3.10 Analysis of floristic composition
3.10.2 TWINSPAN
TWINSPAN (Two-Way INdicator SPecies ANalysis procedure) has been very widely used by plant ecologists since its development more than 30 years ago (Hill et al. 1975). This method can be used with presence–absence, percentage cover, or abundance data. TWINSPAN progressively divides a data set into groups based on all of the information content of the data, rather than merging individuals into groups as is done in cluster analysis (Shaw 2003). Results are presented in the form of a dendrogram, but the reciprocal averaging ordination method is used to order the samples or sites. As a result, the outputs of TWINSPAN analysis are less prone to misinterpretation than dendrograms produced by standard cluster analysis (Shaw 2003). A particularly valuable feature of TWINSPAN is that it allows indicator species that are characteristic of each group to be identified, and therefore the method is especially useful when there is a need to identify species that can be used to characterize particular communities (Henderson 2003). In addition, both the samples and species are ordered along a gradient in the TWINSPAN output tables, which can greatly help data interpretation (Shaw 2003). An unusual feature of the method is the use of artificial constructs called ‘pseudospecies’, which are used to convert continuous data (such as percentage cover of different species) into categorical variables. Full details of the method are provided by Hill (1979).
Although TWINSPAN output can be rather complicated, the method has been
0.565 0.424 0.283
Dissimilarity
0.141 0
Site 1 Site 2 Site 5 Site 6 Site 7 Site 10
Site 12 Site 13 Site 11 Site 18 Site 14 Site 15 Site 20 Site 16 Site 19 Site 17 Site 3 Site 4 Site 8 Site 9
Fig. 3.16 A dendrogram showing the results of a cluster analysis. The dendrogram illustrates the degree of similarity between sites according to their species
composition. The diagram was produced by using CAP (Table 3.2). (From Henderson 2003.)
very widely used and is recognized as a standard technique, with few criticisms levied against it. Its main limitation is that it only considers one axis of variation (Shaw 2003).
3.10.3 Ordination
A wide variety of different ordination methods are available that can be used to analyse the relationships between sites or samples in terms of their species com- position. The best method is arguably the one that gives the clearest and most easily interpreted results, and therefore it may be worth trying a variety of different meth- ods and comparing the results (Henderson 2003). Ordination methods that are commonly used in forest ecology are considered below. A word of caution is appro- priate, regardless of which method is preferred. These techniques provide little use- ful information unless there is some genuine pattern to be detected and differences exist between individual samples of vegetation. A great deal of time can be wasted exploring multivariate analyses that produce little of value in the way of clear results. Ordination outputs can be dominated by outliers and swamped by noise.
One solution to this problem is to use sample plots that are large enough to include sufficient stems in the sample, even in sites with low stem densities. Also, do not be too disheartened if no clear pattern emerges in the results: ecological data can just be like that.
Principal components analysis (PCA)
PCA is most appropriate for use with abundance data. The method enables the relationship between samples to be illustrated in a two- or three-dimensional space by producing a plot of the results (Figure 3.17). This can then be interpreted visually. The analysis is usually done on a correlation matrix that includes all of the correlation coefficients between the variables included in the analysis. If the species vary greatly in abundance between samples the data will probably need to be transformed before analysis, using either a square-root or logarithmic transform- ation. The latter procedure cannot handle zeros, and therefore 1 is often added to all of the observations before the transformation (Henderson 2003). However, as this can distort the output, it is generally preferable to use the square-root transformation.
Often it is necessary to normalize the data before analysis. This is because multivariate datasets often consist of very different variables: for example, the cover of different tree species might be measured on a scale of 0–100%, whereas soil potassium concentration might vary between 5 and 20 mg 100 g–1. To analyse such data, they should be normalized to ensure that they are comparable. This is usually achieved by converting them to Z scores. Each observation (Xi) can be converted to a Zscore (Zi) as follows (Shaw 2003):
ZiXi s
Analysis of floristic composition | 139
where is the mean of a sample and sis the standard deviation. The Zscore has no units (it is the number of standard deviations each observation is from the mean of the sample), and therefore data that have been normalized in this way can be read- ily compared in the same analysis.
Outputs of PCA are usually visualized by plotting the sites or samples to be com- pared on the two or three main axes of variation detected by the analysis. Samples that are grouped more closely together are more similar in terms of their species composition. Attention should be paid to the proportion of the variability in the data set that is explained by these axes; the higher the proportion, the more robust the results. For data sets with more than 20 species, the first three main axes should account for more than 30% of the variance for the results to be of reasonable value (Henderson 2003).
PCA is very popular among plant ecologists because it is relatively easy to do.
