Getting into Shape: An Empirical Comparison of Traditional Truss-Based Morphometric Methods with a Newer Geometric Method Applied to New World Cichlids

Body shape is a difficult, but important, trait to quantify. Researchers have traditionally used multivariate analysis of several linear measures ('trusses') across the body form to quantify shape. Newer geometric morphometric methods claim to better estimate shape because they analyze the geometry among the locations of all landmarks simultaneously rather than the linear distances between pairs of landmarks. We tested this claim by comparing the results of several traditional morphometric analyses against a newer geometric analysis involving thin-plate splines (TPS), all applied to a common data set of morphologically variable new world cichlids Amphilophus citrinellus and A. zaliosus. The TPS method yielded slightly stronger evidence of morphological differences among forms, although traditional methods also distinguished the two species. Perhaps our most important result was the idiosyncratic interpretation of shape variation among the traditional truss-based methods, whereas the generation of deformation grids using the TPS approach yielded clear and visually interpretable figures. Our results indicate that geometric morphometrics can be a more effective way to analyze and interpret body form, but also that traditional methods can be relied upon to provide statistical evidence of shape differences, although not necessarily accurate information about the nature of variation in shape.     

一类捕食-被捕食系统周期解的存在性

对于二维非自治捕食-被捕食系统,本文讨论了它的解的有界性,进而得到周期解和正周期解的存在性。     

Geometric morphometries and the analysis of higher taxa: a case study based on the metendosternite of the Scarabaeoidea (Coleoptera)

A geometric morphometric analysis of families belonging to the Scarabaeoidea, using landmarks from three two-dimensional views (frontal, dorsal and lateral) of an internally situated rigid structure, the metendosternite, was carried out. Procrustes distances matrices were obtained to produce phenograms from the three analyses. Relative warp analyses were also performed and the first two relative warps for the three data sets plotted against each other. The metendosternite is an internally situated anatomical structure that has largely been neglected in past studies. However, it proved to be useful in geometric morphometric studies, because it is rigid and landmarks can be easily identified. Geometric morphometries is shown to be a powerful tool to identify phenetic relationships between higher level taxa, and the metendosternite is a new structure available for beetle systematisists.     

A probabilistic approach to estimating species pools from large compositional matrices

Abstract. Species pools are increasingly recognized as important controls of local plant community structure and diversity. While existing approaches to estimate their content and size either rely on phytosociological expert knowledge or on simple response models across environmental gradients, the proposed application of phytosociological smoothing according to Beals exploits the full information of plant co‐occurrence patterns statistically. Where numerous representative compositional data are available, the new method yields robust estimates of the potential of sites to harbour plant species. To test the new method, a large phytosociological databank covering the forested regions of Oregon (US) was subsampled randomly and evenly across strata defined by geographic regions and elevation belts. The resulting matrix of species presence/absence in 874 plots was smoothed by calculating Beals' index of sociological favourability, which estimates the probability of encountering each species at each site from the actual plot composition and the pattern of species co‐occurrence in the matrix. In a second step, the resulting lists of sociologically probable species were intersected with complete species lists for each of 14 geographical subregions. Species pools were compared to observed species composition and richness. Species pool size exhibited much clearer spatial trends than plot richness and could be modelled much better as a function of climatic factors. In this framework the goal of modelling species pools is not to test a hypothesis, but to bridge the gap between manageable scales of empirical observation and the spatio‐temporal hierarchy of diversity patterns.     

