A simple method for visualization of influential landmarks when using euclidean distance matrix analysis

Euclidean distance matrix analysis (EDMA) differs from most other morphometric methods for the analysis of landmark coordinate data in that it is coordinate-system invariant. However, strict adherence to coordinate-system invariance (for both biological and statistical reasons) introduces some difficulty in using graphic aids for the analysis and interpretation of EDMA results. We present a simple and effective graphic method to help localize important differences in form, growth, or shape by identifying “influential” landmarks. Examples are presented using simulated data and real data involving both children with craniofacial dysmorphologies and sexual dimorphism in adult Macaca fascicularis. Am J Phys Anthropol 107:273–283, 1998. © 1998 Wiley-Liss, Inc.     

A Monte Carlo study of the inferential properties of three methods of shape comparison

Three inferential morphometric methods, Euclidean distance matrix analysis (EDMA), Bookstein's edge-matching method (EMM), and the Procrustes method, were applied to facial landmark data. A Monte Carlo simulation was conducted with three sample sizes, ranging from n = 10 to 50, to assess type I error rates and the power of the tests to detect group differences for two- and three-dimensional representations of forms. Type I error rates for EMM were at or below nominal levels in both two and three dimensions. Procrustes in 2D and EDMA in 2D and 3D produced inflated type I error rates in all conditions, but approached acceptable levels with moderate cell sizes. Procrustes maintained error rates below the nominal levels in 2D. The power of EMM was high compared with the other methods in both 2D and 3D, but, conflicting EMM decisions were provided depending on which pair (2D) or triad (3D) of landmarks were selected as reference points. EDMA and Procrustes were more powerful in 2D data than for 3D data. Interpretation of these results must take into account that the data used in this simulation were selected because they represent real data that might have been collected during a study or experiment. These data had characteristics which violated assumptions central to the methods here with unequal variances about landmarks, correlated errors, and correlated landmark locations; therefore these results may not generalize to all conditions, such as cases with no violations of assumptions. This simulation demonstrates, however, limitations of each procedure that should be considered when making inferences about shape comparisons. © 1996 Wiley-Liss, Inc.     

Sequence ordinations: a multivariate analysis approach to analysing large sequence data sets

Ordination is a powerful method for analysing complex data setsbut has been largely ignored in sequence analysis. This papershows how to use principal coordinates analysis to find low–dimensionalrepresentations of distance matrices derived from aligned setsof sequences. The method takes a matrix of Euclidean distancesbetween all pairs of sequence and finds a coordinate space wherethe distances are exactly preserved The main problem is to finda measure of distance between aligned sequences that is Euclidean.The simplest distance function is the square root of the percentagedifference (as measured by identities) between two sequences,where one ignores any positions in the alignment where thereis a gap in any sequence. If one does not ignore positions witha gap, the distances cannot be guaranteed to be Euclidean butthe deleterious effects are trivial. Two examples of using themethod are shown. A set of 226 aligned globins were analysedand the resulting ordination very successfully represents theknown patterns of relationship between the sequences. In theother example, a set of 610 aligned 5S rRNA sequences were analysed.Sequence ordinations complement phylogenetic analyses. Theyshould not be viewed as a complete alternative.     

Using digital images to reconstruct three‐dimensional biological forms: a new tool for morphological studies

We examined two image‐based methods, photogrammetry and stereo vision, used for reconstructing the three‐dimensional form of biological organisms under field conditions. We also developed and tested a third ‘hybrid’ method, which combines the other two techniques. We tested these three methodologies using two different cameras to obtain digital images of museum and field sampled specimens of giant tortoises. Both the precision and repeatability of the methods were assessed statistically on the same specimens by comparing geodesic and Euclidean measurements made on the digital models with linear measurements obtained with caliper and flexible tape. We found no substantial difference between the three methods in measuring the Euclidean distance between landmarks, but spatially denser models (stereo vision and ‘hybrid’) were more accurate for geodesic distances. The use of different digital cameras did not influence the results. Image‐based methods require only inexpensive instruments and appropriate software, and allow reconstruction of the three‐dimensional forms (including their curved surfaces) of organisms sampled in the field. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 95 , 425–436.     

