Controls on Ecosystem Structure and Function - Fundamentals of Ecosystem Science - page 217

simplest to fit to data, especially if data are scarce; they do describe the relationships
between controller and response variable well in some cases. They also are easy to
understand and apply—a given change in the controlling variable produces the same
proportional response over the entire range of the controlling variable.
Nevertheless, relationships between controller and response in ecosystems can follow
many different mathematical functions. A few nonlinear functions are of special interest.
Increases in the controlling variable can lead to decelerating ( Figure 11.6c ) or accelerating
responses ( Figure 11.6d ) in the ecosystem. Alternatively, the value of the response variable
may be maximized or minimized at some intermediate value of the controlling variable,
so that the sign of the relationship between the control and the response variable actually
changes ( Figure 11.6e ). The relationship between the control and the response variable
may include a threshold, at which the response of the system changes abruptly
( Figure 11.6f ). In all of these cases, the response of the ecosystem to a given change in the
controlling variable depends critically on the position of the system along the x-axis.
Some especially important relationships in ecosystem science are hysteretic
( Figure 11.6g ). In such cases, the value of the response variable depends on the history of
the system as well as on the present state of the controlling variable. Probably the best-
known case of hysteresis in ecosystem science is the response of shallow lakes to
phosphorus loading. Broadly speaking, shallow lakes can exist in two states: a clear-water
state dominated by submersed plants when phosphorus loads are low, or a turbid-water
state dominated by phytoplankton when phosphorus loads are high. These two states
differ in many attributes, including biogeochemical cycling, habitat value for fish and
water birds, and recreational value for people, so this transition is of considerable practi-
cal significance. Both states include a number of self-stabilizing mechanisms that resist
change back to the alternative state. As a result, the transition from the turbid-water state
back to the clear-water state occurs at a lower value of phosphorus loading than the
reverse transition from clear water to turbid water, and it is not always possible to predict
the state of the lake simply from current phosphorus loadings.
Knowing the shape of the mathematical function between controller and response is of
great intellectual and practical importance. For instance, consider how you might respond
to a proposal for a 25% increase in the controlling variable—say impervious surface in
a watershed—if you were managing an ecosystem variable such as nuisance algal blooms.
Knowing which of the forms given in Figure 11.6 that the response of the phytoplankton
would take would allow you to give a much more robust and informed opinion.

Feedbacks Are Almost Always Important
In highly connected systems such as ecosystems, interaction pathways often lead to
feedbacks. That is, a change in one part of the system causes a change in another part of
the system, which in turn comes back to affect the original component. Such feedback
loops may be short or long, and may be negative (the response from the system opposes
the initial change) or positive (the response from the system reinforces the initial change).
Feedbacks are almost always important in ecosystems, and untangling the effects of
feedbacks can be critical to understanding system response or predicting how an