The development of numerical classification and ordination

Summary

The paper reviews the constraints and influences which have affected the development of numerical classification and ordination of vegetation.

Initial development of ordination techniques and their reception by ecologists was hindered by the mistaken idea that ordination involved acceptance of variation in vegetation as a continuum, as well as by a general suspicion of mathematical approaches.

Three distinct approaches to ordination, largely unrecognised at the time, are apparent in earlier work: direct gradient analysis, reduction in dimensionality and path-seeking (catenation) (Dale 1975).

Modifications of simple initial techniques made them more efficient at the cost of increased computation. Acceptance of heavier computation as computers increased in capacity and speed turned attention to prineipal component analysis and the superficially similar factor analysis. These have been widely misunderstood largely because they were initially applied in the same way as in the analysis of psychological data, in which different constraints and objectives apply. The initial failure to recognise that principal component analysis involves a preliminary data transformation, the form of which depends on answers to biological, not mathematical, questions, was particularly unfortunate.

Principal component analysis has limitations as a technique of ordination resulting from its assumptions of linearity and additivity of plant responses. Attempts to devise more effective techniques raise questions about the practical importance of non-linearity if the objective is data-exploration rather than elucidating the nature of species-response curves and about the adequacy of using simulated data as test data when we do not know how to simulate realistic data.

Data-exploration has been more prominent in practical uses of ordination but many methodological developments have concentrated rather on species-response curves.

Numerical classification also met obstacles to its acceptance additional to a general aversion to numerical techniques. The first numerical techniques were presented in the context of the relationships of a particular set of data, rather than of a generally valid system, which was the more familiar concept in non-numerical classification.

Both numerical and non-numerical classification aim to produce as homogeneous groups as possible. The distinctive contribution of numerical methods is to allow the data to indicate the most efficient criteria of classification; this was an unfamiliar idea.

The strategy of classification may be either divisive or agglomerative and either monothetic or polythetic. Choice of strategy in earlier work was not only constrained by computational limitation but may also have been influenced by an author's previous experience of non-numerical classification. As with ordination, the distinction between preliminary data transformation and subsequent analysis was at first not appreciated.

Numerical classification has been influenced by parallel numerical developments in formal taxonomy. Because objectives and assumptions are not always the same, this influence has not been altogether helpful.

The limitations of real data suggest that developments of technique are at risk of becoming too concerned with refinements of methodology. Increasingly complex methods and increasing availability of programmes for such methods carry the risk that they may be used without adequate understanding of what they do.