet of Odontesthes nigricans were analysed in order to provide an insight into the life history of the species and furthermore, to assess their possible use as a tool for discriminating silverside populations from the South Atlantic Ocean (Punta María) and Beagle Channel waters (Varela Bay). The age and growth analysis was performed by counting daily increments and annual marks in sagittae otoliths. Length-at-age data of individuals <65 mm standard length (SL) were fitted to the Laird–Gompertz model (SLt = 6.22 exp 2.45 [1−exp (−0.02t)]), which provided an excellent description of the pattern of daily growth for O. nigricans juveniles from Varela Bay. The spawning period was also assessed through back-calculation of hatching dates and it extended from November to February. The count of annual marks in larger individuals identified 7 year classes (0+ to 6+) in Varela Bay and 6 year classes (0+ to 5+) in Punta María. The von Bertalanffy growth model explained more than 95% of the growth patterns observed in O. nigricans from Varela Bay (SLt = 245.49 [1 − exp −0.24(t+0.46)]) and Punta María (SLt = 345.09 [1 − exp −0.15(t+0.31)]). Particularly, k and SL∞ varied significantly between sampling sites; reaching Punta María a larger SL∞ value with a lower k. Otolith shape variation was also explored using elliptical Fourier analysis and it showed significant differences between Varela Bay and Punta María populations. Furthermore, gut content analysis characterized O. nigricans as an invertebrate predator, being benthic organisms the most important components of its diet, which also showed significant site dependence. The use of all these analyses contributed to a holistic approach which maximized the likelihood of correctly identifying both O. nigricans populations in the southernmost limit of the species distribution.

A quantitative analysis of the wing outlines of owlflies (Insecta: Neuroptera: Ascalaphidae)

We quantitatively described and analyzed variation in the wing outlines of owlflies using 135 forewings and 135 hindwings from eight species in five genera. We captured and digitized images of the wing outlines from 135 individual specimens and subjected them to Elliptic Fourier analysis to produce matrices of Fourier coefficients based on 20 harmonics. The first five principal components extracted from the Fourier coefficient matrices described the wing outlines, explaining 94.87% of the total forewing variation and 95.06% of the total hindwing variation. Relationships among species were estimated using multivariate analysis of variance, principal component analysis, and cluster analysis. The results indicated highly significant differences in the wing outlines among the eight owlfly species. Pair-wise comparisons indicated significant differences between 96% of the species pairs based on the forewing outlines and between 100% of the species pairs based on the hindwing outlines. The results of the cluster analysis were partially consistent with the existing classification system of Ascalaphidae. Our results show that quantitative data of wing outlines can effectively differentiate Libelloides from the other four owlfly genera.

Shell‐shape and morphometric variability in Mytilus galloprovincialis from micro‐tidal environments: responses to different hydrodynamic drivers

AbstractTidal conditions differently influence inter‐tidal organisms in terms of general physiological and metabolic responses. In this study we investigated the morphological response in shells of Mytilus galloprovincialis native to different micro‐tidal coastal environments in the Northern Adriatic Sea. Our purpose was to highlight the ecophenotypic variability across tidal levels and to elucidate how tidal currents and waves produced by anthropogenic activities may play a part in modulating shell morphology. Three sampling sites were selected: an open‐sea area 15 km off‐shore and two sites within the lagoon of Venice, the first near one of its three inlets, and the other one in the proximity of Venice city centre. At each sampling site, organisms were seasonally collected at different depths within their vertical zonation, either in the inter‐tidal zone – i.e. at both the highest and lowest tide zonation limits, and subtidally. The mussel shells were analysed by investigation of their morphometric relationships (height/length and width/length ratios) and by elliptic Fourier analysis of the shell contours. Shell thickness and condition index were also evaluated for a better comprehension of energy allocation/partitioning. Estimates based on long‐term measurements, visual observation, wind statistics and wave growth laws allowed an evaluation of the forces acting on shells. At the open‐sea site, the observed phenotypic variability of both shell shape and thickness was clearly related to the tidal vertical zonation. At the two lagoon sites, the currents generated by tidal flow through the inlet and the waves caused by the frequent passage of boats influenced both shell shape and thickness. A trade‐off between protection and growth was apparent along the tide gradient, as emphasized by the differences in the partitioning and allocation of energy between shell and flesh production.

