Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis

Indirect gradient analysis, or ordination, is primarily a method of exploratory data analysis. However, to support biological interpretations of resulting axes as vegetation gradients, or later confirmatory analyses and statistical tests, these axes need to be stable or at least robust into minor sampling effects. We develop a computer-intensive bootstrap (resampling) approach to estimate sampling effects on solutions from nonlinear ordination.We apply this approach to simulated data and to three forest data sets from North Carolina, USA and examine the resulting patterns of local and global instability in detrended correspondence analysis (DCA) solutions. We propose a bootstrap coefficient, scaled rank variance (SRV), to estimate remaining instability in species ranks after rotating axes to a common global orientation. In analysis of simulated data, bootstrap SRV was generally consistent with an equivalent estimate from repeated sampling. In an example using field data SRV, bootstrapped DCA showed good recovery of the order of common species along the first two axes, but poor recovery of later axes. We also suggest some criteria to use with the SRV to decide how many axes to retain and attempt to interpret.Abbreviations DCA= detrended correspondence analysis - SRV= scaled rank variance     

Instability of ordination results under changes in input data order: explanations and remedies

Abstract. Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order-dependent programming error in the non-linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred on axes 3 and 4, but one should not assume that published two-dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web ( http://www.helsinki.fi/jhoksane/ ). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site.     

High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach

Two modified DLT algorithms are presented that improve the accuracy of three-dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods. The improvement in the linear modified DLT (MDLT) algorithm is achieved by satisfying certain orthogonality conditions in the form of a non-linear constraint, thereby effectively eliminating a redundant DLT parameter. In the non-linear MDLT algorithm, the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized. The highest reconstruction accuracy of 0.733 mm rms mean error was obtained with the non-linear MDLT algorithm. This corresponds to a spatial resolution of about one part in 2860 or 0.035% overall accuracy. The accuracy obtainable with the linear MDLT was found to be slightly less and about 0.041% (0.833 mm rms mean error).     

Using species‐environmental amplitudes to predict pH values from vegetation

Question: Species optima or indicator values are frequently used to predict environmental variables from species composition. The present study focuses on the question whether predictions can be improved by using species environmental amplitudes instead of single values representing species optima. Location: Semi‐natural, deciduous hardwood forests of northwestern Germany. Methods: Based on a data set of 558 relevés, species responses (presence/absence) to pH were modelled with Huisman‐Olff‐Fresco (HOF) regression models. Species amplitudes were derived from response curves using three different methods. To predict the pH from vegetation, a maximum amplitude overlap method was applied. For comparison, predictions resulting from several established methods, i. e. maximum likelihood/present and absent species, maximum likelihood/present species only, mean weighted averages and mean Ellenberg indicator values were calculated. The predictive success (squared Pearson's r and root mean square error of prediction) was evaluated using an independent data set of 151 relevés. Results: Predictions based upon amplitudes defined by maximum Cohen's x probability threshold yield the best results of all amplitude definitions (R²= 0.75, RMSEP = 0.52). Provided there is an even distribution of the environmental variable, amplitudes defined by predicted probability exceeding prevalence are also suitable (R²= 0.76, RMSEP = 0.55). The prediction success is comparable to maximum likelihood (present species only) and – after rescaling – to mean weighted averages. Predicted values show a good linearity to observed pH values as opposed to a curvilinear relationship of mean Ellenberg indicator values. Transformation or rescaling of the predicted values is not required. Conclusions: Species amplitudes given by a minimum and maximum boundary for each species can be used to efficiently predict environmental variables from species composition. The predictive success is superior to mean Ellenberg indicator values and comparable to mean indicator values based on species weighted averages.     

Data manipulation and gradient length estimation in DCA ordination

Abstract. The effects of different kinds of data manipulation on gradient length estimation by non-linear rescal-ing (as in DCA ordination) are evaluated by considering the first axis inDCA ordinations of 11 field data sets from four investigations. Gradient length estimates are dependent on the range of the abundance scale; the more the scale favours the quantitative aspect (abundance) of the data over the qualitative aspect (presence), the longer the DCA axes. The gradient length estimate decreases when infrequent species are deleted. A new formula is proposed to replace the option for downweighting of rare species in DCA, as the option presently available has some undesirable properties. Some implications for interpretation of gradient length estimates by non-linear rescaling in general (and in DCA in particular) and for comparison of gradient length estimates between studies, are discussed. The potential of non-linear rescaling of gradients for estimation of β diversity is emphasized.     

