Use of Systems Theory, Directed Graphs, and Pulse Process Models in an Adaptive Approach to Agroecosystem Health and Sustainability - Integrated Assessment of Health and Sustainability of Agroecosystems - page 109

table 4.5 (continued)
Impact of Gitangu community's Goals based on Pulse Process analysis

community Goals

Ver tex

tot als
+

126 14 16 15 5 10 8 8 8 16 16 10

− 8 1 1 1 0 0 1 1 1 1 1 0

+ Positive impact; − negative impact; ± ambivalent; . no impact
a Impacts that are not sensitive to weight changes

4.3.3 k i A wA m A g i r A
Figure 4.5 is a cognitive map depicting relationships among factors influencing
health and sustainability as perceived by residents of Kiawamagira village. Vertex 2
has cognitive centrality, with a total degree of 15, followed by vertices 1, 17, and 24,
each with a total degree of 7. None of the vertices is a sink, but nine of them (3, 8,
15, 16, 20, 33, 34, 35, 37) are sources. Vertex 35 was ambivalent, being a source and
having both positive (providing employment and manure) and negative (contributing
to the pollution of the stream) impacts.
The digraph is balanced with reference to community goals, producing no
indeterminate or ambivalent impacts (Table 4.6). The impacts of community goals
increase to 107 if the arc [31, 30] is inverted. This also reduces the negative impacts
to 0. Removing arcs [2, 29], [24, 2], and [28, 2] reduces the positive impacts of com-
munity goals to 79, 81, and 83, respectively, while reducing the negative impacts to
1, 8, and 8, respectively. Inverting the arcs [24, 2], [1, 2], [2, 5], and [12, 2] reduces
the positive impacts of community goals to 75, 79, 81, and 82, respectively, while
increasing the negative impacts to 23, 21, 19, and 16, respectively. It is unstable under
all simple pulse processes if all arcs are given unit weight and time lag. The largest
eigenvalue under this process is 2.58. Simple autonomous pulses, with equal weights
and time lags on each arc, result in impacts similar to those determined through
geometric analysis since the digraph is balanced. Because of this, no impacts are
sensitive to changes in the weight.
There are two main strong components. The first consists of vertices 1, 2, 5, 25,
27, 28, 29, 30, and 31 interlinked into 7 two-arc and 2 three-arc positive-feedback
loops. The second component comprises vertices 6, 7, and 24. Among the simplest
stabilizing strategies for the first strong component is inverting any 3 two-arc cycles
linked to vertex 2. The second strong component is pulse stable under all simple
autonomous pulse processes. This component becomes value stable if arc [6, 24] or
arc [24, 6] is removed.