**3. Methods of classification analysis**

Classification method is an act of putting things in groups. Most commonly in community ecology, the "things" are samples or communities. Classification can be completely subjective, or it can be objective and computer-assisted (even if arbitrary). Hierarchical classification means that the groups are nested within other groups. There are two general kinds of hierarchical classification: divisive and agglomerative. A Divisive method starts with the entire set of samples, and progressively divides it into smaller and smaller groups. An agglomerative method starts with small groups of few samples, and progressively groups them into larger and larger clusters, until the entire data set is sampled (Pielou, 1984).

Cluster analysis, on the other hand, seeks to divide the n quadrates into groups of high internal similarity with respect to species or characters used. In the classical approach of Williams & Lambert (1959), the so-called Association-Analysis, communities are defined by the presence or absence of single species. This is highly dependent on the vagaries of sampling; many workers have felt the method may result in botanical over simplification, so that nowadays polythetic methods are more usually applied.

From the above discution, it can be seen that ordination and cluster analysis are not competing approaches and provided the ecologist is cautious in making inferences, both can reasonably be applied in the examination of multivariate samples (Pritchard & Anderson, 1971).

In classification of species the basic idea is that a characteristic species combination (or at least a group of differentiated species) should gather samples containing these species into clusters of similar samples (Tavili & Jafari, 2009).

In fact, Classification assumes from the outset that the species assemblages fall into discontinuous group, whereas ordination starts from the idea that such assemblages very gradually

### **3.1. Cluster analysis**

224 Multivariate Analysis in Management, Engineering and the Sciences

recorded using ordinal scale of Van-der-Marrel (1979).

presence/absence, or any number of abundance measures.

A quantitative survey of the vegetation is carried out during 2009-2010. In each of the studied types, soil and vegetative attributes were described within quadrates located along three 150m transverse transects. Quadrate size was determined for each vegetation type using the minimal area method. Considering variation of vegetation and environmental factors, forty five quadrates with a distance of 50m from each other were established in each vegetation type. Sampling method was randomized systematic. Floristic list, density and canopy cover percentage were determined in each quadrate. Vegetation cover data were

In fact, the cover data transformed using an eight-point scale ((0–1=0.5, 1–2.5=1.75, 2.5–

Sample data may include measures of density, biomass, frequency, importance values,

Ordination can help us find structure in these complicated data sets. By using various mathematical calculations, ordination techniques will identify similarity between species and samples. Results are then projected onto two dimensions in such a way that species and samples most similar to one another will be close together, and species and samples most

*A.sieberi-E.ceratoides* 28.2016 45.6333 22.1667 21 ... *H.strobilaceum* 8.04E+00 2.83667 26.8 29.3333 ... *A.sieberi-Z.eurypterum* 35.5167 50.0333 17.5 16 ... *Z.eurypterum-A.sieberi* 27.5933 36.44 16.6667 23.6667 ... *A.au-As.ssp-B.tomentelus* 28.48 47.6433 26.4533 33.1667 ... *S.rosmarinus* 28.15 37.475 22.8333 20.6667 ...

Data analysis was performed on the species, averaging all plots per site. All numerical

Classification method is an act of putting things in groups. Most commonly in community ecology, the "things" are samples or communities. Classification can be completely subjective, or it can be objective and computer-assisted (even if arbitrary). Hierarchical classification means that the groups are nested within other groups. There are two general kinds of hierarchical classification: divisive and agglomerative. A Divisive method starts with the entire set of samples, and progressively divides it into smaller and smaller groups. An agglomerative method starts with small groups of few samples, and progressively

analyses were done with the PC-ORD, V. 4 package (McCune and Mefford, 1999).

Q Q Q Q Q gr1 gr2 clay1 clay2 ...

5=3.75, 5–7.5=6.25, 7.5–12.5=10, 12.5–17.5=15, 17.5–22.5=20, 22.5–27.5=25, >27.5=30)

dissimilar from one another will appear farther apart (as shown at this study).

6 type 22 factor

**Table 2.** Data matrix using in Ordination

**3. Methods of classification analysis** 

Clustering, sometimes simply a synonym of classification, but more usually referring to agglomerative classification.

Clustering is a straightforward method to show association data, however, the confidence of the nodes are highly dependent on data quality, and levels of similarity for cluster nodes is dependent on the similarity index used. Krebs (1999) shows that mean linkage is superior to single and complete linkage methods for ecological purposes because the other two are extremes, either producing long or tight, compact clusters respectively. There are, however, no guidelines as to which mean-linkage method is the best (Swan, 1970).

The objective of Cluster Analysis is to graphically show the relationship between cluster analyses and your individual data points.

The resulting graph makes it easy to see similarities and differences between rows in the same group, rows in different groups, columns in the same group, and columns in different groups. Groups of rows and columns relate to each other, could be seen graphically. Twoway clustering refers to doing a cluster analysis on both the rows and columns of your matrix, followed by graphing the two dendrograms simultaneously, adjacent to a representation of your main matrix. Rows and columns of your main matrix are re-ordered to match the order of items in your dendrogram (Mucina, 1997).

Fig 1 showed dendrogram of Cluster analysis (study area: North East of Semnan rangelands, Iran). Grouping was performed using Euclidean distance and the Ward method. Species with less than 2 entries in the matrix were deleted from the analysis.

