comparative study of nonmetric ordinations

(1) Several nonmetric multidimensional scaling programs (PARAMAP, POLYCON, ALSCAL and SIBSON) were applied to simulated and real plant community data in order to test their effectiveness as ordination techniques in comparison to reciprocal averaging (RA) and an improved version of RA: detrended correspondence analysis (DCA). (2) Nonmetric ordination gave better results than did RA for data having three to four dimensions, whereas RA was superior to nonmetric ordination for one dimension. For two dimensions there was little difference. Experimental variation of the sample-set (beta) diversity and of noise showed that neither method had consistent advantages over the other. For most ecological uses RA is preferable because it requires much less computation than do nonmetric methods. DCA was superior to RA and to nonmetric ordination, and needs exceptionally little computer time and storage. (3) The programs PARAMAP, POLYCON, ALSCAL and SIBSON differ little in the solutions produced, but they differ considerably in computing speed, quality of the initial configuration (and hence ability to avoid local minima), and convenience of output. Dissimilarities can be weighted by POLYCON, and SIBSON can use local scaling, but neither of these features improved results. In general ALSCAL was best. (4) Because its assumptions are unusually simple and general, nonmetric ordination results are of special interest for models of vegetation structure. The results presented are consistent with a bell-shaped model of species response to environmental gradients, and with an error function relationship between sample similarity and ecological separation.