1 Feedback Loops in Flower Gardening Paul Newton, Linda Tompkins, Marianne Krasny, and Karl North October 29, 2004

2 Diagramming feedback loops can help us to solve practical problems. It can help us to understand how different factors influence each other. Use the scenario on the slides 3- 9 to introduce feedback loops to students.

3 0 maximum possible Behavior-Over-Time-Graph (BOTG) Year The year is Students have observed declining flower production in their school flower garden (the acreage of the garden is constant). The students are concerned that their gardens production rate might continue to decline in the future. They would like to reverse the downward trend. Their Problem Statement: What can we do to create the desired future? Desired Future Feared Future Flower production (flowers/year)

4 What caused this decline in production? You can develop a dynamic hypothesis for changes in flower production. Lets Begin with flower production, which is the variable of concern graphed in the Behavior-Over-Time-Graph (BOTG) on the previous slide… Dynamic Hypothesis

5 The more flowers produced per year, the more seeds are produced… The (+) sign signifies that a change in flower production causes a change in seeds in the same direction as the change in flower production. This would also indicate that a decline in flower production would result in a decline in seeds produced. Dynamic Hypothesis

6 And the more seeds, the more flowers are produced. These two links form a Reinforcing [R] feedback loop. A reinforcing loop acts to reinforce a change in any variable in the loop, in the same direction as the original change. That is, if any variable in the loop is increased, each circuit around the loop acts to increase the variable above what it would have been had the change not occurred. (Conversely, if any variable in the loop is decreased, each circuit around the loop acts to decrease the variable below what it would have been had the change not occurred.) The plus arrow thus indicates the two variables change in the same direction. The more flower production, the more seeds; the more seeds, the more flower production, ad infinitum, producing continuously increasing growth in both seeds and flower production. Dynamic Hypothesis

7 But more flower production, over time, acts to decrease soil quality… Hence the (-) sign signifies that a change in flower production causes a change in soil quality in the opposite direction from the change in flower production. As flower production increases, soil quality decreases. If fewer flowers were grown, the quality of the soil would decrease less than had fewer flowers not been grown. Thus the (-) sign indicates the two variables change in the opposite direction. Dynamic Hypothesis

8 Reductions in soil quality cause corresponding reductions in flower production. These two new links form a Balancing [B] feedback loop. A balancing loop acts to reverse a change in any variable in the loop. That is, if any variable in the loop is increased, each circuit around the loop acts to decrease the variable below what it would have been had the change not occurred. (Conversely, if any variable in the loop is decreased, each circuit around the loop acts to increase the variable above what it would have been had the change not occurred.) The minus arrow thus indicates the two variables change in the opposite direction. Flower production, in the absence of other influences, always causes soil quality to decrease. Decreased soil quality causes a decrease in flower production. Shifts in feedback loop dominance cause changes in behavior. Refer back to the graph on slide 3. What caused the growth the first couple of years? What caused the decline? Looking at the diagram above, the first loop dominated early on, and the second after that. (See more discussion on the following slide.) Dynamic Hypothesis

9 Why Feedback Loops? Feedback loops cause behaviors over time. Shifts in feedback loop dominance cause shifts in behaviors over time. By drawing feedback loops, you can understand how behaviors change over time. For example, the reinforcing [R] loop could be responsible for the increasing rate of flower production beginning in 2000 (more flowers more seeds more flowers more seeds ad infinitum). Then, sometime in 2001, the curve reverses. Even though flower production is still increasing, it increases more and more slowly. This declining rate of flower production indicates that, with declining soil quality, the balancing [B] loop is now stronger than the reinforcing [R] loop. The balancing [B] loop initially acts to slow increase in flower production, and then causes flower production to decline beginning around Flower Production (flowers/ year) Desired Future Feared Future Feedback loops cause behavior over time. [R] Loop Dominant [B] Loop Dominant Year

10 1. Now that your students have been introduced to feedback loops, they can work in small groups to draw a second behavior-over-time-graph (BOTG). This graph should show changes in soil quality for the past four years, and should project desired and feared future soil quality over the next four years. Student BOTGs should look something like the following BOTG sketch, showing a decline in soil quality after a year or two of flower production, with continued decline to the present (2004). It should also show a feared future of continuing decline in soil quality causing continued decline in flower production, and a desired future of improvements in both soil quality and flower production. Student Activities

