On comparing biological shapes: detection of influential landmarks.

For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form consists of size and shape. Several approaches for comparing biological forms using landmark data are available. If the two biological forms are demonstrated to be different, the next important issue is to localize the differences by identifying those areas which differ most between the two objects. In this paper we suggest a technique to detect influential landmarks, those which contribute most to the difference between forms. We study the effectiveness of the technique using three-dimensional simulated data sets and two examples. Results suggest that the technique is useful in the study of biological form and its variation.     

A New Method for Estimation of Resource Selection Probability Function

ABSTRACT Weighted distributions can be used to fit various forms of resource selection probability functions (RSPF) under the use-versus-available study design (Lele and Keim 2006). Although valid, the numerical maximization procedure used by Lele and Keim (2006) is unstable because of the inherent roughness of the Monte Carlo likelihood function. We used a combination of the methods of partial likelihood and data cloning to obtain maximum likelihood estimators of the RSPF in a numerically stable fashion. We demonstrated the methodology using simulated data sets generated under the log—log RSPF model and a reanalysis of telemetry data presented in Lele and Keim (2006) using the logistic RSPF model. The new method for estimation of RSPF can be used to understand differential selection of resources by animals, an essential component of studies in conservation biology, wildlife management, and applied ecology.     

A New Distribution-Free Approach to Constructing the Confidence Region for Multiple Parameters

Construction of confidence intervals or regions is an important part of statistical inference. The usual approach to constructing a confidence interval for a single parameter or confidence region for two or more parameters requires that the distribution of estimated parameters is known or can be assumed. In reality, the sampling distributions of parameters of biological importance are often unknown or difficult to be characterized. Distribution-free nonparametric resampling methods such as bootstrapping and permutation have been widely used to construct the confidence interval for a single parameter. There are also several parametric (ellipse) and nonparametric (convex hull peeling, bagplot and HPDregionplot) methods available for constructing confidence regions for two or more parameters. However, these methods have some key deficiencies including biased estimation of the true coverage rate, failure to account for the shape of the distribution inherent in the data and difficulty to implement. The purpose of this paper is to develop a new distribution-free method for constructing the confidence region that is based only on a few basic geometrical principles and accounts for the actual shape of the distribution inherent in the real data. The new method is implemented in an R package, distfree.cr/R. The statistical properties of the new method are evaluated and compared with those of the other methods through Monte Carlo simulation. Our new method outperforms the other methods regardless of whether the samples are taken from normal or non-normal bivariate distributions. In addition, the superiority of our method is consistent across different sample sizes and different levels of correlation between the two variables. We also analyze three biological data sets to illustrate the use of our new method for genomics and other biological researches.     

Variation in reaction norms: Statistical considerations and biological interpretation

Analysis of reaction norms, the functions by which the phenotype produced by a given genotype depends on the environment, is critical to studying many aspects of phenotypic evolution. Different techniques are available for quantifying different aspects of reaction norm variation. We examine what biological inferences can be drawn from some of the more readily applicable analyses for studying reaction norms. We adopt a strongly biologically motivated view, but draw on statistical theory to highlight strengths and drawbacks of different techniques. In particular, consideration of some formal statistical theory leads to revision of some recently, and forcefully, advocated opinions on reaction norm analysis. We clarify what simple analysis of the slope between mean phenotype in two environments can tell us about reaction norms, explore the conditions under which polynomial regression can provide robust inferences about reaction norm shape, and explore how different existing approaches may be used to draw inferences about variation in reaction norm shape. We show how mixed model‐based approaches can provide more robust inferences than more commonly used multistep statistical approaches, and derive new metrics of the relative importance of variation in reaction norm intercepts, slopes, and curvatures.     

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.     