Shape disparity of bovid (Mammalia,Artiodactyla) horn sheaths and horn cores allows discrimination by species in 3D geometric morphometric analyses

The bony cranial structures of even‐toed hoofed mammals are important for understanding ecology and behavior of ruminants. Horns, the cranial appendages of the family Bovidae, are covered in a layer of keratin that is often not preserved in the fossil record; however, this keratin sheath is intimately involved in the processes that influence horn shape evolution. To understand the relationship between these two components of horns, we quantified both core and sheath shape for four extant species using three‐dimensional geometric morphometric analyses in separate, core‐ and sheath‐specific morphospaces as well as a combined morphospace. We assessed correlations between the horn and sheath morphospaces using two‐block partial least squares regression, a Mantel test of pairwise distances between species, and Procrustes ANOVA. We measured disparity in the combined morphospace as Procrustes distances between mean shapes of cores and sheaths within and between species and as Procrustes variance. We also tested whether core and sheath shapes could be discriminated by taxon with a canonical variate analysis. Results show that horn core and sheath morphospaces are strongly correlated. The differences in shape between a species' core and sheath were statistically significant, but not as great as those between the cores and sheaths of different species when close relatives were not considered, and core and sheath Procrustes variances are not significantly different within species. Cores and sheath shapes were highly identifiable and were assigned to the correct clade 93% of the time in the canonical variate analysis. Based on these tests, horn cores are distinguishable in geometric morphometric analyses, extending the possibility of using geometric morphometrics to study the ecology and evolution of bovid horns to the fossil record.     

An Integrated Approach for Landmark-Based Resistant Shape Analysis in 3D

The study of shape changes in morphology has seen a significant renovation in the last 20 years, particularly as a consequence of the development of geometric morphometric methods based on Cartesian coordinates of points. In order to extract information about shape differences when Cartesian coordinates are used, it is necessary to establish a common reference frame or system for all specimens to be compared. Therefore, a central issue in coordinate-based methods is which criterion should be used to align these configurations of points, since shape differences highly depend on those alignments. This is usually accomplished by aligning the configurations in a way that the sum of squared distances between coordinates of homologous points (landmarks) is minimized: the least-squares superimposition method. However, it is widely recognized that this method has some limitations when shape differences are not homogeneous across landmarks. Here we present an integrated approach for the resistant shape comparison of 3D landmark sets. It includes a new ordinary resistant Procrustes superimposition and its corresponding generalized resistant Procrustes version. In addition, they are combined with existing resistant multivariate statistical techniques for depicting the results. We demonstrate, by using both simulated and real datasets, that resistant Procrustes better detects and measures localized shape variation whenever present in up to half but one of the landmarks. The resistant Procrustes results are highly concordant with a priori biological information, and might dramatically improve the quality of inferences on patterns of shape variation.     

Cooperative proton and calcium binding by sarcoplasmic reticulum ATPase.

The classic work on binding of calcium to CaATPase is analyzed by an objective non-linear least squares procedure of 74 data points over six pH values. Binding of two calciums to the basic form of the sites occurs with an equilibrium stability constant product of log K1K2 = 13.2. Owing to competition from protons, this value drops in acidic and neutral solutions, becoming, for example, 11.9 at pH 6.8. Binding of the two calciums is so strongly cooperative that its extent is difficult to estimate reliably; there is very little of the one calcium species. Two protons are also bound cooperatively to the calcium sites. In solutions of calcium free protein, at pH less than 7.6 the predominant species holds two protons at the calcium sites, while at greater pH the dominant species bears no protons; there is very little of the intermediate one proton species. The analysis also reveals the likely presence of a small, less than statistical, amount of a ternary complex bearing one calcium and one proton.     

