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 104

table 4.3 (continued)
Impact of Githima community's Goals based on a Pulse Process analysis

community Goals

Ver tex

31 (Illiteracy) + + + + . + ± a + +

32 ( Health care) . . . . . . . . + a

33 (Lifestyle) . . . . . . . . .

34 (Birth rate) . . . . . . . . .

tot als
+ 154 22 24 20 20 1 20 9 17 21

− 20 3 3 3 3 0 3 0 2 3

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

4.3.2 g i t A n g u
Figure 4.4 is a cognitive map depicting Gitangu community's perception of factors
influencing agroecosystem health and sustainability. Vertices 6 and 11 had cognitive
centrality, each with a total degree of 10, followed by vertices 4, 3, and 1, which had
total degrees of 9, 8, and 7, respectively. The digraph has no sinks, but six of the
vertices (5, 10, 17, 18, 20, and 21) are sources.
The impacts of community goals—based on a geometric analysis—are shown in
Table 4.4. All goals except health, security, and secondary schools had indeterminate
impacts on vertices 11, 14, 15, and 16. This results from the presence of three equal-
length (three arcs in each) paths from vertex 6 to vertex 11, with two positive in effect
and one negative. Ambivalent impacts occur at vertices 13, 16, and 27, indicating
the presence of counteracting paths. The total number of positive impacts of com-
munity goals increases to 147 if arc [12, 27] is inverted and to 137 if it is removed.
In both cases, the negative impacts reduce to zero. Positive impacts also increase if
arc [27, 11] is removed (136) or inverted (128), but the negative impacts remain 10.
Removing arc [6, 12] increases positive impacts (to 113), but negative impacts are
reduced to 1. The number of positive impacts of community goals reduces to 70 or
less if any one of arcs [13, 4], [2, 3], [3, 8], and [3, 7] are inverted.
The digraph is unstable under all simple autonomous pulse processes if all arcs
are taken as having unit weight and time lag. The largest eigenvalue is 2.29. The
impact of community goals under a simple autonomous pulse process is shown in
Table 4.5. All impacts are positive or ambivalent except at vertex 27, where eight of
the goals have negative impact. Most (165/193) of the impacts of community goals are