On The Empirical Performance Of Non-Metric
Multidimensional Scaling In Vegetation Studies
V. K. Salako
1
, A. Adebanji
2
and R. Glèlè Kakaï
1
1
Faculty of Agronomic sciences, University of Abomey-Calavi,
01 BP 526, Cotonou, Bénin
Email: gleleromain@yahoo.fr
2
Department of Mathematics, Kwame Nkrumah
University of Science and Technology, Kumasi, Ghana
Email: tinuadebanji@gmail.com
ABSTRACT
Non-metric multidimensional scaling (NMDS) is widely used as a routine method for
ordination in vegetation studies. Its use in statistical softwares often requires the choice of
several options on which the accuracy of results will depend. This study focuses on the
combined effect of sample size, similarity/dissimilarity indexes, data standardization and
structure of data matrix (abundance and binary) on NMDS efficiency based on real data
from the Lama Forest Reserve in Southern-Bénin. The Spearman’s Rank Correlation
coefficient and the s-stress were used as an assessment criterion. All the four factors were
found to influence the efficiency of the NMDS and the samples (plots) standardization to
equal totals gave the best results among standardization procedures considered. The
Jaccard and Sorensen similarity/dissimilarity indexes performed equally whatever the nature
of the matrix. However, with binary matrices, Sokal and Michener similarity index performed
better. A quadratic relationship was noted between s-stress and sample size. A lower
optimal sample size (75 plots) was observed for the binary matrices than for the abundance
ones (90 plots).
Keywords: Non-metric multidimensional scaling, efficiency, vegetation studies.
Mathematics Subject Classification: 91C15, 68U20
1. INTRODUCTION
In vegetation studies, ordination aims at sorting samples and/or species along a few axes which must
represent the main compositional gradients in the data set, using either abundance or
presence/absence data (Økland, 1996). It seeks a parsimonious representation of samples and/or
species in a space of low dimensionality. Parsimony in this context implies that distances between
samples and/or species in ordination space optimally represent their original dissimilarities (between
samples or species) in variable space, in some defined sense (Kenkel and Orloçi, 1986). Common
goals of ordination methods in vegetation studies are: description and recognition of vegetation
distribution patterns, identification of plant’s communities and examination of plants and communities
distribution in relation to environmental factors and gradients (Kenkel and Orloçi, 1986; Kent and
Ballard, 1988; Podani, 2006).
International Journal of Applied Mathematics and Statistics,
Int. J. Appl. Math. Stat.; Vol. 36; Issue No. 6; Year 2013,
ISSN 0973-1377 (Print), ISSN 0973-7545 (Online)
Copyright © 2013 by CESER Publications
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