Sample size and sampling error in geometric morphometric studies of size and shape

Geometric morphometric studies are increasingly becoming common in systematics and palaeontology. The samples in such studies are often small, due to the paucity of material available for analysis. However, very few studies have tried to assess the impact of sampling error on analytical results. Here, this issue is addressed empirically using repeated randomized selection experiments to build progressively smaller samples from an original dataset of ∼400 vervet monkey (Cercopithecus aethiops) skulls. Size and shape parameters (including mean size and shape, size and shape variances, angles of allometric trajectories) that are commonly used in geometric morphometric studies, are estimated first in the original sample and then in the random subsamples. Estimates are then compared to give an indication of what is the minimum desirable sample size for each parameter. Mean size, standard deviation of size and variance of shape are found to be fairly accurate even in relatively small samples. In contrast, mean shapes and angles between static allometric trajectories are strongly affected by sampling error. If confirmed in other groups, our findings may have substantial implications for studies of morphological variation in present and fossil species. By performing rarefaction analyses like those presented in our study, morphometricians can be easily provided with important clues on how a simple but crucial factor like sample size can alter results of their studies.     

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.     

The evolution of cranial form and function in theropod dinosaurs: insights from geometric morphometrics

Theropod dinosaurs, an iconic clade of fossil species including Tyrannosaurus and Velociraptor, developed a great diversity of body size, skull form and feeding habits over their 160+ million year evolutionary history. Here, we utilize geometric morphometrics to study broad patterns in theropod skull shape variation and compare the distribution of taxa in cranial morphospace (form) to both phylogeny and quantitative metrics of biting behaviour (function). We find that theropod skulls primarily differ in relative anteroposterior length and snout depth and to a lesser extent in orbit size and depth of the cheek region, and oviraptorosaurs deviate most strongly from the "typical" and ancestral theropod morphologies. Noncarnivorous taxa generally fall out in distinct regions of morphospace and exhibit greater overall disparity than carnivorous taxa, whereas large-bodied carnivores independently converge on the same region of morphospace. The distribution of taxa in morphospace is strongly correlated with phylogeny but only weakly correlated with functional biting behaviour. These results imply that phylogeny, not biting function, was the major determinant of theropod skull shape.     

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。     

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.     

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.     

A new interpretation of the bee fossil Melitta willardi Cockerell (Hymenoptera,Melittidae) based on geometric morphometrics of the wing

Although bees are one of the major lineages of pollinators and are today quite diverse, few well-preserved fossils are available from which to establish the tempo of their diversification/extinction since the Early Cretaceous. Here we present a reassessment of the taxonomic affinities of Melitta willardi Cockerell 1909, preserved as a compression fossil from the Florissant shales of Colorado, USA. Based on geometric morphometric wing shape analyses M. willardi cannot be confidently assigned to the genus Melitta Kirby (Anthophila, Melittidae). Instead, the species exhibits phenotypic affinity with the subfamily Andreninae (Anthophila, Andrenidae), but does not appear to belong to any of the known genera therein. Accordingly, we describe a new genus, Andrenopteryx gen. n., based on wing shape as well as additional morphological features and to accommodate M. willardi. The new combination Andrenopteryx willardi (Cockerell) is established.     

Geographic and gender shape differences in the carapace of Liocarcinus depurator (Brachyura: Portunidae) using geometric morphometrics and the influence of a digitizing method

The current work describes the use of geometric morphometrics in the study of the portunid crab Liocarcinus depurator carapace shape variation along the Mediterranean coast of Spain. As a first step, the differences in shape induced by digitizing the carapace with either a digital camera or a flat bed scanner were investigated. Carapace shape information inferred from the camera images proved different from that obtained from the scanner images. This difference was greater than any shape variation because of crab gender or sample location. Carapace shape was analysed using multiple analysis of covariance (with centroid size as a covariate) of the partial warps and uniform components indicating differences between genders and between sample location; however, significant three-way interaction implied that such differences were gender and location specific. Landmarks identifying carapace width, carapace length and posterior carapace width showed greatest variation; hence gender and location differences were further analysed through the interrelationships between these linear measures. Regression analysis of the relationship between posterior carapace width and the ratio of carapace width to carapace length indicated clear differences between locations but not between genders. Crabs from the Alborán Sea had proportionally wider posterior carapaces than those from Alicante or North Catalonia. This finding may represent the difference between a southern influx of an Atlantic population distinguishable from a more northerly Mediterranean one, which would be in agreement with the overall oceanographic surface circulation pattern in the western Mediterranean.     

The systematics of Australian Daphnia (Cladocera: Daphniidae). Multivariate morphometrics

Forty nine characters were measured in each of 76 male and 200 female Daphnia including specimens from all eleven taxa described from the genus in Australia, except D. jollyi. Separate multivariate analyses (cluster, principal components and discriminant) of males and females each revealed only five morphological groups in the genus corresponding to the species D. occidentalis, D. lumholtzi, D. cephalata, D. nivalis, and a conglomerate of all other taxa described from the D. carinata complex, D. carinata (sensu lato). Interpretation of the male results was straightforward, but that for females was not because of the occurrence of an environmentally induced seasonal change in morphology (cyclomorphosis) in females. Log transformations of the female data successfully isolated the effects of cyclomorphosis. The seasonal morphs formed two groups which were further differentiated into taxonomic groups.     