Classification and Ordination Methods as a Tool for Analyzing of Plant Communities 227

Cluster analysis can be performed using either presence–absence or quantitative data. Each pair of sites is evaluated on the degree of similarity, and then combined sequentially into clusters to

In fact, the aim is to form a hierarchical classification (i.e. groups, containing subgroups) which is usually displayed by a dendrogram (as shown in above). The groups are formed from the most similar objects are first joined to form the first cluster, which is then considered an object, and the joining continues until all the objects are joined in the final

The procedure has two basic steps: in the first step, the similarity matrix is calculated for all the pairs of the objects (the matrix is symmetric, and on the diagonal there are either zeroes – for dissimilarity – or the maximum possible similarity values). In the second step, the objects are clustered (joined, amalgamated) so that after each amalgamation, the newly formed group is considered to be an object, and the similarities of the remaining objects to the newly formed one are recalculated. The individual procedures (algorithms) differ in the

Major types of hierarchical, agglomerative, polythetic clustering strategies followed:

5. Centroid: It (weighted) mean of a multivariate data set. Can be represented by a vector. For many ordination techniques, the centroid is a vector of zeros (that is, the scores are centered and standardized). In a direct gradient analysis, a categorical variable is often

This analysis of the vegetation–environment relations and the classification of the Semnan rangelands, is also relevant for the rangelands of arid and semi arid in Iran, and provides a

Although clustering is an agglomerative classification technique and TWINSPAN is divisive, both produced comparable results. In addition, TWINSPAN provided indicator

In addition, to identify species with particular diagnostic value and to confirm clustering results, the floristic data were classified with the two way indicator species analysis

The TWINSPAN method is one of the more popular classification programs used in plant community ecology (Hill 1979; Hill et al. 1975). The two approaches differ between two

6. Ward's Method (Ward's is also know as Orloci's and Minimum Variance Method)

form a dendrogram with the branching point representing the measure of similarity.

cluster, containing all the objects (fig 2).

1. Nearest Neighbor 2. Farthest Neighbor

4. Group Average

7. Flexible Beta 8. McQuitty's Method

species.

(TWINSPAN) (Hill, 1979).

**3.2. TWINSPAN** 

3. Median

way they recalculate the similarities (Leps & Smilauer, 2003).

best represented by a centroid in the ordination diagram.

base line for other studies intended to conserve and restore this ecosystem.

**Figure 2.** Dendrogram of the cluster grouping of the study sites

Cluster analysis can be performed using either presence–absence or quantitative data. Each pair of sites is evaluated on the degree of similarity, and then combined sequentially into clusters to form a dendrogram with the branching point representing the measure of similarity.

In fact, the aim is to form a hierarchical classification (i.e. groups, containing subgroups) which is usually displayed by a dendrogram (as shown in above). The groups are formed from the most similar objects are first joined to form the first cluster, which is then considered an object, and the joining continues until all the objects are joined in the final cluster, containing all the objects (fig 2).

The procedure has two basic steps: in the first step, the similarity matrix is calculated for all the pairs of the objects (the matrix is symmetric, and on the diagonal there are either zeroes – for dissimilarity – or the maximum possible similarity values). In the second step, the objects are clustered (joined, amalgamated) so that after each amalgamation, the newly formed group is considered to be an object, and the similarities of the remaining objects to the newly formed one are recalculated. The individual procedures (algorithms) differ in the way they recalculate the similarities (Leps & Smilauer, 2003).

Major types of hierarchical, agglomerative, polythetic clustering strategies followed:


226 Multivariate Analysis in Management, Engineering and the Sciences

**Figure 2.** Dendrogram of the cluster grouping of the study sites


This analysis of the vegetation–environment relations and the classification of the Semnan rangelands, is also relevant for the rangelands of arid and semi arid in Iran, and provides a base line for other studies intended to conserve and restore this ecosystem.

Although clustering is an agglomerative classification technique and TWINSPAN is divisive, both produced comparable results. In addition, TWINSPAN provided indicator species.

In addition, to identify species with particular diagnostic value and to confirm clustering results, the floristic data were classified with the two way indicator species analysis (TWINSPAN) (Hill, 1979).

#### **3.2. TWINSPAN**

The TWINSPAN method is one of the more popular classification programs used in plant community ecology (Hill 1979; Hill et al. 1975). The two approaches differ between two

classification methods is that, TWINSPAN creates groups and also finds indicator species for those groups, while Cluster analysis requires a before-the-fact assignment of group membership as input. In this case, will be used hierarchical clustering to identify groups for vegetation classification. TWINSPAN produces no graphical output. The biggest volume of the result is the description of each division. For each division, TWINSPAN identifies the indicator pseudo species and their signs (positive or negative for one end of the ordination or the other) and lists the samples assigned to each subgroup. Two popular agglomerative polythetic techniques are Group Average and Flexible. McCune et al. (2002) recommend Ward's method in addition. Gauch (1982a) preferred to use divisive polythetic techniques such as TWINSPAN.

Classification and Ordination Methods as a Tool for Analyzing of Plant Communities 229

**Figure 3.** TWINSPAN of the vegetation cover in 270 quadrates and 9 species

This method works with qualitative data only. In order not to lose the information about the species abundances, the concepts of pseudo-species and pseudo-species cut levels were introduced. Each species can be represented by several pseudo-species, depending on its quantity in the sample. A pseudo-species is present if the species quantity exceeds the corresponding cut level.

TWINSPAN is a program for classifying species and samples, producing an ordered twoway table of their occurrence. The process of classification is hierarchical; samples are successively divided into categories, and species are then divided into categories on the basis of the sample classification. TWINSPAN, like DECORANA, has been widely used by ecologists.

For example, TWINSPAN was performed for vegetation analysis in 270 plots using ordinal scale of Van-der-Marrel (1979). The end of results file is the two-way ordred table summarizing the classification (Fig3). The table has species (not pesudo species) as rows and samples as columns.The results of TWINSPAN classification are presented in Fig.4. According to the above-mentioned table, figure, and also eigenvalue of each division, vegetation of the study area was classified in to six main types. Each type differs from the other in terms of it's environmental needs.

These types are as follows:

