Elliptic Fourier Analysis Research Articles

Identificación de stocks de <i>Engraulis ringens</i> en Chile utilizando morfometría de otolitos

Anchovy (Engraulis ringens) population units were analyzed in three zones off the coast of Chile: 1: Arica-Iquique, 2: Coquimbo and 3: Talcahuano-Valdivia from samples obtaineds during the 2012 spawning season. We used 50 left sagittae otoliths from each zone to perform a morphometric analysis, which included basic measurements, shape indexes and contour analysis (elliptical Fourier analysis). A MANOVA and Tukey multiple comparison analyses, applied on basic measures and shape indexes showed significant differences between zone 3 and zones 1 and 2. A classification by Canonical Discriminant analysis of elliptical Fourier harmonics, indicated significant differences among zones. It is concluded, therefore, that otolith shape analysis could be used to discriminate population units of Engraulis ringens. Better results were achieved using elliptic Fourier coefficients than using only shape indices.

Geometric morphometry of pupae to identify four medically important flies (Order: Diptera) in Thailand

Abstract. Chaiphongpachara T, Tubsamut P. 2019. Geometric morphometry of pupae to identify four medically important flies (Order: Diptera) in Thailand. Biodiversitas 20: 1504-1509. In this study, we evaluated an outline-based geometric morphometric (GM) approach for species identification from pupae of four common flies medically important in Thailand, Chrysomya megacephala, Lucilia cuprina, Musca domestica, and Boettcherisca nathani. For size estimation, mean perimeter length was used. For shape analysis, Elliptic Fourier Analysis was performed to produce the contour shape variables, which was calculated as Normalised Elliptic Fourier coefficients. Then, principal component analysis was performed on the Normalized Fourier coefficients for discriminant analysis, and used to estimate pupal shape variation among the species. The difference in size and shape between the fly species was analyzed using a non-parametric test based on 1000 permutations after Bonferroni correction for the significance level (p < 0.05). In the size analysis, the mean perimeter length for pupae of B. nathani was the largest (20.35 mm) followed by C. megacephala (14.73 mm), while that for M. domestica was the smallest (11.82 mm). The size differences were statistically significant between all species (p < 0.05). The contour shapes of all pupae were significantly different among all species. The results of this study can be used as a basis for the future application of GM to identify other types of flies via their pupae.

Maturation of the human foetal basioccipital: quantifying shape changes in second and third trimesters using elliptic Fourier analysis.

During prenatal development, the brain is considered the best maturation criterion for the estimation of foetal physiological age, regardless of the conditions of pregnancy. Unfortunately, the brain lyses very quickly after death, but fortunately, the brain also has a major influence over osseous structures of the cranial base during development. Therefore, we considered the osseous structures of the cranial base potential indirect maturation indicators of foetal age. Because of its early formation and robustness, the basioccipital is a cranial base bone that is often used for studies in biological anthropology. Studies generally use conventional morphometry and bone size ratio to highlight morphological changes occurring during the foetal period and to create age estimation methods. These methods usually define thresholds beyond which the morphology of the basioccipital changes, but do not fully consider the form that might be valuable precisely to visualize its development or improve age estimation methods. Using geometric morphometric methods, the present study aims to analyse the development of the basioccipital during the second and third trimesters of foetal life by quantifying and visualizing shape changes in the inferior view. Basioccipital shapes are used as direct indicators of the maturation of the cranial base and as indirect indicators of the maturation of the brain and, by extension, the whole body. A sample of 221 anonymized computed tomographic (CT) scans of normal foetuses, ranging from 18 to 41 gestational weeks (GW), was used. Elliptic Fourier analysis (EFA) was used to quantify the basioccipital outline, and maturation stages were established to visualize shape changes with a principal component analysis. Our study allowed us precisely to quantify and continuously visualize shape changes occurring during prenatal life. Additionally, this study provides the first evidence of two distinct linear shape trajectories of the basioccipital. Foetuses aged between 18 and 26 GW have a rapid shape change with well-individualized stages, whereas shape changes are less visible in the second trajectory (27-41 GW). Furthermore, intra-stage shape variation is higher for the basioccipital at the beginning of the second and third trimesters than at the first trimester. By using geometric morphometric methods and EFA, this study shows that it was possible to go beyond classical methods. Indeed, the developed methodology enabled the first quantification of the overall shape changes of the basioccipital between gestational ages. The morphological shape changes throughout the foetal period can be useful for anthropological studies and provide new perspectives for immature age estimation methods.

