Aberrant crypt foci and semiparametric modeling of correlated binary data

Summary .   Motivated by the spatial modeling of aberrant crypt foci (ACF) in colon carcinogenesis, we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent Gaussian spatial process that accounts for short-range dependencies. The mean is modeled in a general way using regression splines. The mean function can be viewed as a fixed effect and is estimated with a penalty for regularization. With the latent process viewed as another random effect, the model becomes a generalized linear mixed model. In our motivating data set and other applications, the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation (REML), so pairwise likelihood, a special case of composite likelihood, is used instead. We develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications, including, but not limited to, the problem that motivated this work. The splines have penalty parameters that must converge to zero asymptotically: we derive theory for this along with a data-driven method for selecting the penalty parameter, a method that is shown in simulations to improve greatly upon standard devices, such as likelihood crossvalidation. Finally, we apply the methods to the data from our experiment ACF. We discover an unexpected location for peak formation of ACF.     

Enigmatic Diversity of the Maxillary Sinus in Macaques and Its Possible Role as a Spatial Compromise in Craniofacial Modifications

Understanding the evolutionary significance of morphological diversity is a major goal of evolutionary biology. Paranasal sinuses, which are pneumatized hollow spaces in the face, have attracted attention from researchers as one of the most intriguing traits that show unexpected variations. Macaques are one genus of primates that have accomplished adaptive radiation and therefore present an excellent opportunity to investigate the phenotypic diversification process. Using the large data set of computed tomography images of macaques (172 specimens from 17 species), we applied geometric morphometrics and multivariate analyses to quantitatively evaluate the maxillary sinus (one of the largest paranasal sinuses), the outer craniofacial shape, and nasal cavity. We then applied phylogenetic comparative methods to test their morphological interactions, phylogenetic, and ecogeographical significances. The results showed that the relative maxillary sinus size was significantly associated with the relative nasal cavity size and with the zygomaxillary surface shape. The relative nasal cavity size had ecogeographical correlations and high phylogenetic signal, whereas the zygomaxillary surface shapes were ecogeographically and phylogenetically irrelevant. The significant interactions with multiple surrounding traits that have experienced different evolutionary processes probably enable the maxillary sinus to show enigmatic diversity, which is independent of phylogeny and ecology. The pliable nature of the maxillary sinus, which is positioned between the nasal airways and the outer face, may play a role as a spatial compromise in craniofacial modifications.     

THE IMPORTANCE OF DIATOM CELL SIZE IN COMMUNITY ANALYSIS1

The large variation in size and shape in diatoms is shown by morphometric measurements of 515 benthic and pelagic diatom species from the Baltic Sea area. The largest mean cell dimension (mostly the apical axis) varied between 4.2 and 653 μm, cell surface area between 55 and 344,000 μm², and cell volume between 21 and 14.2 × 10⁶μm³. The shape‐related index, length to width ratio, was between 1.0 and 63.3 and the shape‐ and size‐related index, surface area to volume ratio, was between 0.02 and 3.13. Diatom community analysis by multivariate statistics is usually based on counts of a fixed number of diatom valves with species scores irrespective of cell size. This procedure underestimates the large species for two reasons. First, the importance of a species with higher cell volume is usually larger in a community. Second, larger species usually have lower abundances and their occurrence in the diatom counts is stochastic. This article shows that co‐occurring small and large diatom species can respond very differently to environmental constraints. Large epiphytic diatoms responded most to macroalgal host species and small epiphytic diatoms most to environmental conditions at the sampling site. Large epilithic diatoms responded strongly to salinity, whereas small epilithic diatoms did so less clearly. The conclusion is that different scale‐dependent responses are possible within one data set. The results from the test data also show that important ecological information from diatom data can be missed when the large species are neglected or underestimated.     