Analysis of craniofacial growth in Crouzon syndrome using landmark data

Finite-element scaling analysis (FESA), generalized procrustes analysis (GPA), and Euclidean distance matrix analysis (EDMA) are applied in a two-dimensional study of craniofacial growth in normal children and those affected with Crouzon syndrome. Longitudinal data are used and growth is measured as change local to 10 craniofacial landmarks. Although details of the results vary among the methods, all 3 methods determine Crouzon growth to be different from normal. Nuances of the methods, especially the use of superimposition in GPA and lack of superimposition in 2 others are partly responsible for the varying results. Although Crouzon craniofacial morphology is often obvious at birth, this study demonstrates that there are general differences between normal postnatal growth patterns and those of the Crouzon individual. These patterns of malgrowth are in part responsible for the adult morphology of the Crouzon craniofacial complex.     

A Field Evaluation of Distance Measurement Error in Auditory Avian Point Count Surveys

ABSTRACT Detection distance is an important and common auxiliary variable measured during avian point count surveys. Distance data are used to determine the area sampled and to model the detection process using distance sampling theory. In densely forested habitats, visual detections of birds are rare, and most estimates of detection distance are based on auditory cues. Distance sampling theory assumes detection distances are measured accurately, but empirical validation of this assumption for auditory detections is lacking. We used a song playback system to simulate avian point counts with known distances in a forested habitat to determine the error structure of distance estimates based on auditory detections. We conducted field evaluations with 6 experienced observers both before and after distance estimation training. We conducted additional studies to determine the effect of height and speaker orientation (toward or away from observers) on distance estimation error. Distance estimation errors for all evaluations were substantial, although training reduced errors and bias in distance estimates by approximately 15%. Measurement errors showed a nonlinear relationship to distance. Our results suggest observers were not able to differentiate distances beyond 65 m. The height from which we played songs had no effect on distance estimation errors in this habitat. The orientation of the song source did have a large effect on distance estimation errors; observers generally doubled their distance estimates for songs played away from them compared with distance estimates for songs played directly toward them. These findings, which we based on realistic field conditions, suggest measures of uncertainty in distance estimates to auditory detections are substantially higher than assumed by most researchers. This means aural point count estimates of avian abundance based on distance methods deserve careful scrutiny because they are likely biased.     

Missing data in craniometrics: a simulation study

Craniometric measurements represent a useful tool for studying the differentiation of mammal populations. However, the fragility of skulls often leads to incomplete data matrices. Damaged specimens or incomplete sets of measurements are usually discarded prior to statistical analysis. We assessed the performance of two strategies that avoid elimination of observations: (1) pairwise deletion of missing cells, and (2) estimation of missing data using available measurements. The effect of these distinct approaches on the computation of inter-individual distances and population differentiation analyses were evaluated using craniometric measurements obtained from insular populations of deer micePeromyscus maniculatus (Wagner, 1845). In our simulations, Euclidean distances were greatly altered by pairwise deletion, whereas Gower’s distance coefficient corrected for missing data provided accurate results. Among the different estimation methods compared in this paper, the regression-based approximations weighted by coefficients of determination (r ²) outperformed the competing approaches. We further show that incomplete sets of craniometric measurements can be used to compute distance matrices, provided that an appropriate coefficient is selected. However, the application of estimation procedures provides a flexible approach that allows researchers to analyse incomplete data sets.     

Cranial growth in the squirrel monkey (Saimiri sciureus): a quantitative analysis using three dimensional coordinate data.

Improvements in data gathering technology have made it possible to quickly and accurately digitize large numbers of objects. The three dimensional coordinates of 44 homologous landmarks were obtained from a sample of 104 squirrel monkey (Saimiri sciureus) crania. After sorting by sex, the crania were assigned to one of four dental age groups. Two quantitative methods, Euclidean distance matrix analysis (EDMA) and finite element scaling analysis (FESA), were used to study craniofacial form change during growth within each sex. Form differences between the sexes at each developmental age were also examined. Both sexes show a small amount of cranial growth overall; however, there are areas of substantial local growth. These areas include the anterior neurocranium and basicranium, the basioccipital, and the anterior palate. Sexual dimorphism in the craniofacial complex is minimal. The most dimorphic regions are the orbitonasal portion of the lower face, the cranial base, and the palate.     

