Environmental Engineering Reference
In-Depth Information
Fig. 6.12 Dynamics of alternative ecosystem states, sensu Scheffer et al. (1993) (further explana-
tions in the text)
immediate return to the former stable state. For example, if the upper branch
represents a macrophyte-dominated lake and the lower branch an algal-dominated
lake, and nutrient input increases along the
x
-axis, then the nutrient input to the lake
must be reduced to a much lower level (left black dot) to cause a transition from
algal- to macrophyte dominated than the nutrient level (right black dot) at which the
reverse transition occurred. Dong et al. (2002) found the same dynamics for a
system of algae and periphyton in a model which describes functional group
interactions in the Everglades marshland. Currently this kind of dynamics is
intensively discussed for transitions in reefs systems from coral dominated to
algae dominated states (see also Chap. 17).
In the following, we use an abstract model to investigate the relations and conditions
of hysteresis. The calculation of the isoclines will facilitate the overview. Equation
(6.20) represents a predator-prey model with nonlinear interactions for the prey and a
logistic growth of the predators. In (
6.20
), the predator death rate
b
plays the role of the
critical parameter leading to the transition between different equilibria points.
þ
dN
1
dTime
¼
N
1
3
N
1
2
A
P
3
þ
P
2
P
1
N
1
þ
P
01
P
02
N
1
N
1
N
2
dN
2
dTime
¼
N
2
2
N
1
N
2
b
(6.20)