Co-inertia analysis: an alternative method for studying species–environment relationships

• 1 Methods used for the study of species–environment relationships can be grouped into: (i) simple indirect and direct gradient analysis and multivariate direct gradient analysis (e.g. canonical correspondence analysis), all of which search for non-symmetric patterns between environmental data sets and species data sets; and (ii) analysis of juxtaposed tables, canonical correlation analysis, and intertable ordination, which examine species–environment relationships by considering each data set equally. Different analytical techniques are appropriate for fulfilling different objectives.
• 2 We propose a method, co-inertia analysis, that can synthesize various approaches encountered in the ecological literature. Co-inertia analysis is based on the mathematically coherent Euclidean model and can be universally reproduced (i.e. independently of software) because of its numerical stability. The method performs simultaneous analysis of two tables. The optimizing criterion in co-inertia analysis is that the resulting sample scores (environmental scores and faunistic scores) are the most covariant. Such analysis is particularly suitable for the simultaneous detection of faunistic and environmental features in studies of ecosystem structure.
• 3 The method was demonstrated using faunistic and environmental data from Friday (Freshwater Biology 18, 87-104, 1987). In this example, non-symmetric analyses is inappropriate because of the large number of variables (species and environmental variables) compared with the small number of samples.
• 4 Co-inertia analysis is an extension of the analysis of cross tables previously attempted by others. It serves as a general method to relate any kinds of data set, using any kinds of standard analysis (e.g. principal components analysis, correspondence analysis, multiple correspondence analysis) or between-class and within-class analyses.

     

Symmetry breaking in interspecific Drosophila hybrids is not due to developmental noise

Hybrids from crosses of different species have been reported to display decreased developmental stability when compared to their pure species, which is conventionally attributed to a breakdown of coadapted gene complexes. Drosophila subobscura and its close relative D. madeirensis were hybridized in the laboratory to test the hypothesis that genuine fluctuating asymmetry, measured as the within-individual variance between right and left wings that results from random perturbations in development, would significantly increase after interspecific hybridization. When sires of D. subobscura were mated to heterospecific females following a hybrid half-sib breeding design, F1 hybrid females showed a large bilateral asymmetry with a substantial proportion of individuals having an asymmetric index larger than 5% of total wing size. Such an anomaly, however, cannot be plainly explained by an increase of developmental instability in hybrids but is the result of some aberrant developmental processes. Our findings suggest that interspecific hybrids are as able as their parents to buffer developmental noise, notwithstanding the fact that their proper bilateral development can be harshly compromised. Together with the low correspondence between the co-variation structures of the interindividual genetic components and the within-individual ones from a Procrustes analysis, our data also suggest that the underlying processes that control (genetic) canalization and developmental stability do not share a common mechanism. We argue that the conventional account of decreased developmental stability in interspecific hybrids needs to be reappraised.     

Ordination of boreal heath-like vegetation with principal component analysis,correspondence analysis and multidimensional scaling

Four relatively homogeneous field data sets were analyzed, representing boreal, heath-like forest-floor and rock vegetation in Finland, corresponding to Finnish Calluna and Cladina site types. The methods used were principal component analysis (PCA) of covariance matrices, orthogonal correspondence analysis or reciprocal averaging (RA), detrended correspondence analysis (DCA), and linear and nonmetric multidimensional scaling (MDS). RA and DCA gave ordinations in which every species had nearly equal weight. MDS and PCA gave results determined mostly by a few dominant species. MDS and PCA ordinations were very similar to RA and DCA ones when the original data were standardized so that for each species the mean of positive occurrences was the same while quantitative differences within species were retained. RA and PCA were generally very good and reliable, providing that the impact of rare species and outlier relevés was removed in RA. DCA was slightly less reliable than RA. MDS was sensitive to uneven sampling patterns and was the least reliable method compared.     

Breast volume assessment based on 3D surface geometry: verification of the method using MR imaging

Differences in breast volume and contour are subjectively estimated by surgeons. 3D surface imaging using 3D scanners provides objective breast volume quantification, but precision and accuracy of the method requires verification. Breast volumes of five test individuals were assessed using a 3D surface scanner. Magnetic resonance imaging (MRI) reference volumes were obtained to verify and compare the 3D scan measurements. The anatomical thorax wall curvature was segmented using MRI data and compared to the interpolated curvature of the posterior breast volume delimitation of 3D scan data. MRI showed higher measurement precision, mean deviation (expressed as percentage of volume) of 1.10+/-0.34% compared to 1.63+/-0.53% for the 3D scanner. Mean MRI [right (left) breasts: 638 (629)+/-143 (138) cc] and 3D scan [right (left) breasts: 493 (497)+/-112 (116) cc] breast volumes significantly correlated [right (left) breasts: r=0.982 (0.977), p=0.003 (0.004)]. The posterior thorax wall of the 3D scan model showed high agreement with the MRI thorax wall curvature [mean positive (negative) deviation: 0.33 (-0.17)+/-0.37 cm]. High correspondence and correlation of 3D scan data with MRI-based verifications support 3D surface imaging as sufficiently precise and accurate for breast volume measurements.     

