Cause–effect relationships

The final matrix was used to collect participants’ views on the relative strength of the interactions and a graph of cause and effect was produced. The sum of rows, showing how a component affects all other parts of the system (cause), and the sum of columns, the effect other components have on this diagonal element (effect), were plotted (effect against cause).

This graphical representation of cause and effect is presented in Figure 4. The central line drawn from the origin shows C-E space where cause and effect are equal.

The longer the distance between the origin and the point for a component, the greater the sum of cause and effect, showing strengthening interaction between the component and the rest of the system. Points on or close to the line show the component being affected by the system as much as the component affects the rest of the system. Points above the diagonal line, indicate that the component influences the rest of the system less than the system influences them, i.e.

they are subordinate components. Points below the diagonal line are dominant components that influence the system more strongly than the system influences them.

Air deposition, interception

Deposition, interception, rainfall

Deposition, interception, rainfall

deposition, interception,

rainfall

i = 1, j = 7 i,j = 1,7

deposition, interception,

rainfall

deposition, interception,

rainfall

resuspension Leaf translocation wash-off wash-off leaf-fall,

pruning translocation

resuspension translocation Wood and stem

throughfall +

stemflow throughfall +

stemflow translocation leaf-fall,

pruning translocation

resuspension splash splash Soil root uptake root uptake uptake resuspension

resuspension splash splash migration Ground cover

leaf-fall,

dieback splash/

resuspension

translocation exudation exudation,

root uptake Roots ^exudate _transfer, mycorrhiza

dieback

bioturbation bioturbation,

excretion mycorrhizal

processes Micro-orgs excretion

resuspension resuspension splash dissolution root uptake,

breakdown uptake Debris resuspension

resuspension translocation fruit-fall fruit-fall wash-off Fruit

Notes:

An example of the row and column notation is given in row 1 column 7.

FIG. 3. Interaction matrix with 9 diagonal elements describing the contamination of fruit trees following a deposit from atmosphere.

The diagram suggests that there are perhaps three clusters. The Soil component appears on its own to the far right above the central line (labelled 2), showing that soil interacts strongly with other components but is on balance subordinate to the rest of the system. The Air, Leaf and Wood and Stem components are in a cluster closer to the origin (labelled 3), showing a weaker interaction with the system as a whole than in the case of soil, but all of these are dominant components. The arc passing through this cluster is for a constant distance from the origin and is placed to highlight the fact that the participants thought the strength of interaction for both Air and Leaf with the rest of the system was similar.

The average scores (of 18 participants) for row and column totals are presented in Table 9 along with the relative standard deviation (RSD). The relative standard deviation gives a view on the differences in opinion within the working group. For example, although the participants were in agreement about the strength of the impact Air has on the system (RSD = 0.3) there was less agreement about the impact of the system on Air (RSD = 0.59). For Leaf (0.34 and 0.33, respectively) and Wood and Stem (0.37/0.38), their opinion appears more consistent. In the case of soil, participants were in agreement about the impact of the system on Soil (RSD = 0.37) but were in less agreement about the impact of Soil on the system (RSD = 0.43).

The final cluster (labelled 1) has the weakest interactions with the system and includes Ground cover, Roots, Micro-organisms, Debris and Fruit. This last cluster is where the participants showed most disagreement overall (RSD ranging from 0.44 to 0.89). The uncertainty in the result for Micro-organisms reflects our lack of understanding.

This analysis shows the strength of the interaction of specific components with the system as a whole. An interaction may be part of an important pathway, for example the impact of soil on plants is effected partly through the roots, but roots may score low overall, as there are relatively few interactions with other parts of the system. It is clear from the cause–effect diagram that a model for fruit will need to concentrate effort on the interaction of air, leaf, wood and stem with soil as a subordinate component. Although this is not an unexpected result for this scenario it is has been reached through consensus and is based on a systematic analysis of the problem.

TABLE 9. CAUSE EFFECT DATA SET (N=18) WITH RELATIVE STANDARD DEVIATION

Average (n=18) Relative standard deviation Cause

1. Air 21.0 0.3

2. Leaf 18.3 0.34

3. Wood and stem 15.6 0.37

4. Soil 17.9 0.43

5. Ground cover 9.4 0.68

6. Roots 9.8 0.65

7. Micro-organisms 9.0 0.89

8. Debris 11.2 0.52

9. Fruit 8.5 0.64

Effect

1. Air 8.8 0.59

2. Leaf 13.8 0.33

3. Wood and stem 13.4 0.38

4. Soil 21.3 0.37

5. Ground cover 16.6 0.44

6. Roots 10.3 0.47

7. Micro-organisms 8.7 0.82

8. Debris 13.2 0.55

9. Fruit 14.7 0.51

TABLE 10. RANKING INTERACTION OF DIAGONAL ELEMENTS

Influence of On Strength of interaction (n=18)

Air Leaf 4.9 Soil Roots 4.2 Air Soil 4.1

Air Ground Cover 3.8

Leaf Fruit 3.5

Leaf Soil 3.4

Leaf Debris 3.2

Leaf Wood and Stem 3.1

Wood and Stem Fruit 3.1

Roots Wood and Stem 2.9

Air Wood and Stem 2.9

Soil Micro-organisms 2.9

Air Fruit 2.8

Debris Soil 2.8

Ground Cover Wood and Stem 2.8

Soil Ground Cover 2.7

Wood and Stem Leaf 2.6

Wood and Stem Soil 2.6

Micro-organisms Roots 2.5

Wood and Stem Roots 2.4

Leaf Ground Cover 2.4

Air Debris 2.3

Wood and Stem Debris 2.3

Soil Fruit 2.3

Debris Ground Cover 2.3

Soil Wood and Stem 2.2

Fruit Soil 2.2

Soil Air 2.0

Roots Micro-organisms 2.0

Micro-organisms Debris 2.0