Linear and geometric morphometrics as tools to resolve species circumscription in the Pseudolaelia vellozicola complex (Orchidaceae, Laeliinae)

Background and aims – Pseudolaelia is a genus endemic to eastern Brazil, with 12 accepted species predominantly distributed across granitic inselbergs of the Brazilian Atlantic Forest. The aim of the present study was to distinguish between the very similar taxa P. aguadocensis, P. oliveirana, P. regentii and P. vellozicola, using morphometric data acquired as linear measurements and outlines capture with Elliptic Fourier Analysis (EFA) of the floral parts. Material and methods – We sampled 208 specimens from 11 natural populations of the above taxa. We measured 20 floral variables and for the EFA, and we extracted 24 shape variables from the Fourier coefficient matrices, which describe the outlines of the floral parts. In both cases the data were analyzed with multivariate methods (both ordination and clustering). Key results – We could not find morphological discontinuities with sufficient magnitude to consider P. aguadocensis, P. oliveirana and P. regentii as distinct species from P. vellozicola. Conclusions – We propose that P. vellozicola should be considered a polymorphic and widely distributed species, generally supported by both methods.

A Comparison of Châtelperronian and Protoaurignacian Core Technology Using Data Derived from 3D Models

This study uses data extracted from 3D models to compare blade cores from the Châtelperronian and Protoaurignacian stone tool industries. These technocomplexes are at the center of the debate surrounding the interactions between Neanderthals and anatomically modern humans approximately 45 to 40,000 years ago. We created 3D models of lithic cores from the sites of Roc de Combe and Les Cottes using a standardized photogrammetry protocol. We then used data derived from these 3D models to make quantitative comparisons of artifact attributes that have previously been argued to distinguish the two stone tool industries in question. These attributes include the angle between the platform and flaking surfaces, the shape of core cross sections, and the angle between core axes. The conception of this study was not to privilege the use of new technological and statistical approaches over more traditional or qualitative forms of lithic analysis. Rather, our aim was to experiment with using digital tool to develop nuanced, reproducible ways to describe variability in lithic artifacts. Our results support the hypothesis that there is a difference in the angle between core surfaces between these two industries. Our analysis also indicates a difference in the angle between core axes, although we are more cautious in interpreting these results. An elliptical Fourier analysis of core cross section shape was inconclusive. We discuss what archaeological and methodological factors may have contributed to our results, and the roles of both qualitative and quantitative observations in archaeological research. 3D artifact models generated for this study are included as supplemental data and are available for use by other researchers.

Biological Characteristics of Dendrochirus zebra (Cuvier, 1829) (Scorpaeniformes: Scorpaenidae) from Nha Trang Bay, South China Sea

The biological characteristics of the zebra turkeyfish Dendrochirus zebra (Cuvier, 1829) from Nha Trang Bay, South China Sea, including the total length (TL) to body weight (W) relationship, body size at first sexual maturity, otolith growth, gonad structure, and ultrastructure of the envelopes of ovulated oocytes, were studied. The TL–W relationship is different in the males and females, which is connected with their different growth rates. The largest fish are mostly males. The females differ from males in three from six otolith (sagitta) shape indices and in otolith contours described based on elliptic Fourier analysis. Mature spermatozoa are observed in spermiducts of males larger than 106 mm TL, and 50% of the females reach sexual maturity by 113 mm TL. A positive allometry was found between linear growth of the urinary bladder and body length of the males. The envelope of an ovulated oocyte consists of a three-layered zona radiatа 0.6–0.9 μm in width and a weakly expressed chorion approximately 0.2 μm in width. The features of D. zebra biology are discussed based on the published data for other representatives of the suborder Scorpaenoidei and subfamily Pteroinae.