Anatomies and lifestyles,morphometrics and niche metrics: Tools for studying primate evolution

In recent years, comparative observations of primate anatomies have been extended using measurements and computer analyses: morphometrics. A question then follows. Can we extend field observations of animal lifestyles using measurement and computer analysis, using, in other words, a new «niche metrics», for comparison with the morphometrics of animal anatomies? This has been attempted (Oxnard, Crompton & Lieberman, 1990) by «measuring» 17 lifestyle variables (on locomotion, environment and diet) for 28 prosimian primate species. These data have been analysed by multivariate statistical methods entirely similar to those used in morphometrics. The results define groups of prosimian species that seem not to be related directly with taxonomy and evolution, but with functional adaptation to lifestyle. Comparisons between the morphometric and niche metric results reveal a degree of similarity of species grouping in each that is apparently related to adaptation and remarkably detailed. But further study of both the morphometric and niche metric results suggests that questions pertaining to evolution may also be asked. Thus, both morphometric investigations seeking clusterings of anatomical variables and niche metric studies seeking clustering of higher taxonomic groups of species produce results that seem to be of developmental and phylogenetic rather than directly adaptive import. Through the combination of these two approaches, it may eventually be possible to partition both evolutionary and adaptive components, even though, of course, there must always be overlap between them.     

Effect of different larval rearing temperatures on the productivity (Ro) and morphology of the malaria vector Anopheles superpictus Grassi (Diptera: Culicidae) using geometric morphometrics

Temperature affects both the biology and morphology of mosquito vectors. Geometric morphometrics is a useful new tool for capturing and analyzing differences in shape and size in many morphological parameters, including wings. We have used this technique for capturing the differences in the wings of the malaria vector Anopheles superpictus, using cohorts reared at six different constant temperatures (15°, 20°, 25°, 27°, 30°, and 35° C) and also searched for potential correlations with the life tables of the species. We studied wing shape in both male and female adults, using 22 landmarks on the wing in relation to ecological parameters, including the development rate. The ecological zero was calculated as 9.93° C and the thermal constant as 296.34 day‐degrees. The rearing temperature affects egg, larval, and pupal development and also the total time from egg to adult. As rearing temperatures increased, longevity decreased in both sexes. In An. superpictus, R_o value and productivity correlated with the statistically significant gradual deformations in the wing shape related to size in both sexes. These deformations directly linked to differences in immature rearing temperatures. Analysis using PCA and UPGMA phenograms showed that although wings of females became narrower dorsoventrally as the temperature increased, they became broader in males. Comparisons of the wing landmarks indicated the medial part of the wing was most affected by larval rearing temperatures, showing relatively more deformations. Algorithmic values of the life tables were determined in correlation with the results of geometric morphometrics. Comparisons of centroid sizes in the cohorts showed that overall wing size became smaller in both sexes in response to higher rearing temperatures.     

Geometric morphometrics of the scapula of South American caviomorph rodents (Rodentia: Hystricognathi): Form, function and phylogeny

The scapula of the ecomorphologically diverse South American caviomorph rodents was studied through geometric morphometric techniques, using landmarks and semilandmarks to capture the shape of this complex morphological structure. Representatives of 33 species from all caviomorph superfamilies, as well as Hystrix cristata for comparisons, were analyzed. Marked differences in scapular shape were found among the major caviomorph lineages analyzed, particularly in the shape and length of the scapular spine and development of the great scapular notch. Shape differences were not influenced by body size, and only partially influenced by locomotor mode. Thus, at this scale of analysis, phylogenetic history seems to be the strongest factor influencing scapular shape. The scapular shape of erethizontids, chinchillids and Cuniculus paca could represent the less specialized state with respect to the highly differentiated scapula of octodontoids and most cavioids. In this sense, the characteristic scapular morphologies of octodontoids and cavioids could reflect particular functional capabilities and constraints associated with the evolution of prevalent locomotor modes within each lineage.     

Testing evolutionary stasis and trends in first lower molar shape of extinct Italian populations of Terricola savii (Arvicolidae,Rodentia) by means of geometric morphometrics

Extinct populations of Terricola savii have been investigated in order to analyse evolutionary stasis and correlation of first lower molar shape with climatic proxies by means of geometric morphometrics. Evolutionary stasis, its recognition and explanation are central topics in evolutionary paleobiology. In this study, tooth shape variation of the arvicolid T. savii has been analysed through time. In addition to explicit multivariate tests of stasis based on landmark and semi‐landmark geometric morphometrics, first lower molar M₁ shape has been decomposed in orthogonal axes of variation and tested for correlation with climate changes. Multivariate tests were consistent with evolutionary stasis. Yet, according to univariate tests, the dominant dimension of shape variation shows a temporal trend well correlated with a climatic proxy, i.e. δ¹⁸O. The remaining variation does not show any trend. Adaptation to current climatic condition might occur even without affecting shape as a whole. Phenotypic plasticity of this species could be invoked to explain evolutionary stasis, as a long time pattern.     

Endpoint error in smoothing and differentiating raw kinematic data: An evaluation of four popular methods

‘Endpoint error’ describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's (1982, J. Biomechanics 15, 99–105) modification of the Pezzack et al. (1977, J. Biomechanics, 10, 377–382) raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack et al. (1977) data set. In fact, the quintic spline performed best with non-padded data (cumulative error=48.0 rad s⁻²). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error=226.6 rad s⁻²). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error=68.8 rad s⁻²) than when applied to analogous subsets padded by reflection (average cumulative error=86.1 rad s⁻²).     

Combining geometric morphometrics,molecular phylogeny,and micropaleontology to assess evolutionary patterns in Mallomonas (Synurophyceae: Heterokontophyta)

Synurophytes, also known as scaled chrysophytes, are ecologically important algae that produce an array of siliceous structures upon which their taxonomy is based. Despite occupying a key position within the photosynthetic heterokonts, the evolutionary history of synurophytes remains poorly constrained. Here, modern and Middle Eocene siliceous scales of the morphotaxon Mallomonas insignis are used as a model to investigate synurophyte evolutionary patterns. Structural details of scale morphology were examined comparatively with scanning electron microscopy and scored for geometric morphometric analyses to assess the stability of shape characters. Although consistent size differences exist (modern scales are larger than Eocene counterparts), the populations cannot be differentiated on the basis of shape or microstructural detail, implying considerable evolutionary stasis in scale morphology. A time‐calibrated relaxed molecular clock analysis using a three‐gene concatenated data set (27 strains) suggests that the M. insignis lineage predates the available fossil record, having diverged from closest congeneric taxa in the Cretaceous (≥94 Ma). However, the molecular analysis also implies that considerable genetic variability is present within several morphotaxa of Mallomonas, implying that substantial genetic variability has arisen despite the retention of uniform scale morphologies, and resulting in the widespread occurrence of cryptic taxa. Results from the synurophyte lineage are consistent with the notion of protracted ghost ranges (>10 Ma) implied by the molecular phylogenies of other algal groups, together pointing to the paucity of the fossil record of these organisms on these timescales.     

Geographic phenetic variation of two eastern-Mediterranean non-commensal mouse species, Mus macedonicus and M. cypriacus (Rodentia: Muridae) based on traditional and geometric approaches to morphometrics

We tested the hypothesis that skull shape within the genus Mus may vary with geographic location by assessing the extent and spatial distribution of phenotypic skull variation within and among two wild mouse species, M. macedonicus and M. cypriacus, using traditional and geometric morphometrics including a rather novel application of sliding semilandmarks. Shape was shown to be significantly correlated both with longitude and latitude in M. macedonicus, yet the correlation between morphometric and geographic distances was not significant, and morphometric differences between Asian and European populations were not higher than those within the particular continents. The phylogenetic signal was found to be stronger in dental characters than in cranial ones, however, overall concordance between the pattern of morphometric variation and the presumed history of M. macedonicus was rather weak. In both species, the dorsal and ventral sides of the skull were shown to covary in many aspects though there were also some differences between them, making the functional interpretation of these differences difficult. Discrimination between M. cypriacus and M. macedonicus as well as discrimination between two M. macedonicus subspecies was highly reliable using both traditional and geometric morphometric tools to analyze skull measurements.     

Floral and vegetative morphometrics of five Pleurothallis (Orchidaceae) species: correlation with taxonomy,phylogeny, genetic variability and pollination systems

Morphometric analyses of vegetative and floral characters were conducted in 21 populations of five Pleurothallis (Orchidaceae) species occurring in Brazilian 'campo rupestre' vegetation. A phylogenetic analysis of this species group was also carried out using nuclear ribosomal DNA internal transcribed spacers (ITS1 and ITS2). Results of the ordination and cluster analyses agree with species' delimitation revealed by taxonomic and allozyme studies. The groups formed in ordination analysis correspond to the pollinator groups determined in a previous pollination study. Relationships among the species in the cluster analysis using only vegetative characters are similar to those found in a previous allozyme study, but those indicated by cluster analysis using only floral characters differ. These results support the hypothesis that floral similarities are due to convergence driven by similar pollination mechanisms, and therefore floral traits may not be good indicators of phylogenetic relationships in this group. The results of the phylogenetic analysis support this conclusion to some extent. There is no correlation between genetic (allozyme) and morphological variability in the populations nor in the way this variability is distributed among conspecific populations. We describe a new subspecies of Pleurothallis ochreata based on differences in vegetative and chemical characters as well as geographic distribution. Absence of differentiation in floral characters, attraction of the same pollinator species, interfertility and genetic similarity support the argument for subspecific rather than specific status.