4.3 Statistical Methods
57
4.3.1.3
Multivariate Spatial and Temporal Patterns
Question: Which patterns emerge in chemical, biological and sedimentological
variables along a transect from a mussel bed to a sandflat in the course of one
year?
For the spatial and temporal pattern of chemical, biological and sedimentological variables, there is a priori no statistical reference model. This makes the problem different from the one concerning the distribution pattern of L. conchilega.
Moreover, the multivariate pattern is to be investigated, i.e. the pattern of several
variables simultaneously. Therefore, techniques from multivariate exploratory
statistics are recommended.
A flexible technique, which allows the interpretation of the term "pattern" in
different ways depending on the context, is Multidimensional Scaling (MDS). The
technique was applied to benthic communities by Warwick & Clarke (1991) and
has frequently been used in benthic ecology.
Starting point of the technique is the transition from the data matrix (values of
the variables in the samples) to a matrix of dissimilarities between pairs of samples. The choice of the measure of dissimilarity reflects the ecological question.
The result of the procedure is a graphical representation of all the samples as
points in a low-dimensional Euclidean system of co-ordinates (mostly twodimensional) and is called the configuration. The algorithm, which transforms the
matrix of dissimilarities into the configuration, arranges the samples in such a way
that very similar samples will be placed close to each other and very dissimilar
samples will be placed far away from each other. This requirement cannot be met
in all cases. Whether a configuration found by the algorithm is an adequate representation of the matrix of dissimilarities should be inspected by use of the Shepard
diagram and the stress value. The Shepard diagram should be monotonic and the
stress value should not be beyond 0.15. The technique is explained and discussed
in detail e.g. by Clarke (1993) and Cox & Cox (1994).
4.3.1.4
Case Study: Spatial and Temporal Patterns in Geochemical Variables
Data provided by A. Hild.
Question: Which of the geochemical variables are similar to each other with respect to their spatial and temporal pattern?
Sampling: At 6 stations along a transect one unreplicated sample was taken per
sampling date. For this case study, five time points were chosen and 7 variables
included. The variables had also been measured in the different grain size fractions
of the sediment.
Statistical technique: The Spearman rank-correlation coefficient was used to
measure the similarity between two spatial and temporal patterns. It assumes the
maximum value of I if the measurements of two variables have the same order
along the transect and in the course of time. Thus, pattern is defined here as arrangement of the measured values. For a graphical representation of the similarity
structure MDS is used (compare Sect. 4.3.1.3).
57
4.3.1.3
Multivariate Spatial and Temporal Patterns
Question: Which patterns emerge in chemical, biological and sedimentological
variables along a transect from a mussel bed to a sandflat in the course of one
year?
For the spatial and temporal pattern of chemical, biological and sedimentological variables, there is a priori no statistical reference model. This makes the problem different from the one concerning the distribution pattern of L. conchilega.
Moreover, the multivariate pattern is to be investigated, i.e. the pattern of several
variables simultaneously. Therefore, techniques from multivariate exploratory
statistics are recommended.
A flexible technique, which allows the interpretation of the term "pattern" in
different ways depending on the context, is Multidimensional Scaling (MDS). The
technique was applied to benthic communities by Warwick & Clarke (1991) and
has frequently been used in benthic ecology.
Starting point of the technique is the transition from the data matrix (values of
the variables in the samples) to a matrix of dissimilarities between pairs of samples. The choice of the measure of dissimilarity reflects the ecological question.
The result of the procedure is a graphical representation of all the samples as
points in a low-dimensional Euclidean system of co-ordinates (mostly twodimensional) and is called the configuration. The algorithm, which transforms the
matrix of dissimilarities into the configuration, arranges the samples in such a way
that very similar samples will be placed close to each other and very dissimilar
samples will be placed far away from each other. This requirement cannot be met
in all cases. Whether a configuration found by the algorithm is an adequate representation of the matrix of dissimilarities should be inspected by use of the Shepard
diagram and the stress value. The Shepard diagram should be monotonic and the
stress value should not be beyond 0.15. The technique is explained and discussed
in detail e.g. by Clarke (1993) and Cox & Cox (1994).
4.3.1.4
Case Study: Spatial and Temporal Patterns in Geochemical Variables
Data provided by A. Hild.
Question: Which of the geochemical variables are similar to each other with respect to their spatial and temporal pattern?
Sampling: At 6 stations along a transect one unreplicated sample was taken per
sampling date. For this case study, five time points were chosen and 7 variables
included. The variables had also been measured in the different grain size fractions
of the sediment.
Statistical technique: The Spearman rank-correlation coefficient was used to
measure the similarity between two spatial and temporal patterns. It assumes the
maximum value of I if the measurements of two variables have the same order
along the transect and in the course of time. Thus, pattern is defined here as arrangement of the measured values. For a graphical representation of the similarity
structure MDS is used (compare Sect. 4.3.1.3).