The Application of Elliptic Fourier Analysis in Understanding Biface Shape and Symmetry Through the British Acheulean

Acheulean biface shape and symmetry have fuelled many discussions on past hominin behaviour in regards to the ‘meaning’ of biface technology. However, few studies have attempted to quantify and investigate their diachronic relationship using a substantial dataset of Acheulean bifaces. Using the British archaeological record as a case study, we first perform elliptic Fourier analysis on biface outlines to quantify and better understand the relationship between biface shape and individual interglacial periods. Using the extracted Fourier coefficients, we then detail the nature of symmetry throughout this period, before investigating both shape and symmetry in parallel. The importance of size (through biface length) as a factor in biface shape and symmetry is also considered. Results highlight high levels of symmetry from Marine Isotope Stage (MIS) 13, followed by increasing asymmetry through the British Acheulean. Other observations include a general shift to ‘pointed’ forms during MIS 9 and 7 and the importance of size in high biface symmetry levels. This article concludes by discussing the potential importance of secondary deposition and palimpsest sites in skewing the observed relationships throughout the Palaeolithic.

Application of The Chain Code and Fourier Analysis Techniques for The Investigation of Wrinkles and Distortions on Early Flames

The study of flame commencement and growth in SI engine has attracted the attention of many researchers due to its strong dependence to the in-cylinder flow and its capability to influence flame propagation characteristics in SI engines. Optical visualisation has been one of the prominent techniques utilized in this study of the early flame properties. This work shows the application of Elliptic Fourier analysis (EFA) and image processing tools for the investigation of the early flame details from its shape features. An endoscopic ICCD camera was used to capture the flame images, at an interval of 2° CA starting from ignition onset for a period of 30° CAs (about 3 ms), from a CNG DI single cylinder SI engine operation in stratified and homogeneous charge conditions. The intake configuration was adjusted to acquire tumble or swirl induction, and engine speed was made to vary between 1500 and 2100 rpm. The sequences of collected images were processed to investigate wrinkles, distortion and growth rate of the early flame within the 3 ms combustion duration. Some tools of image processing, such as intensity enhancement, filtering, thresholding and boundary tracing, were applied. Once the flame boundary identified, it was chain coded, and elliptic Fourier function was utilised to characterise the contour. For this purpose, a computer programming code was proposed by the authors for automatic processing of the flame image data. The application of the elliptic Fourier analysis was found useful in the investigation of the early flame characteristics from its shape features; led to the portrayal of wrinkles and distortion levels quantitatively in a simpler way.

Shape outline extraction software (DiaOutline) for elliptic Fourier analysis application in morphometric studies.

Premise of the StudyStudies of plant cell and organ outline using shape analysis for taxonomic and morphological research have increased in the past decade. However, there are a limited number of available modern, intuitive, and easy software tools to conduct this work.MethodsWe developed a tool for shape outline extraction using MATLAB accompanied with R scripts to perform elliptic Fourier analysis. To demonstrate the shape tool, we applied the software and scripts for genera and species shape determinations of diatom (single cell) species with x‐, y‐, and x‐ + y‐shape symmetries.ResultsUsing the shape analysis tool, we were able to identify and distinguish different diatom taxa based on forms representing size diminutions associated with population changes.DiscussionIndependent of symmetry, species were successfully distinguished using supervised and unsupervised analyses. We hope that these shape analysis tools will be used to add another metric to plant science studies.

Controls on Zero‐Order Basin Morphology

Zero‐order basins are common features of soil‐mantled landscapes, defined as unchanneled basins at the head of a drainage network. Their geometry and volume control how quickly sediment may reaccumulate after landslide evacuation and, more broadly, zero order basins govern the movement of water and sediment from hillslopes to the fluvial network. They also deliver water and sediment to the uppermost portions of the fluvial network. Despite this role as the moderator between hillslope and fluvial processes, little analysis on their morphology has been conducted at the landscape scale. We present a method to identify zero‐order basins in landscapes and subsequently quantify their geometric properties using elliptical Fourier analysis. We deploy this method across the Coweeta Hydrologic Laboratory, USA. Properties such as length, relief, width, and concavity follow distinct probability distributions, which may serve as a basis for testing predictions of future landscape evolution models. Surprisingly, in a landscape with an orographic precipitation gradient and large hillslope to channel relief, we observe no correlation between elevation or spatial location and basin geometry. However, we find that two physiographic units in Coweeta have distinct zero‐order basin morphologies. These are the steep, thin soiled, high‐elevation Nantahala Escarpment and the lower‐gradient, lower‐elevation, thick soiled remainder of the basin. Our results indicate that basin slope and area negatively covary, producing the distinct forms observed between the two physiographic units, which we suggest arise through competition between spatially variable soil creep and stochastic landsliding.