11 0 maximum possible Behavior-Over-Time-Graph (BOTG) Desired Future Feared Future Flower production (flowers/year) Year Soil Quality Soil quality at which the B Loop begins to dominate B Loop Dominant R Loop Dominant

12 2.Students should then draw at least one feedback loop that could act to create the Desired Future. Two potential feedback loops for the teachers use are shown on the following slides (through slide 15)

13 Reductions in soil quality cause corresponding reductions in flower production. These two new links form a Balancing [B] feedback loop. A balancing loop acts to reverse a change in any variable in the loop. That is, if any variable in the loop is increased, each circuit around the loop acts to decrease the variable below what it would have been had the change not occurred. (Conversely, if any variable in the loop is decreased, each circuit around the loop acts to increase the variable above what it would have been had the change not occurred.) The minus arrow thus indicates the two variables change in the opposite direction. Flower production, in the absence of other influences, always causes soil quality to decrease. Decreased soil quality causes a decrease in flower production. Dynamic Hypothesis (previous slide sketch repeated here for continuity)

14 Flower production decreasing to less than desired flower production causes gardening practice quality to increase. Increased gardening practice quality in the areas of soil enrichment, especially fertilizing (whether organically or not), causes increased soil quality. Increased soil quality causes increased flower production, completing the description of a new balancing feedback loop. Over time, this balancing feedback loop causes flower production to move toward desired flower production. Dynamic Hypothesis

15 Improved gardening practices also cause increased flower production via mechanisms in addition to enhancement of soil quality. This creates another balancing feedback loop that, over time, tends to cause flower production to increase toward desired flower production. Dynamic Hypothesis

16 3.As a third exercise, students could be asked to draw other feedback loops that they come up with. These loops may, or may not, relate to the BOTGs already drawn. The teacher may choose to give the students a hint that the new loops could relate to variables such as customers, disease, and diversity. The following slides show some, but certainly not all, possibilities that might be useful to the teacher in reviewing student work.

17 Improved gardening practices also cause increased flower production via mechanisms in addition to enhancement of soil quality. This creates another balancing feedback loop that, over time, tends to cause flower production to increase toward desired flower production. Dynamic Hypothesis (previous slide repeated here for continuity)

18 Dynamic Hypothesis The more flower production, the more customers may be solicited to purchase them, and therefore the more customers.

19 Dynamic Hypothesis And the more customers, the more flowers they demand, yielding more flower production. These 2 links form another Reinforcing (R) feedback loop acting to increase both customers and flower production.

20 Dynamic Hypothesis The more customers we have, the more our desired flower production increases so we can meet the demand. Increased desired flower production spurs us to improve our gardening practice quality, which then causes an increase in flower production. And more flower production gives us the opportunity to solicit and capture more customers. Thus is formed yet another Reinforcing (R) feedback loop.

21 Dynamic Hypothesis + More flower production will also mean more diseases, a positive link.

22 Dynamic Hypothesis + But, an increase in disease will cause a decrease in flower production. These last two links form another Balancing (B) feedback loop.

23 Dynamic Hypothesis + Our gardening practice quality also influences the incidence of diseases. The addition of this loop adds two more loops, one reinforcing and one balancing. Can you find and trace out both loops?

24 Dynamic Hypothesis + Research supports that diversity of flowers acts to reduce diseases.

25 Dynamic Hypothesis + And fewer diseases enable more diversity. (Also, more diseases reduce diversity, as diseases often are species-specific.) Thus a reinforcing loop is formed that can act either to increase or decrease both diversity and disease.

26 Dynamic Hypothesis + The more diversity, the more potential customers will be interested in our flowers, and therefore the more customers we will have. Less diversity will likewise reduce our stock of customers. Adding this link creates three new feedback loops (only two loop symbols were added). Two feedback loop symbols were added here, but actually, adding this link creates three new feedback loops, one reinforcing and two balancing; can you find them?

27 Dynamic Hypothesis + And finally (because were running out of space!), more customers means that more diversity will be demanded. Customers will want a variety of flowers to choose from for different occasions. This creates another reinforcing feedback loop that can act, over time, to either continually increase, or decrease, both customers and diversity.