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Keywords:

  • Bray–Curtis coefficient;
  • Correspondence analysis;
  • Ecological distance;
  • Extended dissimilarity;
  • Horseshoe effect;
  • Non-metric multidimensional scaling;
  • Simulated data;
  • Species response models

Abstract

Context

A historical review of ordination studies is presented with particular reference to the pioneering contributions of the late Prof. I. Noy-Meir and their continuing relevance.

Issues

(1) Comparisons of ordination methods are often confounded by differences in the methodological algorithm, dissimilarity measure used and the data standardization employed. (2) Artificial data where ‘truth’ is known offer a means of evaluating ordination approaches but are highly sensitive to the ecological model assumed. (3) Data standardization is frequently used but its influence on ordination is poorly understood and lacks theoretical justification.

Review

Historically, the above issues have been continually raised since the first use of artificial data by Swan in 1970 to demonstrate the ‘horseshoe distortion’. Three distinct conceptual models have been used to generate artificial data, yet no consensus on their suitability has emerged since they were first used in the mid-1970s. Comparative studies had, by the late 1980s, shown that some approaches recovered ‘ecological truth’ better than others. Differences between comparative studies in conceptual models, nature of the data matrices used, different dissimilarity measures, ordination algorithms and evaluations methods limited acceptance of this conclusion. Data standardization alters the properties of the vegetation data matrix. Yet little is known regarding the influence on ordination results of the collective vegetation properties stand abundance, dominance or species richness, which are altered by standardization.

Recent developments

Knowledge of the properties of individual dissimilarity measures and ordination algorithms has increased; a few new methods have emerged. Pragmatism of the type ‘this method gives me useful answers so I do not need to use a better method’ is common. Tests of conceptual models are now occurring based on species distribution modelling.

Conclusions

A consensus is emerging that non-metric multidimensional scaling and dissimilarity measures such as the Bray–Curtis coefficient should be used in preference to correspondence analysis methods based on the χ2 dissimilarity measure. Absence of a comprehensive model of vegetation composition is limiting ordination as a method of community analysis. Inconsistencies between different ordination methods and ecological models first recognized in the 1970s remain today.