Three-dimensional geometric morphometrics of Arvicanthis: implications for systematics and taxonomy

Arvicanthis is an African murid, found throughout sub-Saharan Africa, Sudan and Egypt. Although in the past 10 years several studies have been carried out to assess its systematics, there is still a need for a general revision of the genus. In this study the morphometric relationships between 71 populations throughout the range were investigated. A three-dimensional geometric morphometric approach was used to assess differences in the size and shape of the skull. These were related to the different biogeographical domains characterizing the range of the genus and to molecular and karyotypic phylogenies. Results agree only in part with phylogeny, and show a close relationship with the environmental backgrounds of each species. It is therefore suggested that the adaptation of Arvicanthis to local environment has played an important role in the phenotypic evolution of the skull. This leads to problems in taxonomic definitions based on morphometrics, which should not be used without comparison with other independently derived characters such as the DNA and the karyotype.     

Methods for studying allometry in geometric morphometrics: a comparison of performance

Evolutionary Ecology - Allometry has been the focus of growing interest in studies using geometric morphometric methods to address a wide range of research questions at the interface of ecology and...     

Bias and error in estimates of mean shape in geometric morphometrics

Sampling experiments were performed to investigate mean square error and bias in estimates of mean shape produced by different geometric morphometric methods. The experiments use the isotropic error model, which assumes equal and independent variation at each landmark. The case of three landmarks in the plane (i.e., triangles) was emphasized because it could be investigated systematically and the results displayed on the printed page. The amount of error in the estimates was displayed as RMSE surfaces over the space of all possible configurations of three landmarks. Patterns of bias were shown as vector fields over this same space. Experiments were also performed using particular combinations of four or more landmarks in both two and three dimensions.It was found that the generalized Procrustes analysis method produced estimates with the least error and no pattern of bias. Averages of Bookstein shape coordinates performed well if the longest edge was used as the baseline. The method of moments (Stoyan, 1990, Model. Biomet. J. 32, 843) used in EDMA (Lele, 1993, Math. Geol. 25, 573) exhibits larger errors. When variation is not small, it also shows a pattern of bias for isosceles triangles with one side much shorter than the other two and for triangles whose vertices are approximately collinear causing them to resemble their own reflections. Similar problems were found for the log-distance method of Rao and Suryawanshi (1996, Proc. Nat. Acad. Sci. 95, 4121). These results and their implications for the application of different geometric morphometric methods are discussed.     

Correction to: Methods for studying allometry in geometric morphometrics: a comparison of performance

Evolutionary Ecology -     

Principles and methods of geometric morphometrics

The basic concepts, notions and methods of geometric morphometrics (GM) are considered. This approach implies multivariate analysis of landmark coordinates located following certain rules on the surface of a morphological object. The aim of GM is to reveal differences between morphological objects by their shapes as such, the "size factor" being excluded. The GM is based on the concept of Kendall's space (KS) defined as a hypersphere with points distributed on its surface. These points are the shapes defined as aligned landmark configurations. KS is a non-Euclidian space, its metrics called Procrustes is defined by landmark configuration of a reference shape relative to which other shapes are aligned and compared. The differences among shapes are measured as Procrustes distances between respective points. For the linear methods of multivariate statistics to be applied to comparison of shapes, the respective points are projected onto the tangent plane (tangent space), the tangent point being defined by the reference. There are two principal methods of shape comparisons in GM: the Procrustes superimposition (a version of the least squares analysis) and thin-plate spline analysis. In the first case, Procrustes residuals are the outcome shape variables which remain after isometric alignment of the shapes being compared. Their summation over all landmarks yields Procrustes distances among these shapes. The Procrustes distances can be used in multivariate analyses just as the Euclidian distances. In the second case, the shapes are fitted to the references by stretching/compressing and shearing until complete identity of their landmark configurations. Eigenvectors of resulting bending energy matrix are defined as new shape variables, principal warps which yield another shape space with the origin defined by the reference. Projections of the shapes being compared onto principal warps yield partial warps, and their covariance matrix decomposition into eigenvectors yields relative warps which are similar to principal components (in particular, they are mutually orthogonal). Both partial and relative warps can be used in many multivariate statistic analyses as quantitative shape variables. Results of thin-plate spline analysis can be represented graphically by transformation grid which displays type, amount and localization of the shape differences. Basis rules of sample composition and landmark positioning to be used in GM are considered. At present, rigid (with minimal degrees of freedom) 2D morphological objects are most suitable for GM applications. It is important to recognize three type of real landmarks, and additionally semi-landmarks and "virtual" landmarks. Some procedures of thin-plate spline analysis are considered exemplified by some study cases, as well as applications of some standard multivariate methods to GM results. They make it possible to evaluate correlation between different shapes, as well as between a shape and some non-shape variables (linear measurements etc); to evaluate the differences among organisms by shape of a morphological structure; to identify landmarks which most accounted for both correlation and differences between the shapes. An annotated list of most popular softwares for GM is provided.     

