EME 807
Technologies for Sustainability Systems

1.6 Types of Feedbacks and Their Effects

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1.6 Types of Feedbacks and Their Effects

Positive feedbacks

Imagine that you have some money in your bank account. The more money you have, the more interest you earn annually. That interest is added to your account balance, which earns you even more interest. So we can definitely see how A affects B, and B affects A in this case:

Positive feedback loop consisting of two stocks and two positive couplings (Money in bank and Interest)
Figure 1.11. Positive feedback loop consisting of two stocks and two positive couplings.
Credit: Mark Fedkin

As the two positive couplings act in circles within this loop, your account balance keeps growing. Such a feedback loop is called positive or reinforcing (here is the “+” sign in the loop), because the system sort of feeds itself continuously, amplifying the impacts over time. In the beginning, the growth may seem slow, but year after year, it goes faster and faster (see typical growth in savings in Figure 1.12). The more money is there, the more is added. This kind of growth is called exponential in mathematical terms (and there is an equation to describe this curve as a function of time).

Growth of account balance with 6% interest rate.
Figure 1.12. Growth of account balance with a 6% interest rate.
Credit: Mark Fedkin

Evidently, exponential growth can be a good thing or a bad thing, depending on what stock is growing. Here are some other examples of growth stimulated by positive feedbacks:

  • The more chickens there are in the barn, the more eggs they can lay. The more eggs there are to hatch, the more chicks will be produced that will grow the population of chickens.
  • The more soil is eroded, the fewer trees are able to grow on it. The fewer trees are there to stabilize the soil, the more erosion will occur.
  • The more individuals are infected with a virus, the more people they can potentially infect. The unrestricted dynamics of virus spread follow the infamous exponential curve.
  • In war or conflict, the more damage one side causes to the other, the more hatred and resistance is generated from the other side back to the first. Stronger pushback causes even harsher aggression, thus escalating the conflict.
  • The more a child plays a musical instrument, the more pleasure she gets from the sound, and the more willing she is to practice more.

Now think and add a couple of examples to the list. Can you draw a system diagram for any of these examples?

The positive feedback reinforces any change in whatever direction it goes. For that matter, it can be the reason for growth, and it can be the reason for decline and collapse. For example:

  • Profits fall because investments fall, but investments fall because profits fall…
  • The poorer people are, the harder for them to get an education. The less education they have, the harder for them to get out of poverty.

In the context of sustainability, positive feedbacks are classic de-stabilizers, often catering to short term gains. Although called “positive”, ironically, these feedbacks can be responsible for “runaway” and “snowballing” effects throwing system out of balance and often leading to crisis, especially when system growth starts to push against system boundaries.

Negative feedbacks

Consider this example. The population of deer in the area leads to a higher rate of road collisions. The collisions kill a certain number of deer, thus reducing its population. Once the population of deer goes down, the road collisions become less frequent.

Negative feedback loop consisting of two stocks and positive and negative couplings (# Deer and Collisions).
Figure 1.13. Negative feedback loop consisting of two stocks and positive and negative couplings.
Credit: Mark Fedkin

We can still clearly see here how the result of the first positive coupling affects the initial stock. Such a feedback loop is called negative or balancing feedback (here is the “—“ sign inside the loop), because it does not allow the deer population to grow out of control. Of course, it is a simplified example, and in reality, there may be other ways of regulating the deer population (e.g. hunting) and minimizing collisions (e.g. fences, driver alerts).