The evaluation of macroscopic and microscopic textures of sand grains using elliptic Fourier and principal component analysis: Implications for the discrimination of sedimentary environments

ABSTRACTA method that integrates elliptic Fourier and principal component analysis is a new development in the analysis of the shapes of sand grains. However, conventional elliptic Fourier and principal component analysis based on the variance–covariance matrix of the elliptic Fourier results can determine only the form of sand grains, and fails to quantify fine‐scale boundary smoothness of grains. In this study, sand grains from glacial, fluvial, foreshore and aeolian environments were analysed using both elliptic Fourier and principal component analysis and an extension of elliptic Fourier and principal component analysis based on the correlation matrix to extract information on grain form (macroscopic) and grain boundary smoothness (microscopic) separately. Conventional elliptic Fourier and principal component analysis based on the variance–covariance matrix produces macroscopic particle shape descriptors, such as the elongation index and bump indices. These indices indicate that sand grains exposed to subaqueous transportation (fluvial and foreshore) have forms that are more elongated than those exposed to subaerial transportation (aeolian dunes). However, elliptic Fourier and principal component analysis based on the correlation matrix is, in addition, able to extract microscopic particle features, which can be interpreted in terms of a boundary smoothness index. The boundary smoothness index indicates that the surfaces of glacial grains are the most rugged, whereas the surfaces of aeolian grains are the smoothest. On bivariate plots of the boundary smoothness and elongation indices, samples from fluvial, foreshore, aeolian and glacial environments cluster in discrete regions. In addition, the analysis reveals that glacial grains are exposed to different morphological maturation pathways than those from fluvial, foreshore and aeolian environments.

Tracing functional adaptation in African cichlid fishes through morphometric analysis of fossil teeth: exploring the methods

The sedimentary archive of Crater Lake Challa in East Africa contains abundant fossil teeth of cichlid fishes throughout at least the last 25,000 years. Here, we use morphometric analyses of oral teeth from the two extant Oreochromis species inhabiting Lake Challa to explore the feasibility of tracing adaptive modification of the cichlid trophic apparatus in the lake’s fossil record. We compared the performance of semi-landmark analysis (SLM) and elliptic Fourier analysis in capturing morphological variation in oral tooth crowns, and found that SLM, supplemented with tooth shaft measurements, ensured consistency with whole-body landmark analyses. Whole-body and tooth morphology data both allowed to discern between the indigenous Oreochromis hunteri and the recently introduced Oreochromis korogwe. Both species have an oral jaw arrangement of outer-row bicuspid and inner-rows tricuspid teeth, but O. hunteri has generally more slender teeth with a proportionally taller major cusp than O. korogwe, suggesting fine-scaled resource partitioning. Exploratory analysis of three fossil samples showed that the major tooth types of modern-day Oreochromis are also represented in the fossil record. Their total morphological variation is largely restricted to the morphospace occupied by contemporary teeth, suggesting a close functional relationship between ancient populations and their likely descendant, O. hunteri.

Bifaces in plain sight: testing elliptical Fourier analysis in identifying reduction effects on Late Middle Palaeolithic bifacial tools

Bifaces in plain sight: testing elliptical Fourier analysis in identifying reduction effects on Late Middle Palaeolithic bifacial tools

Plasticity and conservatism in sclerites of a Caribbean octocoral

Species level identification of octocorals is often based on the form of skeletal elements, the sclerites. Morphological variation in sclerites across and within habitats complicates both species delineation and the identification of specimens, both of which are essential for characterizing and understanding octocoral diversity. In order to quantify the effects of environmental plasticity on sclerite morphology, branches from the Caribbean gorgonian Antillogorgia bipinnata were removed from colonies at depths of 18 and 23 m and reciprocally transplanted between those sites and transplanted to an 8 m depth site for 7 months. Images of sclerites from those colonies were compared using elliptical Fourier analyses (EFA) of the sclerite outline. The length of scaphoids produced after transplantation was larger than those in older tissue, suggesting length was affected by the process of transplantation. Shape of scaphoids as detected in the EFA, differed between sites, and the reciprocal crosses suggest some of the difference was a plastic response to the environment. The results demonstrate the presence of some environmental plasticity in sclerite form. However, while detectable using EFA, the differences in form were not apparent in microscopical observations of the sclerites and thus would not affect identification of specimens nor traditional species delineation.

Spatial variation in shape of otoliths for southern garfish Hyporhamphus melanochir – Contribution to stock structure

Otolith morphometrics and shape analyses were used to delineate the sub-population structure and determine the level of mixing of southern garfish in South Australian waters. Adult garfish from the 2+ age class were collected from three sites within each of six regions along the South Australian coast: Northern Gulf St Vincent, Southwest Gulf St Vincent, Kangaroo Island, Northern Spencer Gulf, Southern Spencer Gulf and the West Coast of Eyre Peninsula. This study adopted a multi-stage statistical approach exploring the spatial variation in gross otolith morphology and through elliptical Fourier analysis separately, and in combination, over both broad (regional) and fine (site) spatial scales. Stepwise discriminant function analysis revealed significant separation across both spatial scales; however, overall classification success of garfish to their site of capture was poor (<45%). Despite this, the results indicated some level of structuring within South Australia's southern garfish population, as fish were correctly classified at rates that were 32% better than would be expected by chance. At least six putative regional components with various levels of intermixing were detected based on differences in otolith shape. This result refines the spatial resolution of the fishery and consequently highlights the vulnerability of these regional components to localized depletion, particularly as the resource is currently considered to be over-exploited.