MorphoJ: an integrated software package for geometric morphometrics

Increasingly, data on shape are analysed in combination with molecular genetic or ecological information, so that tools for geometric morphometric analysis are required. Morphometric studies most often use the arrangements of morphological landmarks as the data source and extract shape information from them by Procrustes superimposition. The MorphoJ software combines this approach with a wide range of methods for shape analysis in different biological contexts. The program offers an integrated and user-friendly environment for standard multivariate analyses such as principal components, discriminant analysis and multivariate regression as well as specialized applications including phylogenetics, quantitative genetics and analyses of modularity in shape data. MorphoJ is written in Java and versions for the Windows, Macintosh and Unix/Linux platforms are freely available from http://www.flywings.org.uk/MorphoJ_page.htm.     

From floral induction to floral shape

The initial emphasis in molecular-genetic studies of flower development was on homeotic genes that control organ identity, which is rather invariant between different species. Studies in flower development during the past three years have dealt with more diverse aspects of flower development, including floral induction and floral shape. Genes identified in the respective pathways might hold clues to the diversity of modern angiosperms.     

几何形态测量法在生物形态学研究中的应用

形态分析是生物系统学及其多样性研究中很重要的一部分。随着统计学的发展,我们可以对非常复杂的数据进行分析,这在客观上导致了多变量形态测量的出现。在20世纪80年代,在数据收集和分析上产生了重要突破——标点和标点相对位置的几何信息的匹配,从而可以将多变量分析的标点集叠加到生物原始图上,它不仅仅是生成散点图,而是试图客观反映生物的形态性状。这项研究被称为几何形态测量法(geometricmorphometrics),Rohlf和Marcus(1993)称其为形态测量方法上的一次革命。文章简要介绍了该方法。     

Interspecific comparison of growth and shape within Diapterus (Gerreidae: Perciformes) using geometric morphometrics

Morphometric analyses can generate useful information to solve taxonomic problems by direct comparison of each species representative’s shape or by analyzing its growth patterns. In this study, growth patterns and shape variation of the four fish species belonging to the genus Diapterus (Gerreidae) were analyzed using geometric morphometrics. We examined 287 specimens, D. auratus (n = 65), D. aureolus (n = 76), D. brevirostris (n = 87) and D. rhombeus (n = 59). For the exploration of growth trajectories of each species, the standard length was used as a size measurement, and the Procrustes distance as a morphological variation measurement. We also compared averages of the morphological change direction within each species through a pairwise comparison between vector angles. These analyses were also used to select those fishes whose increase in size did not lead to a significant change in Procrustes distance. Once this subsample was selected, the body shapes of the four species were compared using Canonical variate Analysis and Multivariate Analysis of Variance. Diapterus aureolus showed the most different morphological trajectory and the most divergent vector within the genus. An average of 93% of correct classification was estimated from Mahalanobis distances. The Canonical Variate Analysis generated three statistically significant canonical variates (p < 0.001) and indicated that D. auratus, D. brevirostris, and D. rhombeus presented a more related shape between them than D. aureolus, as indicated in previous studies. In this context, we considered the shape and growth of D. aureolus with regard to its congeners can be an important element for suggesting a taxonomic rearrangement. However, our interpretation should be supported by phylogenetic analysis. Based in our study, we suggest that trajectories analyses can be directly used in morphometric comparisons to detect those specimens affected by allometry.     

中国近代人群上颌前臼齿釉质-齿质连接面形状的三维几何形态测量

牙齿的釉质-齿质连接面(EDJ或Enamel-dentine junction)是釉质表面(OES或Outer enamel surface)形态的发生基础,其形态特征在牙齿发育早期形成,与遗传因素密切相关。为探讨EDJ形状在近代人群中的变异特点,本文使用显微断层扫描技术(micro-CT或micro-computed tomography)扫描了100例采自华中地区近代农业人群的上颌前臼齿(P~3和P~4各50例),并复原了EDJ表面三维结构。采用基于30个标志点(landmark)和半标志点(semi-landmark)的三维几何形态测量量化了上颌前臼齿EDJ表面形状。结果显示,牙齿内部舌侧尖区域变异程度较颊侧尖大。在人群内部,上颌前臼齿的变异方式主要表现在1)颊舌尖相互靠近或远离造成的咬合面深浅的差别;2)颊舌尖齿质最高点(dentine horn)相对高度的差异;3)舌侧尖近远中方向尺寸的变化;4)P~3颊侧尖近中脊的内收与外扩造成的整个轮廓形状的对称性变化;5)P~4整个咬合面轮廓MD/BL比值的大小差别。基于以上发现,本文进一步探讨了上颌前臼齿EDJ形状在两性或不同时代标本之间是否存在差异。平均形状的比较发现男性上颌前臼齿的舌尖相对较宽,颊侧尖近中脊相对较低。但主成分分析(Principal component analysis)和置换检验(Permutation test)显示两性差异未达到显著水平。同样,从新石器时代以来的各样本组之间在EDJ形状上的差别也没有达到统计上的显著水平。这一结果提示中国近代人群上颌前臼齿EDJ表面形状的变异特点至少可以追溯到全新世早期(本文使用标本最早来自距今6000-7000年前的新石器时代阶段)。未来EDJ的三维几何形态测量可通过扩大标本数量进一步探讨不同性别、不同地区人群、不同演化阶段之间的差异。     

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.     