Negative feedbacks are mechanisms of stability. They work both ways, not allowing the stock to go too low or too high. These feedbacks are very common in the natural world, where many systems are homeostatic. Some more examples:

  • Warmer weather induces more evaporation from rivers and lakes, thus creating clouds, which cool the air temperature. Once the temperature is cooler, evaporation is reduced, thus resulting in fewer clouds and a sunnier sky.
  • Carbon dioxide concentration in the atmosphere stimulates plant growth. More plants consume carbon dioxide from the atmosphere due to photosynthesis thus bringing its concentration down.
  • Market price variation: if any product becomes of very high demand, its price grows until the supply meets the demand. If the price rises too high, fewer customers would buy it, so the price would go down again.
  • An office worker has to work, but feels sleepy, so he may drink some coffee to get his energy up. But drinking too much coffee can cause some health effects from too much caffeine, and he may decide to limit his coffee consumption. Here, the human decision to drink or not to drink coffee attempts to bring the energy level to the optimal level.
Now think and add a couple of examples to the list. Can you draw a system diagram for any of these examples?

When considering system resilience - the ability to bounce back from disturbances – look for negative feedback loops. Negative feedbacks are also culprits of resistance to change. Sometimes, changing undesirable existing practices is difficult because of feedbacks acting within the system.

Remember, in the case of positive feedback, any induced change accelerates; in the case of negative feedback, on the contrary, change slows down with time as the system reaches the optimum state.

How to determine the sign of feedbacks

Here is the rule of thumb for determining whether a feedback loop is positive or negative: combine signs of all couplings involved in the loops. For example: a loop of 2 positive couplings results in a positive loop: (+1)(+1) = (+1); a loop of 1 negative and 1 positive coupling results in a negative loop (+1)(-1)=(-1)

This is the same rule that we use in math when multiplying negative and positive numbers. If you count an odd number of negative couplings in the closed loop, the feedback is negative. If you count an even number of negative couplings in the loop, the feedback is positive.

This rule becomes especially useful when you analyze the feedback loops consisting of multiple couplings. Let us check out a couple of examples.

Examples of how feedbacks work in systems

Example 1: Albedo feedback in climate science.

Here we will consider the connections between four natural elements: solar energy absorbed by the Earth, atmospheric temperature, polar ice, and Earth albedo (reflective ability) (Figure 1.14). Polar ice caps play an important role in controlling the amount of solar radiation obtained by the Earth. Due to the high reflective ability of ice, overall Earth’s albedo increases with the expansion of polar ice and decreases when ice melts. Here is the positive coupling between polar ice and albedo. When albedo is high, a large fraction of solar radiation is reflected back to space and is not absorbed by the Earth. Therefore, we can draw a negative coupling arrow from albedo to solar energy absorbed by the Earth’s surface. Next, we will establish the positive coupling between the solar absorption and surface temperature. The more energy is absorbed by the earth’s surface, the more heat will be emitted off the ground into the atmosphere, thus raising the atmospheric air temperature. Finally, higher global air temperature will result in a decline in polar caps by causing ice to melt – hence the negative coupling arrow to close the loop of connections. We have a feedback in the system!

System diagram for albedo feedback loop.
Figure 1.14. System diagram for albedo feedback loop.
Credit: Mark Fedkin

To decide whether this feedback loop is negative or positive, we need to count all couplings involved: (+1)(-1)(+1)(-1) = (+1) positive feedback!

What does it mean, and what development can we expect from this system?

As we previously learned, positive feedbacks are destabilizing forces, which often lead to the accelerated shift of system from its current state. Indeed, the currently observed rise in global atmospheric temperature (global warming) is responsible for shrinking the polar ice caps. The fast decline in polar ice is observed in both poles and Greenland {REF}. This change gradually decreases the Earth’s albedo, and that makes the planetary surface absorb more solar radiation, thus pushing the atmospheric temperature further up. That secondary warming causes more ice melting etc. The more this process continues, the more warming is intensified, and the faster ice melts.

There is strong scientific evidence that the cause of the currently observed global temperature rise is anthropogenic CO2 emissions. And albedo feedback is an additional amplifier that can act fast and push the warming to much higher rates than CO2 alone.

This positive feedback can work in reverse as well. In the history of the Earth, the albedo feedback played a big role in establishing the “ice ages” on Earth, which were accompanied by very fast expansion of glaciers (polar caps) towards the continents.

Check Your Understanding

Probing Question

Consider how you would answer the question below, then click on the question to view the answer.



