Andre F. Lotter
Geobotanisches Institut der Universitaet Bern
Abt. Palaeooekologie
Altenbergrain 21
CH-3013 Bern, Switzerland
E-mail: lotter@sgi.unibe.ch
Quaternary science is primarily a non-experimental subject. During the last two to three decades the statistical analysis of Quaternary data has become increasingly important, either as a tool for data exploration or, more recently, in the form of hypothesis testing in confirmatory data analysis. Traditional statistics textbooks, however, would rarely cover the problems that Quaternary scientists have been facing. Books on statistical methods in Quaternary science such as the one I have the pleasure to review, are therefore highly desirable.
Avid readers might remember that Maddy & Brew (1993) were announcing the book in an INQUA newsletter and were looking for possible contributors three years ago. The book has eventually appeared and deserves a review in this newsletter. It is organised in seven chapters each written by different authors and focusing on different aspects of statistical analyses of Quaternary data. The chapters deal with explanatory modelling of uncorrelated and spatially or temporally correlated data, data reduction, ordination, and reconstruction. To each chapter there are one or several examples in order to illustrate the different methods. At the end of the book an index helps to find the relevant key-words in the different chapters. Furthermore, each author provides the relevant literature to his chapter as well as a list of the available software.
The first chapter, written by Warren L. Kovach gives an introduction to "multivariate data analysis." He discusses the problem of data transformation prior to the analysis before going into details of different kinds of cluster analyses. Ordination methods, indirect gradient analyses (principal components analysis, principal co-ordinates analysis, correspondence analysis, detrended correspondence analysis), as well as direct gradient analyses (canonical correspondence analysis) are then explained and exemplified on pollen data.
In chapter two John Walden and John P. Smith discuss simultaneous R- and Q-mode "factor analysis" by using two examples: the reader is guided step by step through the factor analysis of a hypothetical data set using MINITAB software. The second example uses geochemical and geomagnetic data to reconstruct the land-use change in a lake catchment.
In chapter three David G. Green discusses "time and spatial analysis." In a first part, time series methods as a means to identify and model sources of change in time series are presented. The numerical zonation methods using Maher's (1992) SLOTSEE program as well as the cusum method to identify break points in individual curves are applied to pollen data. An extensive paragraph on time series analysis introduces the reader to the basics of this method by explaining filtering, standardisation, cross-correlation, auto-correlation, and spectral analysis. A further paragraph concentrates on spatial data analysis with emphasis on spatial pattern, estimation of number of objects, types, or area covered, as well as sampling fidelity.
If you have a special interest in tree-ring and climate reconstruction then chapter four by Martin C. Bridge gives you an overview and a critical discussion of the basic statistical methods such as, e.g., crossmatching, autocorrelation, and standardisation used in this field of Quaternary science.
In chapter five John S. Brew and Darrel Maddy deal with "generalised linear modelling." After an introduction they explain the general concepts of GLMs in terms of data classification, error functions, link functions, as well as parameter estimation. Three examples on depth-age modelling, logistic regression in relation to fluvial lithology, and log-linear analysis of pebble roundness data (using GLIM software) illustrate the use of these generalised linear models. A separate paragraph on statistical modelling with GLMs explains the procedure of model development step-by-step, such as the choice of variables, error and link functions, as well as model choice and evaluation.
The sixth chapter consists of a comprehensive overview of "quantitative palaeoenvironmental reconstruction" written by H. John B. Birks. After a section on the general theory behind the different models the importance of the basic assumptions and requirements for any quantitative palaeoenvironmental reconstruction are stressed. Statistical aspects of quantitative reconstruction such as linear versus unimodal models, estimation of prediction errors, and critical evaluation of the reconstruction are discussed in detail in this extensive chapter that includes one third of the whole book. The performance of modern biological training sets is assessed by means of the root mean square error and emphasis is laid on the use of a cross-validation through jack-knifing to estimate the root mean error of prediction. The following section on statistical methods first explains linear-based techniques such as classical and inverse linear regression, principal components regression as well as partial least squares regression. Moreover, the use of canonical correlation analysis and redundancy analysis regression makes the link to regression approaches introduced in the first chapter. Then, non-linear unimodal techniques such as maximum likelihood, correspondence analysis, canonical correspondence analysis and the widely used weighted averaging and weighted averaging partial least squares regression techniques are thoroughly presented. The following section on other methods of quantitative environmental reconstruction includes critical discussions of some prominent published examples on modern analogue techniques in relation to poll reconstructions and response surfaces (e.g. the mutual climate range method). The evaluation of environmental reconstruction is discussed in terms of lack-of-fit measures and sample specific root mean square errors of prediction as assessed through bootstrapping. Eventually, a comparison of the different regression techniques is given on the basis of the classical Imbrie & Kipp (1971) foraminifera and sea surface temperature and salinity data-set.
In chapter seven David G. Green gives information on "on-line resources and information services" such as e-mail listservers and newsgroups. He lists some Gopher, WWW, and anonymous FTP site addresses relevant to Quaternary scientists and also gives and example on how to build up a WWW homepage.
I am aware that the editors could not cover every aspect of statistical modelling relevant to Quaternary science. Due to my personal preferences, however, I would have liked to see a chapter on topics important in palaeoecological studies, such as generalised additive models, rates of change, and confirmatory data analysis. Nevertheless, I would very much recommend this book to Quaternary scientists and students in Quaternary science who are looking for an overview on the subject of statistical methods applicable to their data. For those who then want to go into more detail each chapter provides plenty of references that will guide the interested reader to the relevant literature. With its price of £9.00 for QRA members (£16.00 for non-members), this book is good value for money, and I congratulate the editors and authors to its completion.