Using meteorologic data to predict daily ragweed pollen levels

Pollen-related allergy is a common disease resulting in symptoms of hay fever and asthma. Control of symptoms depends (generally) on avoidance and pharmacological treatment. Both of these approaches could benefit from accurate predictions of pollen levels for future days. We have constructed a model that uses meteorological data to predict ragweed pollen levels based on air samples collected daily in Kalamazoo, MI from 1991 to 1994. Ragweed pollen counts were converted to pollen grains/m³ of air (24-h average). We used Poisson regression, which appropriately handles the heterogenous variance associated with pollen data. Using standard statistical model selection procedures, combined with biological considerations, we selected rainfall, wind speed, temperature, and the time measured from the start of the season as the most significant variables. Using our model, we propose a method that uses the weather forecast for the following day to predict the ragweed pollen level. This approach differs from most previous attempts because it uses Poisson regression and because this model needs to be fit iteratively each day. By updating the coefficients of the model based on the information to date, this method allows the fundamental shape of the pollen distribution curve to change from year to year. Application to the Kalamazoo data suggests that the method has good sensitivity and specificity for predicting high pollen days.     

Convergent evolution of floral shape tied to pollinator shifts in Iochrominae (Solanaceae)*

Flower form is one of many floral features thought to be shaped by pollinator‐mediated selection. Although the drivers of variation in flower shape have often been examined in microevolutionary studies, relatively few have tested the relationship between shape evolution and shifts in pollination system across clades. In the present study, we use morphometric approaches to quantify shape variation across the Andean clade Iochrominae and estimate the relationship between changes in shape and shifts in pollination system using phylogenetic comparative methods. We infer multiple shifts from an ancestral state of narrow, tubular flowers toward open, bowl‐shaped, or campanulate flowers as well as one reversal to the tubular form. These transitions in flower shape are significantly correlated with changes in pollination system. Specifically, tubular forms tend to be hummingbird‐pollinated and the open forms tend to be insect‐pollinated, a pattern consistent with experimental work as well as classical floral syndromes. Nonetheless, our study provides one of the few empirical demonstrations of the relationship between flower shape and pollination system at a macroevolutionary scale.     

Human dental arch shape evaluated by Euclidean-distance matrix analysis

Form differences between biological structures can be evaluated using several approaches. When landmark data are available, a recently proposed method (euclidean-distance matrix analysis) seems to be able to differentiate between size and shape differences. This method also localizes those areas which differ most between the two structures. We have applied it to analyze the sexual dimorphism in dental arch form in a sample of 50 men and 45 women. Subjects ranged in age between 20 and 27 years, and had sound dentitions. Fourteen landmarks, corresponding to the centers of gravity (centroids) of the occlusal surfaces of all permanent teeth (right second molar to left second molar), were individualized on the dental casts of subjects. All the possible linear distances between pairs of teeth were computed, thus creating four mean form matrices (one for each arch within sex). Gender differences were tested by using euclidean-distance matrix analysis. No significant differences were demonstrated in the shape of arches, while male arches proved to be slightly bigger than female arches. © 1993 Wiley-Liss, Inc.     

H-CORE: enabling genome-scale Bayesian analysis of biological systems without prior knowledge

The Bayesian network is a popular tool for describing relationships between data entities by representing probabilistic (in)dependencies with a directed acyclic graph (DAG) structure. Relationships have been inferred between biological entities using the Bayesian network model with high-throughput data from biological systems in diverse fields. However, the scalability of those approaches is seriously restricted because of the huge search space for finding an optimal DAG structure in the process of Bayesian network learning. For this reason, most previous approaches limit the number of target entities or use additional knowledge to restrict the search space. In this paper, we use the hierarchical clustering and order restriction (H-CORE) method for the learning of large Bayesian networks by clustering entities and restricting edge directions between those clusters, with the aim of overcoming the scalability problem and thus making it possible to perform genome-scale Bayesian network analysis without additional biological knowledge. We use simulations to show that H-CORE is much faster than the widely used sparse candidate method, whilst being of comparable quality. We have also applied H-CORE to retrieving gene-to-gene relationships in a biological system (The 'Rosetta compendium'). By evaluating learned information through literature mining, we demonstrate that H-CORE enables the genome-scale Bayesian analysis of biological systems without any prior knowledge.     