The Influence of Mimicry on Wing Shape Evolution in the ButterflyPapilio dardanus(Lepidoptera: Papilionidae)

Throughout its range in Africa, Papilio dardanus Brown, 1776 (Lepidoptera: Papilionidae) displays femalelimited mimicry of multiple model species, and the absence of hind wing tails is an important component of their mimetic convergence. Nonmimetic P. dardanus females have a narrow, disjunct distribution (Ethiopia, Madagascar, Comoros), and resemble males in color and by possessing hind wing tails. We used elliptical Fourier analysis to investigate whether mimetic P. dardanus female forms converged on the wing shape of their unpalatable models in the tribes Acraeini and Danaini (Lepidoptera: Nymphalidae). Models varied in forewing and hind wing shapes, and separated in shape space according to phylogenetic affinities. Forewing and hind wing shapes of mimics did not closely match those of models. Nonetheless, we found that mimetic P. dardanus female hind wings differed from conspecific males that had their tails photographically removed to allow standardized comparisons. Four nonmimetic Papilio Linnaeus, 1758 (Lepidoptera: Papilionidae) species did not show significant wing shape dimorphism between sexes, supporting the idea that in P. dardanus females, the evolution of mimicry led to changes in hind wing shape beyond the loss of tails.

Otolith shape and isotopic ratio analyses as a tool to study Spondyliosoma cantharus population structure

Knowledge on population units is critical for understanding population dynamics and providing an adequate fisheries management. Despite its vast distribution and commercial importance, there is no information on black seabream population structure. Different approaches to otolith analysis were used to elucidate on the stock structure of this species. Otoliths from seven areas along the eastern Atlantic: English Channel, Bay of Biscay, Galicia (Spain), Peniche (west coast of Portugal), Algarve (south coast of Portugal), the Canary Islands and Angola were compared through elliptical Fourier analysis and oxygen and carbon stable isotopes ratio. Otolith shape analysis data achieved 80% of correct assigned specimens in discriminant analysis while poor correct assignment levels were achieved with the stable isotopes ratio. However, the PERMANOVA conducted on δ13C and δ18O values revealed significant differences between all areas, with exception of the two Portuguese areas. The results of this study indicate that black seabream spends most of its life in the same area and that the studied populations should probably be considered as different stock units. However, some mixture was detected in the European region pointing for the usefulness of life history parameters and genetic studies to enlighten the stock structure of the species.

Phylogeny, ecology and deep time: 2D outline analysis of anuran skulls from the Early Cretaceous to the Recent

AbstractAnurans have a long fossil record, spanning from the Early Jurassic to the Recent. However, specimens are often severely flattened, limiting their inclusion in quantitative analyses of morphological evolution. We perform a two‐dimensional morphometric analysis of anuran skull outlines, incorporating 42 Early Cretaceous to Miocene species, as well as 93 extant species in 32 families. Outlines were traced in tpsDig2 and analysed with elliptical Fourier analysis. Fourier coefficients were used in MANOVAs, phylogenetic MANOVAs (as significant phylogenetic signal was found) and disparity analyses across multiple ecological and life history groupings. The Neotropical realm showed higher disparity than the Australian, Palaearctic and Oriental realms (p = 0.007, 0.013, 0.038, respectively) suggesting concordance of disparity and diversity. Developmental strategy had a weak effect on skull shape (R2 = 0.02, p = 0.039) and disparity was similar in metamorphosing and direct developing frogs. Ecological niche was a significant discriminator of skull shape (F = 1.43, p = 0.004) but not after phylogenetic correction. Evolutionary allometry had a small but significant influence on the cranial outlines of the combined extant and fossil dataset (R2 = 0.05, p = 0.004). Finally, morphospace occupation appears to have changed over time (F = 1.59, p = 5 × 10−10). However, as with ecological signal, this shift appears to be largely driven by phylogeny and was not significant after phylogenetic correction (R2 = 0.26, p = 0.22). This study thus suggests that frog skull evolution is shaped more by phylogenetic constraints than by ecology.

