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A comparative evaluation of techniques for ecological ordination using simulated vegetation data and an integrated ordination-classification analysis of the Alpine and Subalpine Plant communitites of the Mt. Field Plateau, Tasmania.


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Minchin, PR (1983) A comparative evaluation of techniques for ecological ordination using simulated vegetation data and an integrated ordination-classification analysis of the Alpine and Subalpine Plant communitites of the Mt. Field Plateau, Tasmania. PhD thesis, University of Tasmania.

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This thesis consists of two, inter-related sections. In Part 1,
the relative utility of ordination techniques, for the purpose of
indirect gradient analysis in plant ecology, is studied empirically.
Using simulated data derived from flexible models of vegetation-gradient
relationships. Part 2 is an integrated analysis of vegetation data
obtained by intensive sampling of the subalpine and alpine vegetation of
the Mt. Field Plateau, Tasmania. The results of the direct gradient
analysis of the Mt. Field vegetation were taken into account when
formulating the models used in Part 1. In return, the selection of the
most appropriate methodo1ogy for indirect gradient analysis of the Mt.
Field data drew upon the results of the comparative evaluation of
techniques in Part 1.
Previous studies which have evaluated the performance of
ordination techniques using simulated vegetation data are reviewed.
Most such studies have employed models in which the response profiles of
species along the artificial gradients were Gaussian. Some preliminary
experiments with plausible alternative models have suggested that even
the most promising of recently introduced ordination methods may be
undesirably sensitive to small variations in the model. Since the
available observational evidence does not support the general
applicability of the Gaussian model in nature, the relevance of the
results of comparative studies based on Gaussian models is in doubt.
Noting that present evidence is insufficient to permit the
formulation of a general model of vegetational response to environmental
gradients, the present study attempts to identify ordination methods
which are robust to variations in those features of the model still
subject to debate. A flexible modelling approach was developed, based
on the use of beta functions, which can produce unimodal curves of
varying skewness. The models allow "competition" between species to
introduced, in the form of linear interaction coefficients, thus
producing shouldered, bimodal or multimodal response curves of the types
often observed in direct gradient analyses. Both stand abundance (the
sum of the abundances of all species present in a sample) and alpha
diversity (the number of species per sample) may be varied along
gradients in a flexible manner. Quantitative noise may be introduced,
in the form of random departures from the expected abundance.
Probability of occurrence profiles may optionally be used to introduce
qualitative noise. The models allow both unidimensional compositional
gradients (coenoclines) and two-dimensional patterns (coenoplanes) to be
Using such models, the relative performance of the ordination
techniques Detrended Correspondence Analysis (DCA) "local" Non-metric
Multidimensional Scaling (LNMDS), Principal Co-ordinates Analysis
(PCoA), Principal Components Analysis (PCA) and Gaussian Ordination (GO)
was assessed. Ordination configurations were rotated to best fit with
the original arrangement of samples along the simulated gradient(s)
using Procrustean ana1ysis, and the RMS displacement error was used as a
measure of ordination efficacy. For ordinations of coenoclines, the Kendall rank correlation coefficient was used to assess the accuracy
with which the rank order of samples was recovered. Experiments were
performed on the effects of variation in several properties of the
models, with particular attention being devoted to the robustness of
methods to variations in the shape of response curves, the introduction
of noise and the arrangement of samples.
Experiments with coenocline models confirmed the ineffectiveness
of PCA, except when the beta diversity of the gradient is low (no more
than 4Z). PCoA, operating on a percentage similarity matrix, was
similarly affected. With models containing only unimodal curves, DCA
was generally the most successful of the methods compared. GO was able
to improve significantly on the DCA solutions only when beta diversity
was less than 6Z, quantitative noise levels were low and the curves were
not grossly skewed. When models included shouldered and bimodal curves,
LNMDS was consistently superior to DCA and GO.
PCA and PCoA ordinations of simu1ated coenoplanes were poor unless
the beta diversity of both gradients was low. With 11 rectangu1ar 11
coenoplanes, curvilinear distortion of the longer gradient often