闽南三市绿地景观格局与地表温度的空间关系

深入探索绿地景观格局对热环境的影响机制,对于改善城市生态环境具有重要意义。基于厦门、漳州、泉州三市的Landsat遥感数据,应用景观生态学与空间自相关理论,探讨了绿地景观与地表温度的空间分布特征,并用双变量空间自相关与空间自回归模型分析两者之间的空间关系。结果表明:闽南三市绿地与地表温度均具有显著的空间自相关性;内陆的高海拔地区,绿地分布密集,地表温度较低,而城区、乡镇及大片的耕地,绿地分布较少,地表温度较高;漳州、泉州绿地景观格局对地表温度的影响更显著,厦门最弱;绿地的景观类型比例、最大斑块指数、聚集度指数、平均斑块面积与地表温度呈负相关,斑块密度与地表温度呈正相关;边缘密度、平均形状指数与地表温度的关系存在不确定性;空间滞后模型与空间误差模型能更好地解释绿地景观格局与地表温度的空间关系。     

Smoothing for spatiotemporal models and its application to modeling muskrat-mink interaction

For a set of spatially dependent dynamical models, we propose a method for estimating parameters that control temporal dynamics by spatial smoothing. The new approach is particularly relevant for analyzing spatially distributed panels of short time series. The asymptotic results show that spatial smoothing will improve the estimation in the presence of nugget effect, even when the sample size in each location is large. The proposed methodology is used to analyze the annual mink and muskrat data collected in a period of 25 years in 81 Canadian locations. Based on the proposed method, we are able to model the temporal dynamics which reflects the food chain interaction of the two species.     

A Landmark-Free Method for Three-Dimensional Shape Analysis

Background

The tools and techniques used in morphometrics have always aimed to transform the physical shape of an object into a concise set of numerical data for mathematical analysis. The advent of landmark-based morphometrics opened new avenues of research, but these methods are not without drawbacks. The time investment required of trained individuals to accurately landmark a data set is significant, and the reliance on readily-identifiable physical features can hamper research efforts. This is especially true of those investigating smooth or featureless surfaces.

Methods

In this paper, we present a new method to perform this transformation for data obtained from high-resolution scanning technology. This method uses surface scans, instead of landmarks, to calculate a shape difference metric analogous to Procrustes distance and perform superimposition. This is accomplished by building upon and extending the Iterative Closest Point algorithm. We also explore some new ways this data can be used; for example, we can calculate an averaged surface directly and visualize point-wise shape information over this surface. Finally, we briefly demonstrate this method on a set of primate skulls and compare the results of the new methodology with traditional geometric morphometric analysis.     

Manta Matcher: automated photographic identification of manta rays using keypoint features

For species which bear unique markings, such as natural spot patterning, field work has become increasingly more reliant on visual identification to recognize and catalog particular specimens or to monitor individuals within populations. While many species of interest exhibit characteristic markings that in principle allow individuals to be identified from photographs, scientists are often faced with the task of matching observations against databases of hundreds or thousands of images. We present a novel technique for automated identification of manta rays (Manta alfredi and Manta birostris) by means of a pattern‐matching algorithm applied to images of their ventral surface area. Automated visual identification has recently been developed for several species. However, such methods are typically limited to animals that can be photographed above water, or whose markings exhibit high contrast and appear in regular constellations. While manta rays bear natural patterning across their ventral surface, these patterns vary greatly in their size, shape, contrast, and spatial distribution. Our method is the first to have proven successful at achieving high matching accuracies on a large corpus of manta ray images taken under challenging underwater conditions. Our method is based on automated extraction and matching of keypoint features using the Scale‐Invariant Feature Transform (SIFT) algorithm. In order to cope with the considerable variation in quality of underwater photographs, we also incorporate preprocessing and image enhancement steps. Furthermore, we use a novel pattern‐matching approach that results in better accuracy than the standard SIFT approach and other alternative methods. We present quantitative evaluation results on a data set of 720 images of manta rays taken under widely different conditions. We describe a novel automated pattern representation and matching method that can be used to identify individual manta rays from photographs. The method has been incorporated into a website (mantamatcher.org) which will serve as a global resource for ecological and conservation research. It will allow researchers to manage and track sightings data to establish important life‐history parameters as well as determine other ecological data such as abundance, range, movement patterns, and structure of manta ray populations across the world.     