基于几何形态测量学的植物鉴定方法

物种鉴定是植物研究中的一个重要环节,尤其对近缘种的鉴定是个难点。野外调查和采样时通常使用直接观察形态特征的方法来鉴定物种,容易产生鉴定误差。本文以同域分布的两个近缘种槲树（Quercus dentata Thunb.）和槲栎（Q.aliena Blume）为研究对象,通过叶片形态研究,探讨几何形态测量学方法,并对该方法的植物物种鉴定能力进行总结。该方法除了具备操作简单和分析准确的优势外,还弥补了传统物种鉴定方法的不足,可显著提高植物物种的鉴定能力。     

Ecomorphological correlates of craniodental variation in bears and paleobiological implications for extinct taxa: an approach based on geometric morphometrics

Relative warp analyses of landmarks describing cranial and mandibular shape are used for investigating patterns of morphological variation among extant bears (Mammalia, Carnivora, Ursidae) indicative of diet and feeding behavior. These patterns are used for deriving inferences about the autecology of two extinct species previously assumed to have had different dietary preferences, the North American giant, short-faced bear Arctodus simus and the Eurasian cave bear Ursus spelaeus . Results reveal a set of shared craniodental traits among the herbivorous bears, including short and vaulted skulls with well-developed zygomatic arches, lateralized orbits and small canines, concave jaws with a highly positioned condyle, large moment arms for the temporalis and masseter muscles, and long cheek teeth. In contrast, those bears that consume animal resources have long skulls with small zygomatic arches, frontalized orbits and well-developed canines, and long jaws with a deep mandibular symphysis, low muscle leverages, a condyle situated at the level of the tooth row and reduced cheek teeth. The craniodental morphology of omnivorous bears is intermediate between those of faunivores and herbivores. This is also the case of the short-faced bear and the cave bear, which suggests that previous reconstructions of the feeding ecology of these extinct species (highly carnivorous for A. simus and herbivorous for U. spelaeus ) should be revised.     

Fused traditional and geometric morphometrics demonstrate pinniped whisker diversity

Vibrissae (whiskers) are important components of the mammalian tactile sensory system, and primarily function as detectors of vibrotactile information from the environment. Pinnipeds possess the largest vibrissae among mammals and their vibrissal hair shafts demonstrate a diversity of shapes. The vibrissae of most phocid seals exhibit a beaded morphology with repeating sequences of crests and troughs along their length. However, there are few detailed analyses of pinniped vibrissal morphology, and these are limited to a few species. Therefore, we comparatively characterized differences in vibrissal hair shaft morphologies among phocid species with a beaded profile, phocid species with a smooth profile, and otariids with a smooth profile using traditional and geometric morphometric methods. Traditional morphometric measurements (peak-to-peak distance, crest width, trough width and total length) were collected using digital photographs. Elliptic Fourier analysis (geometric morphometrics) was used to quantify the outlines of whole vibrissae. The traditional and geometric morphometric datasets were subsequently combined by mathematically scaling each to true rank, followed by a single eigendecomposition. Quadratic discriminant function analysis demonstrated that 79.3, 97.8 and 100% of individuals could be correctly classified to their species based on vibrissal shape variables in the traditional, geometric and combined morphometric analyses, respectively. Phocids with beaded vibrissae, phocids with smooth vibrissae, and otariids each occupied distinct morphospace in the geometric morphometric and combined data analyses. Otariids split into two groups in the geometric morphometric analysis and gray seals appeared intermediate between beaded- and smooth-whiskered species in the traditional and combined analyses. Vibrissal hair shafts modulate the transduction of environmental stimuli to the mechanoreceptors in the follicle-sinus complex (F-SC), which results in vibrotactile reception, but it is currently unclear how the diversity of shapes affects environmental signal modulation.     

Principal components analysis of distal humeral shape in Pliocene to recent African hominids: the contribution of geometric morphometrics

The shape of the distal humerus in Homo, Pan (P. paniscus and P. troglodytes), Gorilla, and six australopithecines is compared using a geometric approach (Procrustes superimposition of landmarks). Fourteen landmarks are defined on the humerus in a two-dimensional space. Principal components analysis (PCA) is performed on all superimposed coordinates. I have chosen to discuss the precise place of KNM-KP 271 variously assigned to Australopithecus anamensis, Homo sp., or Praeanthropus africanus, in comparison with a sample of australopithecines. AL 288-1, AL 137-48 (Hadar), STW 431 (Sterkfontein), and TM 1517 (Kromdraai) are commonly attributed to Australopithecus afarensis (the two former), Australopithecus africanus, and Paranthropus robustus, respectively, while the taxonomic place of KNM-ER 739 (Homo or Paranthropus?) is not yet clearly defined. The analysis does not emphasize a particular affinity between KNM-KP 271 and modern Homo, nor with A. afarensis, as previously demonstrated (Lague and Jungers [1996]