obscured variation related to the secondary gradient. LNMDS
consistently improved on DCA solutions for all the coenoplane models
examined. The DCA results, even with noiseless data from some of the
symmetrical, unimodal models, were occasionally very poor. Neither
LNMDS nor DCA gave consistently satisfactory results when coenoplanes
were sampled with cross-shaped or T-shaped sampling patterns, which
simulate field situations where one gradient is expressed only in a
restricted region of another gradient.
The present study suggests a preference for LNMDS as a "general
purpose" approach to indirect gradient analysis. However, practical
limitations of LNMDS may make DCA the method of choice when the number
of samples is large. Significant advances in the methodology of
indirect gradient analysis are unlikely to be made until much more
observational evidence concerning the nature of vegetational response to
environmental gradients is available.
Subalpine and alpine vegetation on the Mt. Field Plateau, a
dolerite capped horst in south-central Tasmania, was intensively sampled
using a stratified, systematic arrangement of 438, 100 sq. m quadrats.
In each sample, cover estimates were made for all vascular plant species
and various site and community characteristics were recorded.
A direct gradient analysis was performed, using altitude and
substrate drainage (estimated on a five point scale) as axes. The
response surfaces for mean cover of 111 species were predominantly
unimodal (80%), although only 45% appeared to be symmetrical. For the
unimodal species, the distribution of modes over the ecoplane was
consistent with random expectation. The frequency distribution of
response surface maxima was approximately 1ograndom for non-woody
species, but the distribution for woody species did not fit lograndom or
lognormal hypotheses.
Mean values of
tallest stratum, total
commun1ty characteristics,
cover and alpha diversity,
such as height
displayed systematic trends in re1ation to altitude and drainage. The pattern of alpha
diversity was further clarified by the division of species into
growth-form groups. Beta (between-habitat) diversity along the drainage
gradient showed a consistent decline with increasing elevation.
The potential value of Generalised Linear Modelling (GLM) as a
more rigorous approach to the fitting of response surfaces was examined
for a selected set of 18 dominant species. An initial qualitative model
was fitted, in order to identify samples where the expected probability
of occurrence of a species was low. Such samples were then omitted when
fitting a predictive model for percentage cover. For all but four of
the species, probability of occurrence was adequately fitted by a
symmetrical, bell-shaped surface. The quantitative (percentage cover)
models for most species had low adjusted r-squared values, indicating a
relatively large amount of 11 noise" variation. The factors which may
have contributed to this noise variation are discussed.
Because of the large number of samples~ which made LNMDS
impracticable, DCA was adopted as a primary approach for indirect
gradient analysis. The first two axes of a DCA ordination, based on
cover class data, defined a coenop1ane to which altitude and drainage
were strongly related. This result supports the choice of these two
complex-gradients as axes for direct gradient analysis. The third axis
was a spurious "interaction~~ axis, resulting from the failure in DCA to
detrend the third and subsequent axes with respect to combinations of
the previously extracted axes. The fourth axis represented a
compositional gradient among subalpine forests on well drained sites,
which was tentatively related to firing history.
DCA based on presence-absence data gave very similar results~
indicating that at these levels of beta diversity, most of the relevant
information concerning the positions of samples on the major underlying
gradients is contained in the qua1itative component of the data. A DCA
ordination of percentage cover data (i.e. midpoints of cover classes)
produced a distorted reconstruction of the altitude X drainage
coenoplane, with one corner projected into a third dimension. The
origin of this type of distortion, which was also noted with some of the
coenoplane models in Part 1, is not clear.
A compound data set was produced by forming the centroids of 60 minimum Sum-of-Squares clusters. Ordinations of this compound data set
by various techniques, including DCA, local and global NMOS, PCoA and
PCA, were compared. The ineffectiveness of PCoA and PCA was readily
apparent. Curvilinear distortion of the altitude X drainage coenoplane
prevented adequate recovery of the tertiary "firing history" gradient.
The NMDS solutions based on local and global criteria were very similar
to each other and they differed from the DCA result only in local details

Item Type: Thesis (PhD)
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Date Deposited: 03 Dec 2013 21:48
Last Modified: 11 Mar 2016 05:56
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