Phylogenetic, ecological and biomechanical constraints on larval form: A comparative morphological analysis of barnacle nauplii.

Barnacle naupliar larvae are differentiated from other zooplankton by their unique pair of frontal lateral horns, frontal filaments, and a pear-shaped cephalic shield. Their morphology impose constraints on their ecological functions and reflect their evolutionary history. To explore the potential functional basis underlying the similarities and differences in barnacle larval form, we conducted a meta-analysis on the shape of the barnacle nauplii’s cephalic shield and examined its relation to larval size, trophic mode, pelagic larval duration and habitat. Nauplii cephalic shield morphology of 102 species were quantified with normalized elliptic Fourier analysis. Most of the species were distributed around the center of the morphospace but a few extreme groups occupied the periphery: nauplii that were large and lecithotrophic. Subsequent principal component regression analyses showed that larval size was a good predictor of the first shape variations axis (aspect ratio). After allometry adjustment, nauplii from different trophic modes differentiated along the second axis of the major shape variations (relative frontal horn length). Habitat was a poor predictor of variations in naupliar body form, but it could be used to differentiate extreme morphology groups from other nauplii. Our result suggests that size-related biomechanical or developmental constraints and feeding requirements are important in shaping the evolution of the naupliar body form. Within the limitations of these functional constraints, habitat drives the divergence of extreme morphology groups from the majority of species. Our comparative morphometrics analysis demonstrated how variations in larval body form can be quantitatively linked to the functional needs that constrain or drive their diversity, and inform further empirical experiments on larval functional morphology.

Morphological predictor of remodelling of the descending thoracic aortic false lumen that remains patent after repair of acute type A dissection.

Some patients achieve complete recovery through false lumen remodelling in the descending aorta after surgery for acute type A aortic dissection. Our goal was to investigate the relationship between false lumen remodelling during later postoperative stages and quantitative analysis of the true lumen shape during the early postoperative stages. We examined 88 surgical patients between January 2007 and December 2016. Three points of the descending aorta were assessed from the 6th (T6), the 9th (T9) and the 11th (T11) vertebral levels. The shape of the true lumen was evaluated during the early postoperative stages, and false lumen remodelling 1 year after surgery was the end point. The parameters obtained by evaluating the shape of the true lumen comprised the first principal component analysis using elliptic Fourier analysis, the minor diameter ratio and the ratio of the area of the true lumen to that of the descending aorta, and the number of contact points on the true lumen wall during the early stages. Using univariate analysis, we detected significant differences in the first principal components, the minor diameter ratio, the area ratio and the number of contact points at each thoracic vertebral level (P < 0.05). The cut-off value of the minor diameter ratio was 0.55, and the area ratio was 0.48 as determined by analysis of the receiver operating characteristic. Multivariable logistic analysis indicated that the first principal component was the most significant predictor from the proximal to the middle descending aorta. Quantitative evaluation of shape of the true lumen in the early postoperative stages after surgery for acute type A dissection can serve as a viable predictor for false lumen remodelling in later stages. Furthermore, the first principal component could serve as a more astute predictor than other quantitative parameters according to multivariate analysis.

Elliptic fourier analysis of leaf shape variation of mangroves found in Camiguin Island, Philippines

Elliptic fourier analysis of leaf shape variation of mangroves found in Camiguin Island, Philippines

Leaflet shape in the endemic South American Oxalis sect. Alpinae: An integrative approach using molecular phylogenetics and geometric morphometrics

Oxalis section Alpinae grows along the Andes, from Ecuador to the austral part of the South American continent. Across the section, leaves are always trifoliolate, but leaflets exhibit wide diversity in shape and size and have often been used as a diagnostic character. This study provides a comprehensive morphometric and phylogenetic framework of Oxalis sect. Alpinae. Thus, the shapes of 312 leaflets representing 14 species of O. sect. Alpinae are examined and elliptic Fourier analysis is used, which is a morphometric approach for the comparison of outlines in order to recognize patterns in shape evolution and to assess if the leaflets are an accurate diagnostic character at the species level. Moreover, a new molecular phylogenetic reconstruction is provided, and it is compared with the morphological space. The leaflet shape diversity cannot be fully explained by phylogenetic relations among species. However, different patterns of shape evolution can be distinguished, and there might be a spectrum from evolutionary lability to the conservatism of shape.