Phagocytosis Dynamics Depends on Target Shape

A complete understanding of phagocytosis requires insight into both its biochemical and physical aspects. One of the ways to explore the physical mechanism of phagocytosis is to probe whether and how the target properties (e.g., size, shape, surface states, stiffness, etc.) affect their uptake. Here we report an imaging-based method to explore phagocytosis kinetics, which is compatible with real-time imaging and can be used to validate existing reports using fixed and stained cells. We measure single-event engulfment time from a large number of phagocytosis events to compare how size and shape of targets determine their engulfment. The data shows an increase in the average engulfment time for increased target size, for spherical particles. The uptake time data on nonspherical particles confirms that target shape plays a more dominant role than target size for phagocytosis: Ellipsoids with an eccentricity of 0.954 and much smaller surface areas than spheres were taken up five times more slowly than spherical targets.     

The role of diet and temperature in shaping cranial diversification of South American human populations: an approach based on spatial regression and divergence rate tests

Aim Understanding the importance of ecological factors in the origin and maintenance of patterns of phenotypic variation among populations, in an explicit geographical context, is one of the main goals of human biology, ecology and evolutionary biology. Here we study the ecological factors responsible for craniofacial variation among human populations from South America. Location South America. Methods We studied a dataset of 718 males from 40 South American populations, coming from groups that inhabited different geographical and ecological regions. Cranial size and shape variation were studied using 30 cranial measurements. We first used spatial correlograms and interpolated maps to address spatial patterns. We then regressed the shape (principal component scores) and size variables against ecology (mean annual temperature and diet) using multiple and multivariate spatial regression. Finally, the expected magnitudes of shape and size divergence under the influence of genetic drift and mutations alone were evaluated using neutral expectation for the divergence rate. Results The spatial correlograms showed a cline affecting the entire South American distribution. Interpolated maps showed that size and allometric shape vary from south‐east to north‐west. Multiple and multivariate regression analyses suggested that diet has the largest and most significant effect on this pattern of size and allometric shape variation. Finally, the results of the divergence rate test suggested that random processes alone cannot account for the morphological divergence exhibited by cranial size and allometric shape scores among southernmost populations. Main conclusions Correlograms, spatial regression and divergence rate analyses showed that although local factors (neutral processes or local environmental conditions) are important to explain spatial interpopulation differentiation in cranial characteristics among these populations, there is significant correlation of cranial size and allometric shape variation with diet. Gene flow among human populations, or local environmental conditions, could explain spatial variation mainly at smaller spatial scales, whereas the large‐scale pattern of the South American dataset is mainly related to the high proportion of carbohydrates and low proportion of proteins consumed.     

Phagocytosis Dynamics Depends on Target Shape

A complete understanding of phagocytosis requires insight into both its biochemical and physical aspects. One of the ways to explore the physical mechanism of phagocytosis is to probe whether and how the target properties (e.g., size, shape, surface states, stiffness, etc.) affect their uptake. Here we report an imaging-based method to explore phagocytosis kinetics, which is compatible with real-time imaging and can be used to validate existing reports using fixed and stained cells. We measure single-event engulfment time from a large number of phagocytosis events to compare how size and shape of targets determine their engulfment. The data shows an increase in the average engulfment time for increased target size, for spherical particles. The uptake time data on nonspherical particles confirms that target shape plays a more dominant role than target size for phagocytosis: Ellipsoids with an eccentricity of 0.954 and much smaller surface areas than spheres were taken up five times more slowly than spherical targets.     

