A comprehensive, but simple-to-use software package for executing a range of standard numerical analysis and operations used in quantitative paleontology has been developed. The program, called PAST (PAleontological STatistics), runs on standard Windows computers and is available free of charge. PAST integrates spreadsheet-type data entry with univariate and multivariate statistics, curve fitting, timeseries analysis, data plotting, and simple phylogenetic analysis. Many of the functions are specific to paleontology and ecology, and these functions are not found in standard, more extensive, statistical packages. PAST also includes fourteen case studies (data files and exercises) illustrating use of the program for paleontological problems, making it a complete educational package for courses in quantitative methods.

/pdf/past-paleontological-statistical-software-package-for-pfvkmizuov.pdf

Past: paleontological statistical software package for education and data analysis

In the early 1980s, a strategy for graphical representation of multivariate (multi-species) abundance data was introduced into marine ecology by, among others, Field, et al. (1982). A decade on, it is instructive to: (i) identify which elements of this often-quoted strategy have proved most useful in practical assessment of community change resulting from pollution impact; and (ii) ask to what extent evolution of techniques in the intervening years has added self-consistency and comprehensiveness to the approach. The pivotal concept has proved to be that of a biologically-relevant definition of similarity of two samples, and its utilization mainly in simple rank form, for example ‘sample A is more similar to sample B than it is to sample C’. Statistical assumptions about the data are thus minimized and the resulting non-parametric techniques will be of very general applicability. From such a starting point, a unified framework needs to encompass: (i) the display of community patterns through clustering and ordination of samples; (ii) identification of species principally responsible for determining sample groupings; (iii) statistical tests for differences in space and time (multivariate analogues of analysis of variance, based on rank similarities); and (iv) the linking of community differences to patterns in the physical and chemical environment (the latter also dictated by rank similarities between samples). Techniques are described that bring such a framework into place, and areas in which problems remain are identified. Accumulated practical experience with these methods is discussed, in particular applications to marine benthos, and it is concluded that they have much to offer practitioners of environmental impact studies on communities.

Non-parametric multivariate analyses of changes in community structure

PAST: paleontological statistics software package for education and data analysis version 2.09

Background The analysis of microbial communities through DNA sequencing brings many challenges: the integration of different types of data with methods from ecology, genetics, phylogenetics, multivariate statistics, visualization and testing. With the increased breadth of experimental designs now being pursued, project-specific statistical analyses are often needed, and these analyses are often difficult (or impossible) for peer researchers to independently reproduce. The vast majority of the requisite tools for performing these analyses reproducibly are already implemented in R and its extensions (packages), but with limited support for high throughput microbiome census data. Results Here we describe a software project, phyloseq, dedicated to the object-oriented representation and analysis of microbiome census data in R. It supports importing data from a variety of common formats, as well as many analysis techniques. These include calibration, filtering, subsetting, agglomeration, multi-table comparisons, diversity analysis, parallelized Fast UniFrac, ordination methods, and production of publication-quality graphics; all in a manner that is easy to document, share, and modify. We show how to apply functions from other R packages to phyloseq-represented data, illustrating the availability of a large number of open source analysis techniques. We discuss the use of phyloseq with tools for reproducible research, a practice common in other fields but still rare in the analysis of highly parallel microbiome census data. We have made available all of the materials necessary to completely reproduce the analysis and figures included in this article, an example of best practices for reproducible research. Conclusions The phyloseq project for R is a new open-source software package, freely available on the web from both GitHub and Bioconductor.

/pdf/phyloseq-an-r-package-for-reproducible-interactive-analysis-1ez1xx3dlr.pdf

phyloseq: an R package for reproducible interactive analysis and graphics of microbiome census data.

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

Experimental Design and Data Analysis for Biologists

Studies by ourselves and others (Swan 1970, Austin & Noy-Meir 1972, Beals 1973, Hill 1973, 1974, Austin 1976a, b, Fasham 1977, Gauch Whittaker & Wentwarth 1977, Noy-Meir & Whittaker 1977, Orloci 1978, Gauch, Whittaker & Singer 1979) have found faults with all ordination techniques currently in use, at least when applied to ecological data specifying the occurrences of species in community samples. These faults certainly do not make existing techniques useless; but they mean that results must be interpreted with caution. Even with the best techniques, the underlying structure of the data is often poorly expressed.