Computational Intelligence and Wavelet Transform Based Metamodel for Efficient Generation of Not-Yet Simulated Waveforms

The design and verification of complex electronic systems, especially the analog and mixed-signal ones, prove to be extremely time consuming tasks, if only circuit-level simulations are involved. A significant amount of time can be saved if a cost effective solution is used for the extensive analysis of the system, under all conceivable conditions. This paper proposes a data-driven method to build fast to evaluate, but also accurate metamodels capable of generating not-yet simulated waveforms as a function of different combinations of the parameters of the system. The necessary data are obtained by early-stage simulation of an electronic control system from the automotive industry. The metamodel development is based on three key elements: a wavelet transform for waveform characterization, a genetic algorithm optimization to detect the optimal wavelet transform and to identify the most relevant decomposition coefficients, and an artificial neuronal network to derive the relevant coefficients of the wavelet transform for any new parameters combination. The resulted metamodels for three different waveform families are fully reliable. They satisfy the required key points: high accuracy (a maximum mean squared error of 7.1x10^-5 for the unity-based normalized waveforms), efficiency (fully affordable computational effort for metamodel build-up: maximum 18 minutes on a general purpose computer), and simplicity (less than 1 second for running the metamodel, the user only provides the parameters combination). The metamodels can be used for very efficient generation of new waveforms, for any possible combination of dependent parameters, offering the possibility to explore the entire design space. A wide range of possibilities becomes achievable for the user, such as: all design corners can be analyzed, possible worst-case situations can be investigated, extreme values of waveforms can be discovered, sensitivity analyses can be performed (the influence of each parameter on the output waveform).     

Terrestrial and aquatic responses to climate change and human impact on the southeastern Tibetan Plateau during the past two centuries

Rapid population growth and economic development have led to increased anthropogenic pressures on the Tibetan Plateau, causing significant land cover changes with potentially severe ecological consequences. To assess whether or not these pressures are also affecting the remote montane‐boreal lakes on the SE Tibetan Plateau, fossil pollen and diatom data from two lakes were synthesized. The interplay of aquatic and terrestrial ecosystem response was explored in respect to climate variability and human activity over the past 200 years. Nonmetric multidimensional scaling and Procrustes rotation analysis were undertaken to determine whether pollen and diatom responses in each lake were similar and synchronous. Detrended canonical correspondence analysis was used to develop quantitative estimates of compositional species turnover. Despite instrumental evidence of significant climatic warming on the southeastern Plateau, the pollen and diatom records indicate very stable species composition throughout their profiles and show only very subtle responses to environmental changes over the past 200 years. The compositional species turnover (0.36–0.94 SD) is relatively low in comparison to the species reorganizations known from the periods during the mid‐ and early‐Holocene (0.64–1.61 SD) on the SE Plateau, and also in comparison to turnover rates of sediment records from climate‐sensitive regions in the circum arctic. Our results indicate that climatically induced ecological thresholds are not yet crossed, but that human activity has an increasing influence, particularly on the terrestrial ecosystem in our study area. Synergistic processes of post‐Little Ice Age warming, 20th century climate warming and extensive reforestations since the 19th century have initiated a change from natural oak‐pine forests to seminatural, likely less resilient pine‐oak forests. Further warming and anthropogenic disturbances would possibly exceed the ecological threshold of these ecosystems and lead to severe ecological consequences.     

Accuracy, stability, and corrective behavior in a visuomotor tracking task: a preliminary study

Visuomotor tracking tasks have been used to elucidate the underlying mechanisms that allow for the coordination of a movement to an environmental event. The main purpose of the present study was to examine the relationship between accuracy and stability of tracking performance and the amount of corrective movements that emerge for various coordination patterns in a unimanual visuomotor tracking task. Participants (N = 6) produced rhythmic elbow flexion-extension motions and were required to track an external sinusoidal signal at five different relative phases, 0°, 45°, 90°, 135°, and 180°. Differential accuracy and stability were found among the five tracking patterns with the 0° relative phase pattern being the most accurate and stable pattern. Corrective movements were correlated with changes in accuracy only for the 0° relative phase pattern, with more corrections emerging for less accurate performance. The amount of corrective movements decreased as the stability of tracking performance increased for the 0°, 45°, and 135° patterns. For the 90° and 180° tracking patterns, the amount of corrective movements was not correlated with pattern accuracy or pattern stability. The results demonstrate that corrective behaviors are an important motor process in maintaining the stability of stable perception-action coordination patterns, while offering little benefit for unstable perception-action patterns.     