On the nature of cavities on protein surfaces: application to the identification of drug-binding sites

In this article we introduce a new method for the identification and the accurate characterization of protein surface cavities. The method is encoded in the program SCREEN (Surface Cavity REcognition and EvaluatioN). As a first test of the utility of our approach we used SCREEN to locate and analyze the surface cavities of a nonredundant set of 99 proteins cocrystallized with drugs. We find that this set of proteins has on average about 14 distinct cavities per protein. In all cases, a drug is bound at one (and sometimes more than one) of these cavities. Using cavity size alone as a criterion for predicting drug-binding sites yields a high balanced error rate of 15.7%, with only 71.7% coverage. Here we characterize each surface cavity by computing a comprehensive set of 408 physicochemical, structural, and geometric attributes. By applying modern machine learning techniques (Random Forests) we were able to develop a classifier that can identify drug-binding cavities with a balanced error rate of 7.2% and coverage of 88.9%. Only 18 of the 408 cavity attributes had a statistically significant role in the prediction. Of these 18 important attributes, almost all involved size and shape rather than physicochemical properties of the surface cavity. The implications of these results are discussed. A SCREEN Web server is available at http://interface.bioc.columbia.edu/screen.     

Quantifying leaf venation patterns: two-dimensional maps

The leaf vasculature plays crucial roles in transport and mechanical support. Understanding how vein patterns develop and what underlies pattern variation between species has many implications from both physiological and evolutionary perspectives. We developed a method for extracting spatial vein pattern data from leaf images, such as vein densities and also the sizes and shapes of the vein reticulations. We used this method to quantify leaf venation patterns of the first rosette leaf of Arabidopsis thaliana throughout a series of developmental stages. In particular, we characterized the size and shape of vein network areoles (loops), which enlarge and are split by new veins as a leaf develops. Pattern parameters varied in time and space. In particular, we observed a distal to proximal gradient in loop shape (length/width ratio) which varied over time, and a margin-to-center gradient in loop sizes. Quantitative analyses of vein patterns at the tissue level provide a two-way link between theoretical models of patterning and molecular experimental work to further explore patterning mechanisms during development. Such analyses could also be used to investigate the effect of environmental factors on vein patterns, or to compare venation patterns from different species for evolutionary studies. The method also provides a framework for gathering and overlaying two-dimensional maps of point, line and surface morphological data.     

Inferring the Nature of Allometry from Geometric Data

The form of an organism is the combination of its size and its shape. For a sample of forms, biologists wish to characterize both mean form and the variation in form. For geometric data, where form is characterized as the spatial locations of homologous points, the first step in analysis superimposes the forms, which requires an assumption about what measure of size is appropriate. Geometric morphometrics adopts centroid size as the natural measure of size, and assumes that variation around the mean form is isometric with size. These assumptions limit the interpretation of the resulting estimates of mean and variance in form. We illustrate these problems using allometric variation in shape. We show that superimposition based on subsets of relatively isometric points can yield superior inferences about the overall pattern of variation. We propose and demonstrate two superimposition techniques based on this idea. In subset superimposition, landmarks are progressively discarded from the data used for superimposition if they result in significant decreases in the variation among the remaining landmarks. In outline superimposition, regularly distributed pseudolandmarks on the continuous outline of a form are used as the basis for superimposition of the landmarks contained within it. Simulations show that these techniques can result in dramatic improvements in the accuracy of estimated variance-covariance matrices among landmarks when our assumptions are roughly satisfied. The pattern of variation inferred by means of our superimposition techniques can be quite different from that recovered from full generalized Procrustes superimposition. The pattern of shape variation in the wings of drosophilid flies appears to meet these assumptions. Adoption of superimposition procedures that incorporate biological assumptions about the nature of size and of the variation in shape can dramatically improve the ability to infer the pattern of variation in geometric morphometric data.     