Example 2: Fish Pond

This example presents a much smaller system that is a very typical example of ecosystem reaching its carrying capacity. Imagine a small pond with a certain population of fish in it. To survive, the fish needs some food and oxygen in the water. The stock of fish is regulated by the factors such as reproduction rate and death rate. Let us identify some key couplings:

  • Reproduction rate is positively coupled with the number of fish. The higher the reproduction rate, the high the fish population
  • Death rate is negatively coupled with the number of fish. The high the death rate (for any reason, e.g. environmental conditions, disease, predators), the lower the fish population

We can depict these relationships in the system notation as follows:

relationships in the system notation (reproduction rate, fish, death rate)
  • Food availability in the pond favors fish growth and reproduction rate. So this is a positive coupling.
  • In a finite-size system like a pond, the food supply can be limited, so if it is too low to support all the fish, fish will starve and die. Hence we can assume the negative coupling with the death rate

Let us add it to the diagram:

diagram (reproduction rate - fish - death rate - food availability)
  • The same as with food, oxygen supply is important for fish population health and growth – this is another positive coupling.
  • The limited oxygen supply due to any factors (e.g. eutrophication, overpopulation, etc) will stress the fish, limits its reproduction, and possibly increase the death rate as well – this another negative coupling.
diagram (oxygen availability, reproduction rate, fish, death rate, food availability)

There are a couple more important arrows to add:

  • The more fish are there in the pond, the less food remains available (food is not unlimited). This is the same situation as we have in any ecosystem, including humans – you need more and more food to feed a larger population. So we will draw a negative coupling between Fish and Food availability.
  • The more fish are there, the less oxygen is available. While the atmosphere can be considered unlimited compared to the size of the pond, oxygen has a limited and quite low solubility in water. Fish will consume it by breathing, but also dead fish decomposition will consume some of it. So there is definitely a negative coupling between the Fish and Oxygen.

Putting these final two connections onto the diagram, we obtain:

diagram (food availability, oxygen availability, fish, death rate, reproduction rate)

Now let us identify the feedbacks. Are there any closed loops in the diagram? To have a complete feedback, we must be able to trace the couplings in one direction.

Check Your Understanding

Self-Check



Now let us determine whether each feedback is negative or positive using the rule of thumb explained in the previous sections. For example, for the upper left loop, starting with Fish, we have:

(-1)(+1)(+1) = (-1) - It is a negative feedback!

We can do the same to identify the other three loops in the diagram:

System diagram for Fish Pond system with four negative feedback loops
Figure 1.15. System diagram for Fish Pond system with four negative feedback loops (colored circles). Multiplication rule of thumb is shown for each loop to determine the feedback sign.
Credit: Mark Fedkin

This system appears to be full of negative feedbacks, and that is quite common for natural ecosystems. There are many regulating factors that keep the population of biological species in check. Once the system starts growing out of its capacity limits (food, oxygen supply), the feedbacks start dialing the numbers down until the optimum state (homeostasis) is restored. This example is a demonstration of how negative feedbacks tend to maintain the stability of the system at a certain level. Here we have as many as four mechanisms that help the system execute this goal.

Feedback loops with human decisions

The beauty and power of the system approach is that it can help explore inter-domain connections. Many systems currently exist at the interface of the natural and technological worlds and hence can include factors of economic, social, and environmental nature.

Many causal connections in the environmental systems are sort of predetermined and dependent on the laws of nature. For instance, if temperature increases, gas solubility in water decreases. If a ton of coal is burned, a certain amount of heat is released. If the ocean becomes more acidic, carbonate shells do not form. Those things are just physics and chemistry – there is no intelligent ruling behind them. However, causal connections may be different in human systems, because very often humans have a choice: to turn left or right; to approve or reject a policy; to invest or not to invest; to start the war or negotiation. Those decisions can make an impact within the system, but it does not mean they control the system. In fact, some intelligent (or dumb) decisions can very much be a product of system behavior. In other words, people may take decisions without realizing that they are being controlled by the system itself!