Wing morphology and flight behavior of pelecaniform seabirds

The selective pressures associated with flight are significant factors in shaping the morphology of volant forms. Tropical seabirds are of particular interest because of their long foraging bouts, which can last hundreds of kilometers in search of unpredictable (spatially and temporally) resources. Here, we contrast wing loading (WL), aspect ratio (AR), and planform shape among five pelecaniform seabirds and correlate morphological diversity with known differences in flight strategies. Overall, WL and AR scaled with body mass. The Great Frigratebird had lower WL than that predicted, whereas the Red-tailed Tropicbird had higher WL than that predicted. The tropicbird also exhibited a lower AR than that predicted. Visualization of planform shape was accomplished by using Thin-plate spline relative warp analysis (TPS/RWA), and three major regions of variations were discovered: wing base, mid-wing, and distal wing/wing tip. As expected, the three boobies were more similar than either the tropicbird or the frigatebird. The tropicbird had a broader distal wing and more rounded wing tip, associated with its greater use of flapping flight. The frigatebird showed the greatest deviation in the distal wing and wing tip associated with the high maneuverability required for aerial pursuit and kleptoparasitism. By using TPS/RWA, important differences were detected in planform shape that would have otherwise gone unnoticed when using only WL and AR. These differences correlated strongly with parameters such as maneuverability, flapping, and soaring flight.     

Time-dependent ROC curves for censored survival data and a diagnostic marker

ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.     

一个具有扩散和时滞的捕食模型的持久性与周期解的存在性

对一类在斑块环境下具有Beddington型功能性反应和时滞现象的非自治捕食系统进行了研究,证明系统在适当的条件下是永久持续生存的;利用重合度理论,得到了一组保证该系统存在正周期解的充分条件．     

Comparison of parameters from rhythmometric models with multiple components on hybrid data

Population multiple components is a statistical tool useful for the analysis of time-dependent hybrid data. With a small number of parameters, it is possible to model and to predict the periodic behavior of a population. In this article, we propose two methods to compare among populations rhythmometric parameters obtained by multiple component analysis. The first is a parametric method based in the usual statistical techniques for comparison of mean vectors in multivariate normal populations. The method, through MANOVA analysis, allows comparison of the MESOR and amplitude-acrophase pair of each component among two or more populations. The second is a nonparametric method, based in bootstrap techniques, to compare parameters from two populations. This test allows one to compare the MESOR, the amplitude, and the acrophase of each fitted component, as well as the global amplitude, orthophase, and bathyphase estimated when all fitted components are harmonics of a fundamental period. The idea is to calculate a confidence interval for the difference of the parameters of interest. If this interval does not contain zero, it can be concluded that the parameters from the two models are different with high probability. An estimation of p-value for the corresponding test can also be calculated. Both methods are illustrated with an example, based on clinical data. The nonparametric test can also be applied to paired data, a special situation of great interest in practice. By the use of similar bootstrap techniques, we illustrate how to construct confidence intervals for any rhythmometric parameter estimated from population multiple components models, including the orthophase, bathyphase, and global amplitude. These tests for comparison of parameters among populations are a needed tool when modeling the nonsinusoidal rhythmic behavior of hybrid data by population multiple component analysis.     

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.     

Time‐Dependent Predictive Accuracy in the Presence of Competing Risks

Summary Competing risks arise naturally in time‐to‐event studies. In this article, we propose time‐dependent accuracy measures for a marker when we have censored survival times and competing risks. Time‐dependent versions of sensitivity or true positive (TP) fraction naturally correspond to consideration of either cumulative (or prevalent) cases that accrue over a fixed time period, or alternatively to incident cases that are observed among event‐free subjects at any select time. Time‐dependent (dynamic) specificity (1–false positive (FP)) can be based on the marker distribution among event‐free subjects. We extend these definitions to incorporate cause of failure for competing risks outcomes. The proposed estimation for cause‐specific cumulative TP/dynamic FP is based on the nearest neighbor estimation of bivariate distribution function of the marker and the event time. On the other hand, incident TP/dynamic FP can be estimated using a possibly nonproportional hazards Cox model for the cause‐specific hazards and riskset reweighting of the marker distribution. The proposed methods extend the time‐dependent predictive accuracy measures of Heagerty, Lumley, and Pepe (2000, Biometrics 56, 337–344) and Heagerty and Zheng (2005, Biometrics 61, 92–105).