Geometric morphometric analysis of mandibular shape diversity in Pan

The aim of this research is to determine whether geometric morphometric (GM) techniques can provide insights into how the shape of the mandibular corpus differs between bonobos and chimpanzees and to explore the potential implications of those results for our understanding of hominin evolution. We focused on this region of the mandible because of the relative frequency with which it has been recovered in the hominin fossil record. In addition, no previous study had explored in-depth three-dimensional (3D) mandibular corpus shape differences between adults of the two Pan species using geometric morphometrics. GM methods enable researchers to quantitatively analyze and visualize 3D shape changes in skeletal elements and provide an important compliment to traditional two-dimensional analyses.Eighteen mandibular landmarks were collected using a Microscribe 3DX portable digitizer. Specimen configurations were superimposed using Generalized Procrustes analysis and the projections of the fitted coordinates to tangent space were analyzed using multivariate statistics. The size-adjusted corpus shapes of Pan paniscus and Pan troglodytes could be assigned to species with approximately 93% accuracy and the Procrustes distance between the two species was significant. Analyses of the residuals from a multivariate linear regression of the data on centroid size suggested that much of the shape difference between the species is size-related. Chimpanzee subspecies and a small sample of Australopithecus specimens could be correctly identified to taxon, at best, only 75% of the time, although the Procrustes distances between these taxa were significant. The shape of the mandibular symphysis was identified as especially useful in differentiating Pan species from one another. This suggests that this region of the mandible has the potential to be informative for taxonomic analyses of fossil hominoids, including hominins. The results also have implications for phylogenetic hypotheses of hominoid evolution.     

Quantitative comparison of 2D and 3D monitoring dimensions in fish behavior analysis

To improve the accuracy and efficiency of fish behavior assessment, this paper focuses on quantitatively exploring the variations and relationships between different monitoring dimensions. A systematic comparison was conducted between 3D and 2D behavioral factors using an infrared tracing system, during both day and night. Significant differences in swimming distance were observed among the different monitoring methods, as determined by two-way ANOVA and Tukey's test. A correction was applied to account for the disparities observed in 2D swimming distance, ensuring accurate measurements. These findings present a cost-effective and efficient approach for obtaining precise 3D distance data. Additionally, a kinematic factor called the “number of U-turns” was proposed to provide a more intuitive characterization of directional changes in fish swimming. Significant differences were observed between 2D and 3D data, with higher percentages of false U-turn counts and missing U-turn counts compared to correct counts in the 2D view. These findings suggest that reducing the monitoring dimension may impact the accurate estimation of swimming motion, potentially resulting in inaccurate outcomes. Finally, the statistical analyses of the non-linear properties of fractal dimension revealed significant differences among the various monitoring methods. This conclusion has practical implications for biologists and physicists, enabling them to improve the accuracy of behavioral phenotyping for organisms exhibiting 3D motion.     

Species delimitation with abc and other coalescent-based methods: a test of accuracy with simulations and an empirical example with lizards of the liolaemus darwinii complex (squamata: liolaemidae)

Species delimitation is a major research focus in evolutionary biology because accurate species boundaries are a prerequisite for the study of speciation. New species delimitation methods (SDMs) can accommodate nonmonophyletic species and gene tree discordance as a result of incomplete lineage sorting via the coalescent model, but do not explicitly accommodate gene flow after divergence. Approximate Bayesian computation (ABC) can incorporate gene flow and estimate other relevant parameters of the speciation process while testing alternative species delimitation hypotheses. We evaluated the accuracy of BPP, SpeDeSTEM, and ABC for delimiting species using simulated data and applied these methods to empirical data from lizards of the Liolaemus darwinii complex. Overall, BPP was the most accurate, ABC showed an intermediate accuracy, and SpeDeSTEM was the least accurate under most simulated conditions. All three SDMs showed lower accuracy when speciation occurred despite gene flow, as found in previous studies, but ABC was the method with the smallest decrease in accuracy. All three SDMs consistently supported the distinctness of southern and northern lineages within L. darwinii. These SDMs based on genetic data should be complemented with novel SDMs based on morphological and ecological data to achieve truly integrative and statistically robust approaches to species discovery.