Comments on Bartolino et al. (2011): limits of cumulative relative frequency distribution curves for hotspot identification

The recent paper by Bartolino et al. (Popul Ecol 53:351–359, 2011) presents a new method to objectively select hotspots using cumulative relative frequency distribution (CRFD) curves. This method is presented as being independent from the selection of any threshold and, therefore, less arbitrary than traditional approaches. We argue that this method, albeit mathematically sound, is based on likewise arbitrary decisions regarding threshold selection. Specifically, the use of the CRFD curve approach requires the occurrence of two criteria for the method to be applied correctly: the selection of a 45° tangent to the curve, and the need to consider the highest relative value of the study parameter corresponding to a 45° slope tangent to the curve. Using two case studies (dealing with species richness and abundance of a particular species), we demonstrate that these two criteria are really unrelated to the underlying causes that shape the spatial pattern of the phenomena under study, but rather related to sampling design and spatial scale; hence, one could likewise use different but valid criteria. Consequently, the CRFD curve approach is based on the selection of a pre-defined threshold that has little, if any, ecological justification, and that heavily influences the final hotspot selection. Therefore, we conclude that the CRFD curve approach itself is not necessarily better and more objective than any of the global methods typically used for hotspot identification. Indeed, mathematical and/or statistical approaches should not be viewed as a panacea to solve conservation problems, but rather used in combination with biological, practical, economic and social considerations.     

Finite element scaling analysis of human craniofacial growth

The study of form change is central to traditional cephalometric research. Unfortunately, traditional cephalometric studies operate within systems of measurement that are based on registration and orientation. Measurements produced in registered systems are insufficient for the craniofacial biologist who is interested in locating morphological differences between forms. In this article we apply a registration-free method called finite element scaling analysis in a study of the form change occurring during growth of the normal human craniofacial complex. The method provides form change data that can be summarized at various morphological levels. Twenty normal male individuals are used to analyze the form change that occurs from age 4 to ages 5, 7, 8, 9, 10, 12, 13, and 15 years. The magnitude and direction of growth expressed as shape and size change specific to craniofacial landmarks are presented. Although exceptions occur, our analysis shows that localized size change is, on the average, greater than localized shape change. The relation between size and shape change during growth shows allometry (shape change increasing during growth along with size change) but at a lesser magnitude and slower rate. We conclude that although shape change occurs throughout ontogeny, the magnitude and rate of shape change in relation to size change diminishes as age increases. This analysis represents new insights into the understanding of human craniofacial growth at various levels of morphological integration.     

Nonlinear relationships and phylogenetically independent contrasts

The method of phylogenetically independent contrasts is commonly used for exploring cross-taxon relationships between traits. Here we show that this phylogenetic comparative method (PCM) can fail to detect correlated evolution when the underlying relationship between traits is nonlinear. Simulations indicate that statistical power can be dramatically reduced when independent contrasts analysis is used on nonlinear relationships. We also reanalyze a published data set and demonstrate that ignoring nonlinearity can affect biological inferences. We suggest that researchers consider the shape of the relationship between traits when using independent contrasts analysis. Alternative PCMs may be more appropriate if data cannot be transformed to meet assumptions of linearity.     

Shear-induced assembly of lambda-phage DNA

Recombinant DNA technology, which is based on the assembly of DNA fragments, forms the backbone of biological and biomedical research. Here we demonstrate that a uniform shear flow can induce and control the assembly of lambda-phage DNA molecules: increasing shear rates form integral DNA multimers of increasing molecular weight. Spontaneous assembly and grouping of end-blunted lambda-phage DNA molecules are negligible. It is suggested that shear-induced DNA assembly is caused by increasing the probability of contact between molecules and by stretching the molecules, which exposes the cohesive ends of the otherwise undeformed lambda-phage DNA molecules. We apply this principle to enhance the kinetics and extent of DNA concatenation in the presence of ligase. This novel approach to controlled DNA assembly could form the basis for improved approaches to gene-chip and recombinant DNA technologies and provide new insight into the rheology of associating polymers.     

