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 124

Geometric analysis was also useful in analyzing the predicates on which the com-
munity goals were based. An arc that, on removal or inversion, results in increase in
the number of positive impacts of community goals can be interpreted as represent-
ing either a constraint or a coping strategy. For example, the arc [6, 9] in the cognitive
digraph from Githima represents negative consequences of the use of agrochemicals
on human health, which constrain their use as a means to increase farm productivity.
In contrast, the arc [12, 27] in the Gitangu digraph represents the trend for younger
people to seek formal employment outside the village as a result of reduced avail-
ability of farmland and therefore represents a coping strategy. Arcs with removal
that results in the reduction of the positive impacts of community goals can be inter-
preted as representing the relationships on which the community goals are based.
An example is Kiawamagira village, where removal of arc [2, 29], analogous to
the assertion that improving dairy productivity would have no effect on incomes,
severely reduces the positive impacts of community goals. These findings therefore
provide an objective and reproducible approach to assessing agroecosystem health
and sustainability goals and objectives and the relationships between them.

4.4.4 p u l s e p r o C e s s m o D e l s
Analyzing the impact of community goals using geometric analyses is limited by
the existence of indeterminacies resulting from some kinds of path imbalances. The
pulse process provides some indication of what the impacts would be under certain
conditions. In this study, the usefulness of this approach was constrained by the
inability to obtain reasonably accurate weights for the arcs in the digraphs. In addi-
tion, the complexity of the digraphs makes it difficult to assess sensitivity to all pos-
sible weight structures. However, the assumption of unit weights and time lags for
the arcs may still provide some useful insights. Also, understanding the sensitivity
of the impact of community goals on the changes in weights of a particular arc pro-
vides a means of generating hypotheses regarding which relationships are likely to
be relatively more important regarding the system's health and sustainability. In the
Mahindi cognitive map, for example, increases in the weights of any of the two-arc
cycles linking vertex 4 to vertices 11 and 9 stabilizes many of the oscillating impacts
of community goals, with the direction of stability depending on the sign and weight
structure of the arcs.
An interesting feature was that the reranking of community goals that was carried
out following the cognitive map exercise was confluent with the summary of impacts
based on the pulse process model. This probably indicates that the communities per-
ceived the relationships to be more or less linear and the arcs as bearing unit weight
and time lags. It would be gainful to provide the results of the current analysis to the
communities for discussion and to give them an opportunity to modify the structure
of the cognitive maps or the ranking of their goals based on these findings.

4.4.5 A s s e s s m e n t o f v A l u e s t A b i l i t y

Stability was interpreted based on the assumption that there are always some limits
to growth in most real-world situations (Perry, 1983). This limit manifests itself—in