Assessing phylogenetic signal with measurement error: a comparison of mantel tests, blomberg et Al.'s k, and phylogenetic distograms

In macroevolutionary studies, different approaches are commonly used to measure phylogenetic signal-the tendency of related taxa to resemble one another-including the K statistic and the Mantel test. The latter was recently criticized for lacking statistical power. Using new simulations, we show that the power of the Mantel test depends on the metrics used to define trait distances and phylogenetic distances between species. Increasing power is obtained by lowering variance and increasing negative skewness in interspecific distances, as obtained using Euclidean trait distances and the complement of Abouheif proximity as a phylogenetic distance. We show realistic situations involving "measurement error" due to intraspecific variability where the Mantel test is more powerful to detect a phylogenetic signal than a permutation test based on the K statistic. We highlight limitations of the K-statistic (univariate measure) and show that its application should take into account measurement errors using repeated measures per species to avoid estimation bias. Finally, we argue that phylogenetic distograms representing Euclidean trait distance as a function of the square root of patristic distance provide an insightful representation of the phylogenetic signal that can be used to assess both the impact of measurement error and the departure from a Brownian evolution model.     

Application of latent semantic indexing to evaluate the similarity of sets of sequences without multiple alignments character-by-character

Most molecular analyses, including phylogenetic inference, are based on sequence alignments. We present an algorithm that estimates relatedness between biomolecules without the requirement of sequence alignment by using a protein frequency matrix that is reduced by singular value decomposition (SVD), in a latent semantic index information retrieval system. Two databases were used: one with 832 proteins from 13 mitochondrial gene families and another composed of 1000 sequences from nine types of proteins retrieved from GenBank. Firstly, 208 sequences from the first database and 200 from the second were randomly selected and compared using edit distance between each pair of sequences and respective cosines and Euclidean distances from SVD. Correlation between cosine and edit distance was -0.32 (P < 0.01) and between Euclidean distance and edit distance was +0.70 (P < 0.01). In order to check the ability of SVD in classifying sequences according to their categories, we used a sample of 202 sequences from the 13 gene families as queries (test set), and the other proteins (630) were used to generate the frequency matrix (training set). The classification algorithm applies a voting scheme based on the five most similar sequences with each query. With a 3-peptide frequency matrix, all 202 queries were correctly classified (accuracy = 100%). This algorithm is very attractive, because sequence alignments are neither generated nor required. In order to achieve results similar to those obtained with edit distance analysis, we recommend that Euclidean distance be used as a similarity measure for protein sequences in latent semantic indexing methods.     

The problem of assessing landmark error in geometric morphometrics: theory, methods, and modifications

Geometric morphometric methods rely on the accurate identification and quantification of landmarks on biological specimens. As in any empirical analysis, the assessment of inter- and intra-observer error is desirable. A review of methods currently being employed to assess measurement error in geometric morphometrics was conducted and three general approaches to the problem were identified. One such approach employs Generalized Procrustes Analysis to superimpose repeatedly digitized landmark configurations, thereby establishing whether repeat measures fall within an acceptable range of variation. The potential problem of this error assessment method (the "Pinocchio effect") is demonstrated and its effect on error studies discussed. An alternative approach involves employing Euclidean distances between the configuration centroid and repeat measures of a landmark to assess the relative repeatability of individual landmarks. This method is also potentially problematic as the inherent geometric properties of the specimen can result in misleading estimates of measurement error. A third approach involved the repeated digitization of landmarks with the specimen held in a constant orientation to assess individual landmark precision. This latter approach is an ideal method for assessing individual landmark precision, but is restrictive in that it does not allow for the incorporation of instrumentally defined or Type III landmarks. Hence, a revised method for assessing landmark error is proposed and described with the aid of worked empirical examples.     

landgenreport: a new r function to simplify landscape genetic analysis using resistance surface layers