西双版纳热带雨林林窗空间分布格局及其特征数与林窗下植物多样性的相关性

林窗作为森林群落中一种重要的干扰方式, 对林下物种构成有着重要的影响。开展林窗空间格局及其特征指数与林下植物多样性关系研究对于探讨林窗对林下生物多样性的影响有重要意义, 有助于进一步了解群落动态, 在物种多样性保护方面也具有指导作用。本研究在西双版纳热带雨林地区随机选取3块大小为1 ha的热带雨林为研究样地, 采用轻小型六旋翼无人机搭载Sony ILCE-A7r可见光传感器, 分别获取各个样地的高清数字影像, 结合数字表面高程模型以及各个样地的地形数据用以确定各样区的林窗分布格局, 并进一步提取出各林窗的景观格局指数。结合地面样方基础调查数据, 对各样地各林窗下植物多样性情况进行统计, 旨在分析热带雨林林窗空间分布格局以及林窗下植物多样性对各林窗空间格局特征的响应情况。研究表明, 西双版纳州热带雨林林窗呈大而分散的空间分布, 林窗空间格局特征指数如林窗形状复杂性指数、林窗面积都与林下植物多样性呈显著正相关关系。在面积小的林窗下, 较之林窗形状复杂性因子, 林窗面积大小对林下植物多样性影响更显著; 在面积达到一定程度后, 相对于面积因子, 林窗形状复杂性指数对林下植物多样性影响更显著, 各样地林窗皆趋于向各自所处样地顶极群落发展。     

Using a sub-pixel mapping model to improve the accuracy of landscape pattern indices

The assessment of landscape spatial patterns is a key issue in landscape management. Landscape pattern indices (LPIs) are tools appropriate for analyzing landscape spatial patterns. LPIs are often derived from raster land cover maps that are extracted from remotely sensed data through hard classification. However, pixel-based hard classification methods suffer from the mixed pixel problem (in which pixels contain more than one land cover class), making for inaccurate classification maps and LPIs. In addition, LPIs generated by hard classification methods are characterized by grain sizes (the sampling unit sizes) that limit the derived landscape pattern to a certain scale. Sub-pixel mapping (SPM) models can enable fine-scale estimation of the spatial patterns of land cover classes without requiring additional data; hence, this is an appropriate downscaling method for land cover mapping. The fraction images generated by soft classification estimate the area proportion of each land cover class within each pixel, and using these images as input enables SPM models to alleviate the mixed pixel problem. At the same time, by transforming fraction images into a finer-scaled hard classification map, SPM models can minimize the influence of grain size on LPIs calculation. In this research, simulated landscape thematic patterns that can provide different landscape spatial patterns, eight commonly used LPIs and a SPM model that maximizes the spatial dependence between neighbouring sub-pixels were applied to assess the efficiency of deriving LPIs from sub-pixel model maps. Results showed that the SPM model can more precisely characterize landscape patterns than hard classification methods can. Landscape fragmentation, class abundance, the uncertainty in SPM, and the spatial resolution of the remotely sensed data influenced LPIs derived from sub-pixel maps. The largest patch index, landscape division, and patch cohesion derived from remotely sensed data with different spatial resolutions through the SPM model were suitable for inter-comparison, whereas the patch density, mean patch area, edge density, landscape shape index, and area-weighted mean shape index derived from the sub-pixel maps were sensitive to the spatial resolution of the remotely sensed data.     

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics.     

A balanced view of scale in spatial statistical analysis

Concepts of spatial scale, such as extent, grain, resolution, range, footprint, support and cartographic ratio are not interchangeable. Because of the potential confusion among the definitions of these terms, we suggest that authors avoid the term "scale" and instead refer to specific concepts. In particular, we are careful to discriminate between observation scales, scales of ecological phenomena and scales used in spatial statistical analysis . When scales of observation or analysis change, that is, when the unit size, shape, spacing or extent are altered, statistical results are expected to change. The kinds of results that may change include estimates of the population mean and variance, the strength and character of spatial autocorrelation and spatial anisotropy, patch and gap sizes and multivariate relationships. The first three of these results (precision of the mean, variance and spatial autocorrelation) can sometimes be estimated using geostatistical support-effect models. We present four case studies of organism abundance and cover illustrating some of these changes and how conclusions about ecological phenomena (process and structure) may be affected. We identify the influence of observational scale on statistical results as a subset of what geographers call the Modifiable Area Unit Problem (MAUP). The way to avoid the MAUP is by careful construction of sampling design and analysis. We recommend a set of considerations for sampling design to allow useful tests for specific scales of a phenomenon under study. We further recommend that ecological studies completely report all components of observation and analysis scales to increase the possibility of cross-study comparisons.