We mentioned before that one of the important system’s properties is function or purpose. The word purpose is more linked to human thinking, so systems can be created to fulfill a particular purpose. The word function is more typical for non-human systems, and function is often visible from the system’s behavior. Please note that human decisions can be made with a purpose in mind, but that purpose in the mind of an individual (perceived or apparent purpose) does not necessarily coincide with the purpose of the system (actual purpose). This is an important distinction. Here are some examples of such dual-purpose dilemma:

  • A musician may initially perceive their career in the music industry as art and a way of self-expression (perceived purpose), but the system may steer them towards songs that gain most popularity and make the most money (actual purpose);
  • A parent chooses to punish their child for bad grades with the purpose to make them work harder and to improve learning (perceived purpose), but punishment may cause the child to hide their grades or cheat for the sake of a better grade (actual purpose);
  • Cat meows loudly in the middle of the night to demand food from the owner. The owner gives the cat the food so that it let her sleep. But guess what – the cat comes back to meow every night now! Perceived purpose = keep the owner happy, actual purpose = keep the cat happy.

Understanding the system behavior can actually help us make smart decisions and steer the system purpose in the desired direction, even those decisions are not always intuitive.

Example 3: Honey Bee Hive

There are a number of environmental factors that sustain the purpose of the honey beehive. It needs a specific habitat with natural flora that provides bees with sources of nectar, clean air and water, which sustain vegetation. Human activities, such as agriculture using pesticides, industrial development, and water and air pollution can be highly disruptive to honey bee populations. We will try to put those factors onto the system diagram (Figure 1.16).

You can identify the positive feedback in this system, which is responsible for ecosystem growth under healthy environmental conditions, with bees and plants mutually benefitting each other. The anthropogenic (human activity) factors, shown by shaded circles, are negatively coupled with different factors in the system. We know that when a positive feedback exists in the system, it can work both ways. A drastic decrease in any of the factors in the loop can result in a fast decline of the entire system.

System diagram for honey bee hive system.
Figure 1.16. System diagram for honey beehive system. The anthropogenic factors (shown by shaded circles) negatively impact the bee population directly and by undermining the key stocks: flora and clean air.
Credit: Mark Fedkin

Human decisions can interfere. For example, a decline in the main stock – honey bee population - below a certain critical level can be an alarm signal for the local conservation agencies, who can work with policy makers to protect the natural habitat and resources from excessive exploitation or pollution. That additional factor, when introduced to the system, creates several negative feedback loops that forcefully regulate the industrial factors and keep the system in balance (Figure 1.17).

Figure 1.17. System diagram for honey bee hive system with policy intervention
Figure 1.17. System diagram for honey bee hive system with policy intervention (shown as colored diamond).
Credit: Mark Fedkin

Check Your Understanding

Probing Question

Consider how you would answer the question below, then click on the question to view the answer.



Sustainability in system thinking

So, what would make the system like the ones exemplified above sustainable? A simple answer within the arbitrarily identified boundaries would be: the balance of the main stocks. The balance does not mean constancy, but rather refers to a range where system can recover from stock fluctuations through internal mechanisms. We already saw how stocks can be regulated by feedback loops that involve both physical forces (natural laws) and intellectual forces (human decisions). Here, we come to an important observation: human decisions need to conform with the natural processes. Natural and human forces must work with each other, not against each other, to support the capacity of the life-providing stocks. This takes us back to the first Hanover Principle of sustainable design. Systems thinking brings us to the right mindset for applying sustainability principles to a variety of case studies we will discuss in the remainder of this course. To extend your learning of the systems approach, you can refer to the additional reading materials:

More reading on systems

Book: D. Meadows, Thinking in Systems, Chelsea Green Publishing, 2008.

This book is a really great reading regardless your professional area – it starts with the basics and leads through the fascinating gallery of systems covering a variety of areas and providing some good examples. It uses slightly different terminology in diagrams than we use in this lesson, but emphasizes the same key ideas.