The outputs are relatively easy to interpret, but the patterns produced can some- times be difficult to relate to environmental variables of interest. It is important to note that no test of significance is provided with the analysis: therefore it can only be used to explore data and generate hypotheses, rather than test them. However, the axis scores (which are generated during the analysis and describe the position of each sample along the principal axes) can be used as data themselves and sub- jected to further analysis, such as regression or analysis of variance (ANOVA) (Shaw 2003). For example, by using ANOVA it would be possible to test whether the axis scores associated with different forest communities were significantly dif- ferent from one another (assuming that the scores are normally distributed). PCA cannot cope with missing values in the data and may be inappropriate where com- munities develop along environmental or temporal gradients (when DCA may be preferred; see below) (Shaw 2003).
Site 2 Site 5
Site 7 Site 10
Site 11
Site 18 Site 17
Principal axis 1
Principal axis 2
Site 3 Site 4
Site 9 Site 1 Site 12
Site 14 Site 15
Site 16 Site 20 Site 13
Site 8
Site 6
–6
–4 –3 –2 –1 0 1 2 3 4
–5 –4 –3 –2 –1 0 1 2 3 4 5 6
Fig. 3.17 The results of a principal components analysis to illustrate differences between sites according to their species composition. (Graphical output produced by using CAP; see Table 3.2). (From Henderson 2003.)
Principal coordinates analysis (PCO)is sometimes confused with PCA, because of its similar abbreviation, but is in fact is a very different technique (sometimes referred to as multidimensional scaling). PCO uses a square matrix of distances between individuals and produces a map from the distances measured. This map can be used as a form of ordination to show the relative position of individuals sampled; usually Euclidean distance is used (Shaw 2003). The method is relatively little used by plant ecologists.
Detrended correspondence analysis (DCA or DECORANA)
DCA is an ordination technique designed specifically to assist with the exploration of ecological data (especially abundance data) and is very widely used by plant ecologists. It is particularly appropriate for use in situations where the sites that are sampled can be arranged along an environmental gradient, such as successional stages in vegetation. In such cases, use of PCA can lead to an artefact in the output (the so-called ‘arch effect’), which DCA was designed to overcome. Ordinations of both species and sites can be plotted on the same figure, which enables the influ- ence of different species on the ordination of the sites to be evaluated visually. The output of DCA is otherwise similar to that of PCA.
Canonical correspondence analysis (CCA)
This method was developed by ter Braak (1986), and is widely used by researchers interested in exploring the relations between community composition and envir- onmental variables. CCA is based on a similar analytical technique to DCA and TWINSPAN, but differs in its inclusion of environmental data within the ordin- ation itself so as to maximize their importance in the output. CCA therefore requires data on the environmental conditions at each site. These may be repre- sented in the form of classificatory variables (such as ‘high’ or ‘low’ altitude) or con- tinuous variables (such as temperature measured in degrees Celsius). The data matrix including the environmental variables measured must have the same num- ber of rows (observations) as the species data, but need not have the same number of columns (variables) (Shaw 2003).
The outputs of the analysis enable the relation between environmental variables and the observed species communities to be evaluated. The method is sensitive to data quality; poor or incomplete data will produce results of little value. It is important that environmental and species data are collected at the same place and at the same time (Shaw 2003). As outputs can be complex, they can be difficult to interpret. As with other ordination methods, it is not possible to statistically test the association between species composition and environmental variables.
Biplot
Often, a main objective of ordination is to explore the relations between floristic composition and environmental variables (such as soil characteristics, aspect or alti- tude). This can usefully be achieved by producing a biplot. Biplots can be produced Analysis of floristic composition | 141
by using different ordination techniques (such as PCA, DCA, and CCA), although the methods used differ according the ordination technique adopted. Biplots enable the properties of the variables measured (such as environmental variables) to be overlaid on top of the main ordination diagram. Usually the former are illustrated as arrows that run from the 0,0 point to the coordinate in question (Shaw 2003).
This can help with data interpretation: for example, if an arrow points to a cluster of points, then this suggests a relation between the variable in question and the sam- ples illustrated by the points in the cluster. For example, an arrow representing soil nitrogen concentration might be associated with a cluster of points representing the composition of a particular forest type. However, it should be remembered that a biplot provides no statistical analysis of the strength of this relation, and illustrates a correlative association rather than any causal relation.
3.10.4 Importance values
Importance values have been widely used as a measure of species composition that combines frequency, abundance and dominance importance values (Grieg-Smith 1957). This can be calculated according to the following equation (Husch et al.
2003):
where Ijis the importance value of the jth species, njis the number of sampling units where the jth species is present, Nis the total number of sampling units, djis the number of individuals of the jth species present in sample population, Dis the total number of individuals in sample population (DΣdj),xjis the sum of size parameter (generally basal area or volume) for the jth species, and Xis the total size parameter across all species XΣxj.