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 121

6. Inadequate
security

iririka

12. Inadequate
health care

4. Poor health

5. Poverty

16. Firewood

3. Income

2. Well water
not potable

15. Employment

17. Forest

1. Water logging during
wet season

8. Water shortage
during dry season

18. Logging

9. Farm productivity

10. Use of agrochemicals

11. Crop diseases

7. Horticulture 14. Dairy production

20. Poor quality
seeds

21. Soil
erosion

13. Lack of fodder

23. Lack of unity
& solidarity

25. “Grabbing” of
public land

24. Poor
leadership

22. Frost

19. Kinale dairy
co-operative

27. People do not know
each other well

26. Lack of knowledge
and information

31. Go-downs

28. Lack of market for
produce

29. Newly settled and
from different areas

30. Inadequate
extension

fIGuRe 4.8 A cognitive map depicting perceptions of factors influencing the health and
sustainability in Thiririka intensive survey site, Kiambu District, Kenya, 1997. See CD for
color image and key.

Positive impacts also increase (to 102) if arc [11, 7] is removed. In all three cases,
the negative impacts are eliminated. Inversion of any one of the arcs [7, 15], [15, 3],
and [7, 9] reduces the positive impacts of community goals to 58, 64, and 64, respec-
tively, while the negative impacts are unaffected except for arc [7, 15], for which the
negative impacts increase to 9.
The digraph is unstable under all simple autonomous pulse processes assuming
unit weight and time lags on all arcs of the digraph. The largest eigenvalue based on
unit arc weights and time lags is 1.62. Based on this pulse process, agrochemical use
and crop diseases have oscillating impacts on vertices 7, 9, 10, and 11. Crop diseases
also have oscillating impacts on vertex 15. Impacts of community goals on other
vertices remain as in Table 4.10. Most (97/107) of the impacts are not sensitive to
increases in weights. The 10 that are weight dependent are the impacts of agrochemi-
cal use and crop diseases on vertices 3, 4, 5, 6, and 8. Impacts are most sensitive to
increases in the weights of arcs [11, 10] and [10, 11].
The digraph consists of five strong components, two of which have two-arc feed-
back loops involving vertices 10 and 11 in one (negative) and 14 and 19 in the other
(positive). The largest strong component, comprising vertices 3, 4, 5, 6, and 9 in 2
two-arc and on three-arc positive-feedback loops, is unstable. One of the simplest
strategies for value stabilizing this component is inverting any one of the arcs in any
of the two-arc feedback loops. The next largest component comprises vertices 23,