**2.3.2 Cluster analysis**

One key objective was the identification of commonalities or differences within the participants' perceptions concerning the local value of ecological indicators suitable for the assessment of sustainability of forest management. Cluster analysis allows the identification of uniform groups of data within a data set (called clusters), meaning groups of data that have sufficient similarities. Cluster analysis has already been applied to analyze perceptions of different stakeholders concerning C&I (Purnomo et al., 2005). Following Gower and Legendre (1986), the simple matching coefficient is used as similarity coefficient. This coefficient is calculated as follows (Gower and Legendre, 1986):

$$\mathbf{S} = (\mathbf{a} + \mathbf{d})/(\mathbf{a} + \mathbf{b} + \mathbf{c} + \mathbf{d})$$

with *S* the similarity coefficient and the standard notation *a* for the number of (+, +) matches, *b* for (+, -), *c* for (-, +) and *d* for (-, -).

Considering the made up data for workshop 1 and 2 and the example indicators 1, 2, 3 and 27 in Tab. 4, the similarity coefficient would be *S = (1+1) / (1+2+0+1) = 2 / 4 = 0,5*.

counted for new elements proposed by villages which got incorporated if they were

**1 2 3 … 27** 

proposed by more than 50 % of villages under each forest use type (Fig. 3a and 3b).

**Workshop 1** 1 1 1 … 0 **Workshop 2** 1 0 0 … 0 **Workshop 3** 0 1 0 … 1 **Village 1** 1 1 0 … 1 **Village 2** 0 0 1 … 1 **…** … … … … … **Village 12** 1 0 0 … 1

Table 1. Binary representation of the stakeholders' perceptions (note: This table is made up

Fig. 3. Decisional Framework for the final set elaboration of indicators. To be accepted in the final list, an indicator had to be accepted by minimum 50 % of the expert workshops and 50

One key objective was the identification of commonalities or differences within the participants' perceptions concerning the local value of ecological indicators suitable for the assessment of sustainability of forest management. Cluster analysis allows the identification of uniform groups of data within a data set (called clusters), meaning groups of data that have sufficient similarities. Cluster analysis has already been applied to analyze perceptions of different stakeholders concerning C&I (Purnomo et al., 2005). Following Gower and Legendre (1986), the simple matching coefficient is used as similarity coefficient. This

S = (a+d)/(a+b+c+d) with *S* the similarity coefficient and the standard notation *a* for the number of (+, +)

Considering the made up data for workshop 1 and 2 and the example indicators 1, 2, 3 and

27 in Tab. 4, the similarity coefficient would be *S = (1+1) / (1+2+0+1) = 2 / 4 = 0,5*.

**Indicator** 

**Stakeholder** 

and does not contain data of the study).

% of the villages for each forest use type.

matches, *b* for (+, -), *c* for (-, +) and *d* for (-, -).

coefficient is calculated as follows (Gower and Legendre, 1986):

**2.3.2 Cluster analysis** 

Given these similarity measures for all possible pairs of stakeholders, the data was organized into useful / meaningful groups, so that those within each group (cluster) were more closely related to one another than subjects in different clusters. Hierarchical clustering can either follow *agglomerative* or *divisive* methods (Janssen and Laatz, 2010; Manning et al., 2008). The output can be illustrated by a so called dendrogram (Fig. 4).

Fig. 4. Example of a dendrogram with fictive data. The agglomerative method makes series of fusions of the n objects into groups whereas the divisive method separates n objects into finer groupings.

As a result of various ways of calculating the distance between the clusters (Janssen and Laatz, 2010; Manning et al., 2008), different fusion procedures exist for the agglomerative method. In *single linkage*, the distance between two clusters is given by the value of the shortest link between two objects of the two clusters. In *complete linkage*, the distance between two clusters is given by the value of the longest link between two objects of the two clusters. In *group average linkage,* the distance between two clusters is defined as the average of distances between all pairs of objects, where each pair is made up of one object from each cluster (Fig. 5). This type of linkage appears to be the most useful for this study, because it takes into account all the possible pairs of distances between the C&I sets.

Fig. 5. Examples of three linkage calculation methods (adapted from Manning et al., 2008). The average linkage method is used in this study for its use of all possible pairs of elements.

Setting Up Locally Appropriate Ecological Criteria and Indicators to

Northern Vietnam (Pomel et al., 2007) the indicator was kept.

**Principle 1 : Ecosystem integrity is maintained** 

1.3.3 Maintain the water

1.3.6 Forest protection/valorisation for

**Criterion Indicator** 

and 3b).

1.1 Extent of forests

1.2 Forest ecosystem health

1.3 Forest ecosystem services

**3.2 Cluster analysis** 

Evaluate Sustainable Forest Management in Dinh Hoa District (Northern Vietnam) 211

The final set was composed out of 15 indicators under 6 criteria and 2 principles (Tab. 3a

One special case was decided to remain included in the final version of the C&I set, Indicator *"1.3.4 Minimization of soil degradation":* This indicator was accepted by 100 % of experts, special use and production forest villages, and rejected by three out of four protection forest villages. Dinh Hoa District is part of the mountainous regions of Vietnam which cover 3/4th of the country, having a complex topography and steep slopes (Werger and Nghia, 2006). Soil degradation and erosion is generally a great risk in the northern mountainous regions of Vietnam (Pomel et al., 2007; Thao, 2001). Land erosion has been identified to be a key point impacting many elements which influence farming systems (like water quality / quantity and soil fertility) thus causing crop yield reduction leading to a general income loss (Thao, 2001; Pomel et al., 2007). Though forests are the main subject of this study plus forests represent the land use option with the smallest erosion rate in

> **Workshops**

1.1.1 Maintain/Improve the forest area 100 100 100 100 Y 1.1.2 Control of forest area loss 100 0 0 0 **N** 

1.2.1 No chemical contamination 67 50 50 75 **N**  1.2.2 No natural degradation 100 100 100 100 Y 1.2.3 No human degradation 100 100 100 100 Y 1.2.4 Regeneration and forest structure 100 100 100 100 Y 1.2.5 Soil/Decomposition 100 100 75 100 Y

1.3.1 Product provision for local people 100 100 100 100 Y 1.3.2 Protection of riparian forests 100 0 0 25 **N** 

quality/quantity 100 100 100 100 Y 1.3.4 Minimize soil degradation 100 25 100 100 Y 1.3.5 Valuation of Carbon sequestration 100 0 0 0 **N** 

tourism 100 75 50 100 Y 1.3.7 Minimize floods 0 (new) 75 100 100 Y 1.3.8 Pleasantness of environment 0 (new) 100 100 100 Y

Table 3. a. Final Indicator selection. Principle 1: Ecosystem integrity is maintained.

As described in section 2.3.2, cluster analysis operates in successive stages of fusions, based on the calculation of similarity coefficients. The final structure of the grouping is determined by the desired number of clusters, or by a previously fixed level of similarity that is considered as "acceptable". There is no general rule for the minimal similarity level. In order to make the results comparable with a previous similar study implemented in Indonesia (Purnomo et al., 2005), 80 % of similarity are specified here as acceptable. For instance, the pairs of clusters (12, 13), (7, 12), (10, 11), (7, 10) and (1, 3) show 100 % similarity (Tab. 4),

**Protection Forest** 

**Special use Forest**

**Acceptance % of agreement on the acceptance of (Yes/No) concerned indicators** 

**Production** 

**Forest Indicator** 