We describe functions recently added to the r package popgenreport that can be used to perform a landscape genetic analysis (LGA) based on landscape resistance surfaces, which aims to detect the effect of landscape features on gene flow. These functions for the first time implement a LGA in a single framework. Although the approach has been shown to be a valuable tool to study gene flow in landscapes, it has not been widely used to date, despite the type of data being widely available. In part, this is likely due to the necessity to use several software packages to perform landscape genetic analyses. To apply LGA functions, two types of data sets are required: a data set with spatially referenced and genotyped individuals, and a resistance layer representing the effect of the landscape. The function outputs three pairwise distance matrices from these data: a genetic distance matrix, a cost distance matrix and a Euclidean distance matrix. Statistical tests are performed to test whether the cost matrix contributes to the understanding of the observed population structure. A full report on the analysis and outputs in the form of plots and tables of all intermediate steps of the LGA is produced. It is possible to customize the LGA to allow for different cost path approaches and measures of genetic distances. The package is written in the r language and is available through the Comprehensive r Archive. Comprehensive tutorials and information on how to install and use the package are provided at the authors’ website ( www.popgenreport.org ).     

Micro‐CT evaluation of murine fetal skeletal development yields greater morphometric precision over traditional clear‐staining methods

Traditional techniques for quantification of murine fetal skeletal development (gross measurements, clear‐staining) are severely limited by specimen processing, soft tissue presence, diffuse staining, and unclear landmarks between which to make measurements. Nondestructive microcomputed tomography (micro‐CT) imaging is a versatile, well‐documented tool traditionally used to generate high‐resolution 3‐D images and quantify microarchitectural parameters of trabecular bone. Although previously described as a tool for phenotyping fetal murine specimens, micro‐CT has not previously been used to directly measure individual fetal skeletal structures. Imaging murine fetal skeletons using micro‐CT enables the researcher to nondestructively quantify fetal skeletal development parameters including limb length, total bone volume, and average bone mineral density, as well as identify skeletal malformations. Micro‐CT measurement of fetal limb lengths correlates well with traditional clear‐staining methods (83.98% agreement), decreases variability in measurements (average standard errors: 6.28% for micro‐CT and 10.82% for clear‐staining), decreases data acquisition time by eliminating the need for tissue processing, and preserves the intact fixed fetus for further analysis. Use of the rigorous micro‐CT technique to generate 3‐D images for digital measurement enables isolation of skeletal structures based on degree of mineralization (local radiodensity), eliminating the complications of blurred stain boundaries and soft tissue inclusion that accompany clear‐staining and gross measurement techniques. Microcomputed tomography provides a facile, accurate, and nondestructive method for determining the developmental state of the fetal skeleton using not only limb lengths and identification of malformations, but total skeletal bone volume and average skeletal mineral density as well. Birth Defects Res (Part B) 2008. © 2008 Wiley‐Liss, Inc.     

Geostatistical modelling on stream networks: developing valid covariance matrices based on hydrologic distance and stream flow

1. Geostatistical models based on Euclidean distance fail to represent the spatial configuration, connectivity, and directionality of sites in a stream network and may not be ecologically relevant for many chemical, physical and biological studies of freshwater streams. Functional distance measures, such as symmetric and asymmetric hydrologic distance, more accurately represent the transfer of organisms, material and energy through stream networks. However, calculating the hydrologic distances for a large study area remains challenging and substituting hydrologic distance for Euclidean distance may violate geostatistical modelling assumptions. 2. We provide a review of geostatistical modelling assumptions and discuss the statistical and ecological consequences of substituting hydrologic distance measures for Euclidean distance. We also describe a new family of autocovariance models that we developed for stream networks, which are based on hydrologic distance measures. 3. We describe the geographical information system (GIS) methodology used to generate spatial data necessary for geostatistical modelling in stream networks. We also provide an example that illustrates the methodology used to create a valid covariance matrix based on asymmetric hydrologic distance and weighted by discharge volume, which can be incorporated into common geostatistical models. 4. The methodology and tools described supply ecologically meaningful and statistically valid geostatistical models for stream networks. They also provide stream ecologists with the opportunity to develop their own functional measures of distance and connectivity, which will improve geostatistical models developed for stream networks in the future. 5. The GIS tools presented here are being made available in order to facilitate the application of valid geostatistical modelling in freshwater ecology.     

