Critical note on the application of the “two-third” spline

The “two-third spline” (2/3S) is a frequently applied method to detrend tree-ring series. It fits a spline with a 50% frequency cutoff at a frequency equal to two-thirds of each sample length in a dataset. It was introduced to ensure a minimum loss of low-frequency variance, which is resolvable during the detrending of ring-width series.In this paper I show potential problems that arise when rusing this method. The 2/3S runs counter the strengths of using a digital filter to detrend – i.e. one is giving up full control over the frequency-removing characteristics of the growth curve and each individual time series retains a different amount of low frequency. Thus, the 2/3S is less suitable for reconstructing climate or to compare environmental impacts on tree growth between groups – both of which comprise the majority of dendrochronological analyses – as it will likely introduce a temporal frequency bias. Within a long chronology it will result in decreasing power to resolve low frequencies towards present in a living-only trees setting, especially when the youngest segment lengths are 100 years and shorter, and more generally during the period where the chronology is constructed from samples with shorter segment lengths compared to the period with longer segment lengths. The frequency bias will also significantly impact regression slopes and correlation coefficients, possibly distorting analyses investigating multiple groups with different mean segment lengths. Highlighting these potential biases, I recommend the community to not use this method on an individual basis but rather to use a fixed spline stiffness for all samples based on the n% criterion (n = 67) of e.g. the mean segment length of the entire dataset.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11–90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7 mm (LCS); 0.29 mm (spline); 0.42 mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3 mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200 ms. Spline interpolation was superior for shorter durations.     

Geometric morphometrics as a tool for interpreting evolutionary transitions in the black fly wing (Diptera: Simuliidae)

A geometric morphometric analysis was conducted on wing‐vein landmarks on exemplar species of the family Simuliidae of the following genera: Parasimulium, Gymnopais, Twinnia, Helodon, Prosimulium, Greniera, Stegopterna, Tlalocomyia, Cnephia, Ectemnia, Metacnephia, Austrosimulium, and Simulium. Generalized least squares superimposition was performed on landmarks, followed by a principal component analysis on resulting Procrustes distances. Patterns of shape change along the principal component axes were visualized using the thin‐plate spline. The analysis revealed wing shape diversity through (1) the insertion points of the subcosta and R₁, resulting in the terminus of the costa exhibiting a trend towards a more apical position on the wing, and (2) the insertion point of the humeral cross vein, resulting in the anterior branch of the media exhibiting a trend toward a more basal position on the wing. Canonical variates analysis of Procrustes distances successfully assigned all exemplar species into their a priori taxonomic groupings. The diversity in wing shape reveals a trend towards decreased length of basal radial cell and increased costalization of anterior wing veins in the evolutionary transition from plesiomorphic prosimuliines to more derived simuliines. The functional significance of these evolutionary transitions is discussed. © 2013 The Linnean Society of London     

Estimating the accuracy of polymerase chain reaction-based tests using endpoint dilution

Polymerase chain reaction (PCR)-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive," yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity, when the target number is 0). However, estimating this "sensitivity curve" is problematic, since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle random variations in the number of target DNA molecules from the underlying test sensitivity. We develop parametric, nonparametric, and semiparametric (spline-based) models for the sensitivity curve. The methods are compared on a new test for M. genitalium.     

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.     

基于几何形态测量学的五种稻蝗前后翅的形态变化研究

【目的】定量分析5种常见稻蝗属昆虫前后翅的形态变化规律。【方法】运用几何形态测量学方法对5种稻蝗雄性前、后翅进行量化分析,并结合主成分分析法(Principal component analysis,PCA)和薄片样条(Thin-plate spline,TPS)分析法探讨稻蝗前后翅的大小和形态变异。【结果】5种稻蝗前、后翅的大小和形态差异都比较显著,前、后翅的相似关系和5种稻蝗的系统发育关系一致。前翅差异的部位主要在缘前脉域、前缘脉域和臀脉域;后翅的差异主要在亚前缘脉域、前缘脉域及轭脉域。【结论】稻蝗前、后翅形态变化的几何形态测量学分析结果与稻蝗系统发育关系一致,可用于稻蝗属种的分类。稻蝗前、后翅发生变化的部位是其飞行时的受力部位,这些部位可以作为稻蝗物种分类特征。     

A geometric morphometric analysis of the shape of the first upper molar in mice of the genus Mus (Muridae, Rodentia)

Phenotypic variation in the shape of the first upper molar among 595 mice, representing nine extant and three extinct taxa of the genus Mus , was studied with thin-plate spline analysis. The reliability of classification of individual specimens into known groups based on their molars varied from 75 to 100%, depending on group and method used. Including 13 sliding semilandmarks to the analysis improved the detection of different kinds of size and shape variation as well as visualization of shape differences between studied groups. Correlation between phylogenetic and morphometric distances suggested about 80% contribution of phylogenetic inertia to the molar shape variation; moreover, the importance of localized versus global shape changes was similar in the detection of phylogenetic signals. Finally, shape changes along individual evolutionary lineages were revealed, suggesting a few cases of reversals, convergence and/or retention of ancestral shape. The evolution of mouse molars has thus been driven by random effects of drift together with stabilizing selection and convergence.     

Computerized restoration of nonhomogeneous deformation of a fossil cranium based on bilateral symmetry

We developed a computerized method of correcting plastic deformation of a fossil skull, based on bilateral symmetry with respect to the midsagittal plane, and applied this method to reconstruction of a fossilized Proconsul heseloni cranium (KNM-RU-7290A). A three-dimensional (3D) model of the fossil was generated using consecutive cross-sectional images retrieved from computed tomography. 3D coordinates of anatomical landmarks that should be located on the midsagittal plane and pairs of landmarks that should be symmetrical with respect to this plane were acquired. These landmarks were then repositioned so that geometrical constraints were satisfied, while translated distances of landmarks were minimized. We adopted a thin-plate spline function to mathematically describe the 3D nonlinear volumetric transformation between acquired and repositioned landmarks. Using this function, the entire fossil shape was transformed, and the effect of reversing the deformation could be visualized. The results indicated that the proposed method was effective in eliminating nonhomogeneous deformation of the fossil skull. The antemortem appearance of the skull cannot be completely restored by this method alone, due to methodological limitations. However, the presented method has a role as an adjunct in complementing conventional restoration techniques on account of its objective nature.     

Relative index of inequality: definition, estimation, and inference

The relative index of inequality (RII) is a commonly used measure of the extent to which the occurrence of an outcome such as chronic illness or early death varies with socioeconomic status or some other background variable. The standard RII estimator applies only to linear variation in incidence rates. In this paper a general definition of the RII is introduced, alternative approaches to point estimation are considered, and a parametric bootstrap method is suggested for the construction of approximate confidence intervals. Estimation based on cubic splines fitted by maximum penalized likelihood is developed in some detail, and the proposed approach handles naturally the commonly needed adjustment for a 'standardizing' covariate such as age. Death rates in a large longitudinal study in England and Wales from 1996-2000 are analyzed in order to illustrate the various methods. A small simulation study explores the relative merits of different estimators. The approach based on cubic splines is found to reduce bias substantially, at the expense of some increase in variance, when variation in incidence rates is nonlinear.     

Varying coefficient model with unknown within-subject covariance for analysis of tumor growth curves

SUMMARY: In this article we develop a nonparametric estimation procedure for the varying coefficient model when the within-subject covariance is unknown. Extending the idea of iterative reweighted least squares to the functional setting, we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients. Smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood. The covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a Kullback-Leibler criterion. Empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors.