Systems Theory/Evolution & Growth

Instability: Not Always Bad?

Instability in systems is not always bad. Growth and evolution are both potential properties of unstable systems and can occur only when there is a net change in one or more system stocks.

Growth

Growth, found in many forms, is essentially the change in the quantities of stocks (levels) within a system. Mostly thought of as a positive increase, growth is the change in the quantities of the system given the normal system structures, i.e. without changing the behavior of the system or the interaction of its components. Different forms of growth exist based on the system’s complexity. All that is required for the positive feedback loops to gain dominance is to have a very small net increase in the system.

Exponential Growth

The result of a dominance of positive feedback loops in a system is the exponential growth of its quantities. Exponential growth doubles the system stock quantities each period of time, regardless of the system size or complexity. This growth will continue within a system until it reaches the “carrying-capacity”. This capacity is the natural limits imposed on the system as to what it can sustain. As the limits are met, the negative feedback loops tend to gain dominance over the positive feedback loops. This slows the growth and even can cause decline in the system if the carrying-capacity limits were exceeded.

Limitations

Resources are not infinite, however. Eventually, real world systems must run out of the resources used to increase exponentially and may do so only after doubling the stocks a few times. Exponential growth in a system may be difficult to notice with only one or two iterations. As the time periods increase in the difference in the previous system state (i.e. the ability to notice change) will also double.

Note: To gain a conceptual idea of the true nature of exponential growth, see examples and explanations in pages 268-272 in Business Dynamics: Systems Thinking and Modeling for a Complex World, Sterman, 2000.

S-Shaped Growth

Exponential growth continues until negative feedback loops (possibly in the form of resource restrictions) slow that growth. The slowing of this exponential growth in return to a stable system can produce the common pattern of an “S-Shaped Growth”. This pattern is dependent on the responsiveness of the negative feedback loop. Delays in the negative feedback loop allow the exponential growth to overshoot the equilibrium goal then create an oscillating graph pattern. Additionally, if the carrying capacity of the system is overshot due to this delay in negative feedback, the result will be a decline (collapse) of the system’s stock(s). This decline often remains until the system reaches the carrying capacity and regains equilibrium.

Patterns of Growth

Growth in a system can occur in patterns other than the standard exponential or S-Shaped models. Linear growth, however, is often rare. What is thought to be linear is often a narrow field of view of a system’s growth. If widened, this narrow view often turns out to be exponential growth.

Evolution

When the growth of a system changes the structure or behaviors of a system, instability will occur, if only briefly. Spontaneity in the system or just simply the release of non-advantageous components makes the system evolve. This evolution is the creation of a new generation of the previous system. Evolution of a system is driven by selection processes that effect the growth and stability of the system. These selection processes select against disadvantages in the system, rather than selecting for processes thought to be advantageous.

Example

Examine the growth of a plant over time. Eventually, the plant’s root system will expand to meet the needs of the plant. However, this root system did not grow in a direct manner. Rather, roots grew in various directions with some roots finding less nutrients and water than others. Thus, the plant naturally selects away from underproductive roots and the productive roots in the nutrient-rich areas thrive.

The example illustrates the process of evolution throughout the plant’s root system (a sub-system of its own). Evolution is a by-product of the system’s growth and periodic instability. As the system experiences periods of growth, the evolutionary choices allow the system to remain productive. Without evolution, the system would eventually be unable to compete with other systems for resources.

References

• Cybernetics:Principles of Systems and cybernetics: an evolutionary perspective

http://intelegen.com/genius/systems_and_cybernetics.htm#Cybernetics%20The%20Principle%20of%20Autocatalytic%20Growth

• Evolutionary Cybernetics.

http://pespmc1.vub.ac.be/EVOLCYB.html

• Lucas, Chris. Emergence and Evolution - Constraints on Form.

http://www.calresco.org/emerge.htm

• Sterman, John. Business Dynamics: Systems Thinking and Modeling for a Complex World. 2000.