On geodetic distance computations in spatial modeling

Statisticians analyzing spatial data often need to detect and model associations based upon distances on the Earth's surface. Accurate computation of distances are sought for exploratory and interpretation purposes, as well as for developing numerically stable estimation algorithms. When the data come from locations on the spherical Earth, application of Euclidean or planar metrics for computing distances is not straightforward. Yet, planar metrics are desirable because of their easier interpretability, easy availability in software packages, and well-established theoretical properties. While distance computations are indispensable in spatial modeling, their importance and impact upon statistical estimation and prediction have gone largely unaddressed. This article explores the different options in using planar metrics and investigates their impact upon spatial modeling.     

Determining the movements of the skeleton using well-configured markers

The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of thelandmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.     

Facial asymmetry: three-dimensional analysis using laser surface scanning

This study evaluates six different techniques with respect to their ability to quantitatively describe facial asymmetry in three dimensions. Three-dimensional facial images were acquired using a Cyberware 3030RGB laser surface scanner. Image processing was performed on a Silicon Graphics Indigo computer workstation. The following techniques for facial asymmetry analysis were developed: asymmetry in the location of anthropometric landmarks, Euclidean distance matrix analysis (EDMA), scalar measurement of the lower ciliary margin and palpebral fissure area, clearance vector mapping, and determination of the volume of asymmetry. Techniques were applied and validated in three anthropometric models: a perfectly symmetrical plastic head model and a plaster head model with and without a unilateral cheek augmentation. In each of the anthropometric test models, each analytical technique was validated by means of static anthropometric facial models and was evaluated for intraobserver and interobserver reliability. Asymmetries in the location of anthropometric landmarks can be accurately determined to within 2 mm in x, y, and z directions of the Cartesian space. EDMA is a useful technique in describing both size and shape changes of discrete areas of the face. Measurement of the lower ciliary margin and palpebral fissure area is reliable. Clearance vector mapping is especially useful in quantifying facial surface asymmetries in facial areas where anthropometric landmarks are scarce. Volume of asymmetry is potentially useful in those patients for whom the use of injections or implants of known volume may be helpful in correcting unilateral facial deficiencies.     

Estimation of gestational and skeletal age in Macaca mulatta.

Results of qualitative and quantitative studies of prenatal skeletal development in Macaca mulatta are presented. Longitudinal radiographic observations were carried out on 20 monkeys of known gestational age, beginning on 120 days of gestation until the neonatal stage of skeletal development. These studies were based on multiple uterotomies on each pregnant female. The technique described provides accurate data on prenatal bone ossification, and permits an accurate estimation of fetal age in pregnant rhesus monkeys with unknown conception dates.     

Integrated criteria to identify the best treatment in plant biotechnology experiments

Plant scientists usually record many indicators in their experiments. The common statistical management involves univariate analyses. Such analyses generally create a split picture of the effects of experimental treatments since each indicator is addressed independently. The Euclidean distance combined with the expert’s criteria seems to show potential as an integrating indicator. The Euclidean distance has been widely used in many scientific fields nevertheless, as far as we know, it has not been frequently employed in plant science experiments. To exemplify the use of the Euclidean distance in this field, we performed an experiment focused on the effects of gibberellic acid on protease excretion during pineapple micropropagation in temporary immersion bioreactors. Five gibberellic acid concentrations were compared: 0.0, 1.4, 2.8, 4.2 and 5.6 μM. Four dependent variables were recorded: increase in fresh shoot mass, protein concentration, proteolytic activity and specific activity in the culture media. The statistical protocol carried out integrated these four dependent variables to easily identify the best gibberellic acid treatment. Based on expert’s criteria the integral analysis provided by the Euclidean distance indicated that 4.2 μM gibberellic acid is the best treatment to produce proteases in the experimental conditions described here. This treatment showed the shortest (statistically significant) Euclidean distance to expert’s criteria (0.61).