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

Hypothesis-testing methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps more intuitive formulation for ANOVA (based on sums of squared distances) to complement the description pro- vided by McArdle and Anderson (in press) for the analysis of any linear model. It is an improvement on previous non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack of formal assumptions of other non-parametric methods. The test- statistic is a multivariate analogue to Fisher's F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.

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A new method for non-parametric multivariate analysis of variance

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

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Experimental Design and Data Analysis for Biologists

Pseudoreplication is defined. as the use of inferential statistics to test for treatment effects with data from experiments where either treatments are not replicated (though samples may be) or replicates are not statistically independent. In ANOVA terminology, it is the testing for treatment effects with an error term inappropriate to the hypothesis being considered. Scrutiny of 176 experi- mental studies published between 1960 and the present revealed that pseudoreplication occurred in 27% of them, or 48% of all such studies that applied inferential statistics. The incidence of pseudo- replication is especially high in studies of marine benthos and small mammals. The critical features of controlled experimentation are reviewed. Nondemonic intrusion is defined as the impingement of chance events on an experiment in progress. As a safeguard against both it and preexisting gradients, interspersion of treatments is argued to be an obligatory feature of good design. Especially in small experiments, adequate interspersion can sometimes be assured only by dispensing with strict random- ization procedures. Comprehension of this conflict between interspersion and randomization is aided by distinguishing pre-layout (or conventional) and layout-specifit alpha (probability of type I error). Suggestions are offered to statisticians and editors of ecological j oumals as to how ecologists' under- standing of experimental design and statistics might be improved.

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Pseudoreplication and the Design of Ecological Field Experiments

Plastics have outgrown most man-made materials and have long been under environmental scrutiny. However, robust global information, particularly about their end-of-life fate, is lacking. By identifying and synthesizing dispersed data on production, use, and end-of-life management of polymer resins, synthetic fibers, and additives, we present the first global analysis of all mass-produced plastics ever manufactured. We estimate that 8300 million metric tons (Mt) as of virgin plastics have been produced to date. As of 2015, approximately 6300 Mt of plastic waste had been generated, around 9% of which had been recycled, 12% was incinerated, and 79% was accumulated in landfills or the natural environment. If current production and waste management trends continue, roughly 12,000 Mt of plastic waste will be in landfills or in the natural environment by 2050.

Production, use, and fate of all plastics ever made

Ecological theories and hypotheses are usually complex because of natural variability in space and time, which often makes the design of experiments difficult. The statistical tests we use require data to be collected carefully and with proper regard to the needs of these tests. This book, first published in 1996, describes how to design ecological experiments from a statistical basis using analysis of variance, so that we can draw reliable conclusions. The logical procedures that lead to a need for experiments are described, followed by an introduction to simple statistical tests. This leads to a detailed account of analysis of variance, looking at procedures, assumptions and problems. One-factor analysis is extended to nested (hierarchical) designs and factorial analysis. Finally, some regression methods for examining relationships between variables are covered. Examples of ecological experiments are used throughout to illustrate the procedures and examine problems. This book will be invaluable to practising ecologists as well as advanced students involved in experimental design.

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Experiments in Ecology: Their Logical Design and Interpretation Using Analysis of Variance

Techniques of analysis of variance in experimental marine biology and ecology

Much sampling to detect and quantify human environmental disturbances is flawed by a lack of appropriate replication. BACI (Before—After—Control—Impact) designs have only a single control location, and any conclusions from them are illogical. Asymmetrical designs using one putatively impacted and several control locations can reliably detect a variety of environmental impacts, including those that do not affect long—run mean abundances, but do alter temporal variance. When abundances of populations in different locations show temporal interaction, the asymmetrical designs allow tests for impact that are not possible in BACI designs. Asymmetrical designs are also extendable to sample at hierarchical spatial and temporal scales. The power of tests using asymmetrical designs is great for non—interactive sets of abundances, but greatest for pulse (short—term) responses to disturbances, large alterations of temporal variance, or combinations of temporal variance, or combinations of sustained, press responses in mean abundance coupled with altered temporal heterogeneity. Power in temporally interactive sets of data is generally poor. Alternatives to pre—disturbance sampling, including generalized assessment of spatial and temporal variances and experimental impacts, may provide better guidance for detection of human disturbances.

On Beyond Baci: Sampling Designs That Might Reliably Detect Environmental Disturbances

Beyond BACI: the detection of environmental impacts on populations in the real, but variable, world

Many marine invertebrates have a planktonic stage of their life history during which widespread dispersal and much mortality occur. The numbers surviving to recruit into habitats occupied by adults are therefore very variable in time and space. Models for the structure and dynamics of benthic assemblages tend to focus on processes causing death - often assuming consistent arrivals of recruits. Supply-side ecology is a newly fashionable term to describe recent interest in the long-realized consequences of variations in recruitment. Such variations have important influences on theory and empirical research in these assemblages.

A. J. Underwood

Papers

Experiments in Ecology: Their Logical Design and Interpretation Using Analysis of Variance

Techniques of analysis of variance in experimental marine biology and ecology

On Beyond Baci: Sampling Designs That Might Reliably Detect Environmental Disturbances

Beyond BACI: the detection of environmental impacts on populations in the real, but variable, world

Supply-side ecology and benthic marine assemblages