A generalized framework for analyzing taxonomic, phylogenetic, and functional community structure based on presence-absence data

Community structure as summarized by presence–absence data is often evaluated via diversity measures by incorporating taxonomic, phylogenetic and functional information on the constituting species. Most commonly, various dissimilarity coefficients are used to express these aspects simultaneously such that the results are not comparable due to the lack of common conceptual basis behind index definitions. A new framework is needed which allows such comparisons, thus facilitating evaluation of the importance of the three sources of extra information in relation to conventional species-based representations. We define taxonomic, phylogenetic and functional beta diversity of species assemblages based on the generalized Jaccard dissimilarity index. This coefficient does not give equal weight to species, because traditional site dissimilarities are lowered by taking into account the taxonomic, phylogenetic or functional similarity of differential species in one site to the species in the other. These, together with the traditional, taxon- (species-) based beta diversity are decomposed into two additive fractions, one due to taxonomic, phylogenetic or functional excess and the other to replacement. In addition to numerical results, taxonomic, phylogenetic and functional community structure is visualized by 2D simplex or ternary plots. Redundancy with respect to taxon-based structure is expressed in terms of centroid distances between point clouds in these diagrams. The approach is illustrated by examples coming from vegetation surveys representing different ecological conditions. We found that beta diversity decreases in the following order: taxon-based, taxonomic (Linnaean), phylogenetic and functional. Therefore, we put forward the beta-redundancy hypothesis suggesting that this ordering may be most often the case in ecological communities, and discuss potential reasons and possible exceptions to this supposed rule. Whereas the pattern of change in diversity may be indicative of fundamental features of the particular community being studied, the effect of the choice of functional traits—a more or less subjective element of the framework—remains to be investigated

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction

A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN

Choosing Attribute Weights for Item Dissimilarity using Clikstream Data with an Application to a Product Catalog Map

In content- and knowledge-based recommender systems often a measure of (dis)similarity between items is used. Frequently, this measure is based on the attributes of the items. However, which attributes are important for the users of the system remains an important question to answer. In this paper, we present an approach to determine attribute weights in a dissimilarity measure using clickstream data of an e-commerce website. Counted is how many times products are sold and based on this a Poisson regression model is estimated. Estimates of this model are then used to determine the attribute weights in the dissimilarity measure. We show an application of this approach on a product catalog of MP3 players provided by Compare Group, owner of the Dutch price comparison site http://www.vergelijk.nl, and show how the dissimilarity measure can be used to improve 2D product catalog visualizations.dissimilarity measure;attribute weights;clickstream data;comparison

Analysis of a data matrix and a graph: Metagenomic data and the phylogenetic tree

In biological experiments researchers often have information in the form of a graph that supplements observed numerical data. Incorporating the knowledge contained in these graphs into an analysis of the numerical data is an important and nontrivial task. We look at the example of metagenomic data---data from a genomic survey of the abundance of different species of bacteria in a sample. Here, the graph of interest is a phylogenetic tree depicting the interspecies relationships among the bacteria species. We illustrate that analysis of the data in a nonstandard inner-product space effectively uses this additional graphical information and produces more meaningful results.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS402 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pattern-based phylogenetic distance estimation and tree reconstruction

We have developed an alignment-free method that calculates phylogenetic distances using a maximum likelihood approach for a model of sequence change on patterns that are discovered in unaligned sequences. To evaluate the phylogenetic accuracy of our method, and to conduct a comprehensive comparison of existing alignment-free methods (freely available as Python package decaf+py at http://www.bioinformatics.org.au), we have created a dataset of reference trees covering a wide range of phylogenetic distances. Amino acid sequences were evolved along the trees and input to the tested methods; from their calculated distances we infered trees whose topologies we compared to the reference trees. We find our pattern-based method statistically superior to all other tested alignment-free methods on this dataset. We also demonstrate the general advantage of alignment-free methods over an approach based on automated alignments when sequences violate the assumption of collinearity. Similarly, we compare methods on empirical data from an existing alignment benchmark set that we used to derive reference distances and trees. Our pattern-based approach yields distances that show a linear relationship to reference distances over a substantially longer range than other alignment-free methods. The pattern-based approach outperforms alignment-free methods and its phylogenetic accuracy is statistically indistinguishable from alignment-based distances.Comment: 21 pages, 3 figures, 2 table

DISTANCE: a framework for software measure construction.

In this paper we present a framework for software measurement that is specifically suited to satisfy the measurement needs of empirical software engineering research. The framework offers an approach to measurement that builds upon the easily imagined, detected and visualised concepts of similarity and dissimilarity between software entities. These concepts are used both to model the software attributes of interest and to define the corresponding software measures. Central to the framework is a process model that embeds constructive procedures for attribute modelling and measure construction into a goal-oriented approach to empirical software engineering studies. The underlying measurement theoretic principles of our approach ensure the construct validity of the resulting measures. The approach was tested on a popular suite of object-oriented design measures. We further show that our measure construction method compares favourably to related work.Software;