Quantitative analysis of suture lines in Carboniferous ammonoids

Abstract. Two morphometric methods are applied and compared for the analysis of suture lines in Early Carboniferous ammonoids of the superfamilies Pericycloidea, Girtyoceratoidea and Goniatitoidea. We analysed (1) classic metric data (proportions of the width and depths or heights of lobes and saddles) using multivariate statistic methods and (2) outline data of the external lobe and the ventrolateral saddle of the same ammonoid taxa using the elliptic Fourier analysis. Both methods lead to similar results and simultaneously demonstrate ontogenetic and phylogenetic trends of these ammonoids. Our results are consistent with three previously suggested evolutionary patterns: (1) a general decrease of the amplitude of lobes and saddles, (2) a proportional widening of the external lobe and (3) a heightening of the median saddle.

Differentiation of Freckled Goatfish Upeneus tragula Richardson, 1846 (Mullidae) in the Coastal Zone of Vietnam Based on Otolith Shape Analysis

Abstract—The shape of otoliths (sagittae) is analyzed in freckled goatfish Upeneus tragula from South Vietnam (Gulf of Thailand), southern Central Vietnam (Nha Phu and Nha Trang bays), and North Vietnam (Ha Long Bay). The shape indices, elliptic Fourier analysis, and canonical discriminant analysis are applied. In the Gulf of Thailand, the samples off Hon Thom (Thom Island, An Thoi Archipelago, to the south of Phu Quoc Island) including the red morph and black morph collected during two subsequent years almost do not differ in otolith shape. A comparison of the samples from four regions of the Gulf of Thailand (40 km to the west of Phu Quoc, pooled sample off Hon Thom, coastal zone to the east of Phu Quoc, and 19 km to the west of Ha Tien) shows a discrimination of the stocks from the west to northeast. Substantial differentiation between the samples from Central and North Vietnam is not registered. The results are discussed in relation to the features of life history of U. tragula and possible relative isolation of some stocks.

Crop-to-wild hybridization in cherries-Empirical evidence from Prunus fruticosa.

Crop cultivation can lead to genetic swamping of indigenous species and thus pose a serious threat for biodiversity. The rare Eurasian tetraploid shrub Prunus fruticosa (ground cherry) is suspected of hybridizing with cultivated allochthonous tetraploid P. cerasus and autochthonous diploid P. avium. Three Prunus taxa (447 individuals of P. fruticosa, 43 of P. cerasus and 73 of P. avium) and their hybrids (198 individuals) were evaluated using analysis of absolute genome size/ploidy level and multivariate morphometrics. Flow cytometry revealed considerable differentiation in absolute genome size at the tetraploid level (average 2C of P. fruticosa = 1.30 pg, average 2C of P. cerasus = 1.42 pg, i.e., a 9.2% difference). The combination of methods used allowed us to ascertain the frequency of hybrids occurring under natural conditions in Central Europe. The morphological evaluation of leaves was based upon distance‐based morphometrics supplemented by elliptic Fourier analysis. The results provided substantial evidence for ongoing hybridization (hybrids occurred in 39.5% of P. fruticosa populations). We detected homoploid introgressive hybridization with alien P. cerasus at the tetraploid level. We also found previously overlooked but frequent triploid hybrids resulting from heteroploid hybridization with indigenous P. avium, which, however, probably represent only the F1 generation. Although both hybrids differ in ploidy, they cannot be distinguished using morphometrics. Hybrids are frequent and may endanger wild populations of genuine P. fruticosa via direct niche competition or, alternatively or in addition, via introgression at the homoploid level (i.e., genetic swamping). The cultivation of cherries thus substantially threatens the existence of genuine P. fruticosa.