Detrended correspondence analysis: an improved ordination technique

Multivariate Analysis in Community Ecology

Ecologists are making increasing use of computer methods in analyzing ecological data on plant and animal communities. Ecological problems naturally involve numerous variables and numerous individuals or samples. Multivariate techniques permit the summary of large, complex sets of data and provide the means to tackle many problems that cannot be investigated experimentally because of practical restraints. Ecologists are thus enabled to group similar species and similar sample sites together, and to generate hypotheses about environmental and historical factors that affect the communities. This timely book presents a full critical description of three methodologies - direct gradient analysis, ordination, and classification - from both theoretical and practical viewpoints. Both traditional and new methods are presented. Using a wide range of illustrative examples, Hugh Gauch provides an up-to-date synthesis of this field, which will be of interest to advanced students and ecologists. These mathematical tools are also used in a wide variety of other areas, from natural resource management and agronomy to the social and political sciences.

Multivariate analysis in community ecology

Yield trials frequently have both significant main effects and a
significant genotype x environment (GE) interaction. Traditional
statistical analyses are not always effective with this data structure:
the usual analysis of variance (ANOVA), having a merely additive
model, identifies the GE interaction as a source but does not analyze
it; principal components analysis (PCA), on the other hand is a
multiplicative model and hence contains no sources for additive
genotype or environment main effects; and linear regression (LR)
analysis is able to effectively analyze interaction terms only where
the pattern fits a specific regression model. The consequence of fitting
inappropriate statistical models to yield trial data is that the
interaction may be declared nonsignificant, although a more appropriate
analysis would find agronomically important and statistically
significant patterns in the interaction. Therefore, agronomists and
plant breeders may fail to perceive important interaction effects.

Statistical Analysis of a Yield Trial

SUMMARY The additive main effects and multiplicative interaction (AMMI) model first applies the additive analysis of variance (ANOVA) model to two-way data, and then applies the multiplicative principal components analysis (PCA) model to the residual from the additive model, that is, to the interaction. AMMI analysis of yield trial data is a useful extension of the more familiar ANOVA, PCA, and linear regression procedures, particularly given a large genotype-by-environment interaction. Model selection and validation are considered from both predictive and postdictive perspectives, using data splitting and F-tests, respectively. A New York soybean yield trial serves as an example. Yield trials generate observations of yield, ordinarily replicated, for a number of genotypes grown in a number of environments (site-year combinations). Often the data are rather noisy, with a standard deviation for plot yields in excess of 25 % of the mean. An additional challenging feature of these data is the frequent presence of important and complex genotype-by-environment (GE) interactions. Plant breeders use yield trials to identify promising genotypes, and agronomists use them to make recommendations for farmers. The level of success in meeting these goals depends critically on two factors: (i) the accuracy of yield estimates, and (ii) the magnitudes of genotype-by-site, genotype-by-year, and genotype-by-site-by-year interactions (Talbot, 1984). In essence, these two factors reflect within-trial accuracy and between-trial predictability. This paper addresses only the first concern. Nothing is said regarding between-trial predictability, or agrotechnology transfer, other than to observe that success with withintrial accuracy is a necessary prelude to success with between-trial predictability. The within-trial accuracy of a statistical model may be assessed by two fundamentally different criteria: Postdictive success concerns a model's fit to its own data, whereas predictive success concerns the fit between a model constructed using part of the data and validation data not used in modelling. In either case, the statistical setting is that of an incompletely specified model, where empirical considerations enter into the decision to include a given' potential source in the model, or alternatively to relegate it to the model's residual (Bancroft, 1964). Whenever the data are noisy, postdiction and prediction are different tasks, and in general the model chosen by predictive criteria will be different and simpler than the model chosen by postdictive criteria. Because the several replicates of a yield trial constitute a noisy sample, a model chosen by predictive criteria may be expected to provide yield estimates that are closer to the true means (and to validation observations) than will a model chosen by postdictive criteria. This claim is readily subjected to experimental test. In what follows, the relative performances of statistical models chosen

Hugh G. Gauch

Papers

Detrended correspondence analysis: an improved ordination technique

Multivariate Analysis in Community Ecology

Multivariate analysis in community ecology

Statistical Analysis of a Yield Trial

Model selection and validation for yield trials with interaction