Structural analysis of interphase X-chromatin based on statistical shape theory

The 3D folding structure formed by different genomic regions of a chromosome is still poorly understood. So far, only relatively simple geometric features, like distances and angles between different genomic regions, have been evaluated. This work is concerned with more complex geometric properties, i.e., the complete shape formed by genomic regions. Our work is based on statistical shape theory and we use different approaches to analyze the considered structures, e.g., shape uniformity test, 3D point-based registration, Fisher distribution, and 3D non-rigid image registration for shape normalization. We have applied these approaches to analyze 3D microscopy images of the X-chromosome where four consecutive genomic regions (BACs) have been simultaneously labeled by multicolor FISH. We have acquired two sets of four consecutive genomic regions with an overlap of three regions. From the experimental results, it turned out that for all data sets the complete structure is non-random. In addition, we found that the shapes of active and inactive X-chromosomal genomic regions are statistically independent. Moreover, we reconstructed the average 3D structure of chromatin in a small genomic region (below 4 Mb) based on five BACs resulting from two overlapping four BAC regions. We found that geometric normalization with respect to the nucleus shape based on non-rigid image registration has a significant influence on the location of the genomic regions.     

Network analysis of gene lists for finding reproducible prognostic breast cancer gene signatures

Many genome-scale studies in molecular biology deliver results in the form of a ranked list of gene names, accordingly to some scoring method. There is always the question how many top-ranked genes to consider for further analysis, for example, in order creating a diagnostic or predictive gene signature for a disease. This question is usually approached from a statistical point of view, without considering any biological properties of top-ranked genes or how they are related to each other functionally. Here we suggest a new method for selecting a number of genes in a ranked gene list such that this set forms the Optimally Functionally Enriched Network (OFTEN), formed by known physical interactions between genes or their products. The method allows associating a network with the gene list, providing easier interpretation of the results and classifying the genes or proteins accordingly to their position in the resulting network. We demonstrate the method on four breast cancer datasets and show that 1) the resulting gene signatures are more reproducible from one dataset to another compared to standard statistical procedures and 2) the overlap of these signatures has significant prognostic potential. The method is implemented in BiNoM Cytoscape plugin (http://binom.curie.fr).     

基于几何形态学的北二星蝽种内形态差异分析(半翅目： 蝽科)(英文)

【目的】北二星蝽Eysarcoris aeneus是一种广泛分布于古北区的重要农业害虫,可危害多种经济作物。其刺肩型和钝肩型前胸背板后侧角长度存在差异,暗示其种内变异的存在。【方法】基于几何形态学的多元回归分析(multivariate regression)、主成分分析(principal component analysis, PCA)、典型变量分析(canonical variate analysis, CVA)和判别函数分析(discriminant function analysis, DFA),对采集于中国19个地区的142头标本(98头北二星蝽标本和44头作为外群的广二星蝽E.ventralis标本)的前翅、后翅、头和小盾片4个性状进行分析比较,研究北二星蝽钝肩型和刺肩型之间的形态变异。【结果】对于所研究的4个性状来说,北二星蝽钝肩型和刺肩型标本间均未检测到异速生长的存在。主成分分析中,钝肩型和刺肩型的标本均有重叠,典型变量分析则显示它们之间存在显著差异(马氏距离和普氏距离的P值均小于0.01)。判别函数分析显示,依据这4个性状两型样本间的正确判别率在67%~89%之间。【结论】结果表明,前翅、后翅、头和小盾片都可以作为北二星蝽钝肩型和刺肩型之间形态变异的评价指标,小盾片特征具有最高水平的鉴别价值;对于所研究的这4个性状来说,北二星蝽钝肩型和刺肩型之间都表现出显著的形状差异,而它们的质心距离差异不显著,说明相对于体型大小差异分析,形状差异分析能更灵敏地揭示谱系间的变异。本研究表明几何形态学可以有效地描述北二星蝽的种内形态变异,为蝽类昆虫种内变异的研究奠定了基础。     

Comparing entire colour patterns as birds see them

Colour patterns and their visual backgrounds consist of a mosaic of patches that vary in colour, brightness, size, shape and position. Most studies of crypsis, aposematism, sexual selection, or other forms of signalling concentrate on one or two patch classes (colours), either ignoring the rest of the colour pattern, or analysing the patches separately. We summarize methods of comparing colour patterns making use of known properties of bird eyes. The methods are easily modifiable for other animal visual systems. We present a new statistical method to compare entire colour patterns rather than comparing multiple pairs of patches. Unlike previous methods, the new method detects differences in the relationships among the colours, not just differences in colours. We present tests of the method's ability to detect a variety of kinds of differences between natural colour patterns and provide suggestions for analysis.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 86 , 405–431.