This book attempts to bring together for the first time many recent methods of multivariate analysis appropriate for ecological data; it concentrates on techniques which explore pattern in data and provide visual displays. It succeeds in this aim. Formal statistical tests are not covered or encouraged; instead the reader is guided by copious examples in methods for summarizing and interpreting real data. The emphasis on data analysis to answer questions of real ecological interest is highlighted.While the main example which runs through the book concerns plants, there are many sets of entomological data. The initial two chapters describe forms of data and initial data summaries, the next two discuss different ordination methods and the comparison of several ordinations. Chapters 5 and 6 cover classification and asymmetry. The final chapter, on computing, is essential; the methods described depend on adequate computing power to analyse the large amounts of data inherent in studies of ecological communities. A useful appendix is given for the relevant matrix algebra required. The chapter on ordination and in particular the sections where principal components analysis and biplots were derived will be difficult for many ecologists to follow. Phrases such as 'subspace of k dimensions' really need some explanation; even a definition would be helpful! There were also several annoying minor errors; for example, the biplot example is highly confusing, and the vectors in the canonical correlation example are not all orthogonal.However, these are minor quibbles. The book represents a brave effort to pass on state-of-theart expertise in a difficult area and represents a rare class of text-book; one that is likely to be of even more use to the research worker than to the student. If it is read patiently it will repay the reader many times over.

SummaryGabriel (1971) proposed a technique for displaying the rows and columns of a twoway table as a two-dimensional biplot so that any element of the table can be approximated by the inner product of vectors corresponding to the appropriate row and column. The technique is useful for investigating the pattern of response of varieties over different environments, and substantially increases the information available from the more familiar methods of regression and principal component analysis without need for additional computation.

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Summary The method of adjusting plot values by covariance on neighbouring plots is applied to the analysis of plant breeding trials. For cereal trials the method is shown to be very effective in reducing variation caused by spatial heterogeneity within replicates and generally performed about as well as a more conventional row and column lattice square analysis. Results obtained from trials with replicated standards suggest that the reduction in estimate of error variance truly reflects the increased accuracy of the estimates of variety means. The method may be used when plot values are affected by the particular varieties occurring in neighbouring plots, and is effective in adjusting for competition effects in sugar beet trials.

SUMMARYA method is proposed for correcting for competition effects in yield trials by joint regression of plot yields on to the yields of neighbours. Estimation of the variety effects and competition coefficient along with tests of significance are described for a sugar-beet trial with single-row plots where competition effects are assumed to extend only to plants in immediately adjacent rows. For designs which are balanced for neighbouring varieties it is feasible to estimate separate varietal competition coefficients which may be partitioned into components for sensitivity and aggressiveness. An example is given of this extended model fitted to a competition diallel of seven species. While species differed in their sensitivity to competition there was no essential difference between inter- and intra-species behaviour. The model is used to assess comparative varietal performance in monocultures from performance in small plot trials.(Note that the general term ‘variety’ is used throughout this paper to refer to progenies at any stage in a selection programme.)