2 Chapter 2: Systems Thinking: a New Way to Tackle Problems

When President Theodore Roosevelt created the Grand Canyon National Game Preserve on November 28, 1906, he set aside the finest deer herd in America. But in doing so, he unintentionally wrote the first chapter of a harsh lesson whose impact is felt to this day in every deer management plan on the continent.

James B. Trefethen, 1967^[1]

Your experience with managing the Kaibab mule deer population probably highlighted just how hard it is to make good decisions when navigating the pressures created by the hopes and expectations of stakeholders like the President, your boss, the American public, and yourself. When you add to those pressures the complex interactions that make up the ecosystem on the Kaibab plateau, you’ve got a recipe for disaster!

Why is that? It’s because that, on their own, human beings are not capable of anticipating the behavior of complex systems like the one you’ve just experienced (Carranza & Rego, 1999) (Arthanari, 2015). There is simply too much going on, and it can take a long time for our actions to play out. We can be deceived by short-term success, all the while unknowingly laying the groundwork for a long-term disaster (Ackermann, Andersen, Bryson, Eden, Finn, & Richardson, 2000).

If you saw the deer population eventually explode to unmanageable levels followed by a collapse due to significant degradation of the Kaibab forest, you should take comfort in knowing that this was the same experience of the people who were tasked with managing the Kaibab in the early 1900’s.  They too found it difficult to get this big complex system of expectations and natural environmental forces to work together toward a desirable outcome. Their best-intentioned actions actually made things worse. Forest and wildlife managers in the region have continued to struggle with the aftermath of the crisis on the Kaibab up to the present time!

Now it’s time to take a fresh look at this problem. We’ll do so by asking you to figuratively put on a new set of glasses so you can see the Kaibab problem in a new light – as the product of an underlying system. To get us started, we first have to define what we mean by saying that something is a “system.”

2.1. What does it mean to call something a “system?”

A system is a collection of interconnected things that together operate toward a certain end (Ackoff, 1994). For example, your body is a system. It’s a collection of organs (heart, lungs, stomach, brain, etc.) that work together to keep you alive and healthy. While distinct from one another, the parts of your body are not independent. Some parts could exist “on their own” (at least for a while), but they have also evolved to be highly interdependent. In systems lingo, we say that your body’s organs are tightly coupled to one another. If one part is injured or removed, the entire body must somehow compensate.  Studying the body’s organs in isolation may be useful and necessary, but to understand how the body works, we need to know more than how the individual parts work. We must also describe how those parts work together, and to what ends they work together.  We need to study the body as a system.

Just like your body, the Kaibab plateau is comprised of many different interacting parts. Instead of working within the confines of your body, the elements in the Kaibab system operate across a wide variety of scales of time and space. The Kaibab system includes populations of living organisms like mule deer, mountain lions, cattle, and various types of plants. This system also includes physical resources (such as soil, air, and water). To make things even more complicated, this system involves political, economic and social forces that shape the way humans interact with the Kaibab through activities like hunting, ranching, or recreation.

All of these elements of the Kaibab system depend on and affect each other in a kind of give-and-take dance.   The animals depend on each other and on the plants for survival. In turn, the plants depend on the work of animals to break up and fertilize the soil as they move across the landscape. The plants depend on the soil, water, and sunshine, but they also impact these things by creating shade that reduces the rate at which water evaporates from the soil. Human activity depends on all of these things working well together. And, of course, humans do things that impact the overall health of the natural ecosystem in both positive and negative ways.

Because of this constant give-and-take dance between all of the components of the system, the status of the system is dynamic (Andersen et al., 1983). That is, the system status is constantly changing. It may not seem that way when you look at family vacation photos from the Kaibab. That’s because many of the changes in this system take days, months, years, or even centuries to play out, and photos capture only a single moment in the life of that dynamic system (Richardson and Pugh, 1985).

This means that problems like the one you’ve encountered on the Kaibab involve dynamic systems – systems that constantly change over time. In order to figure out how to address problems like the Kaibab challenge, we have to develop skills at working with these kinds of systems.

In the following sections, you will learn how to use three important systems thinking practices to help you start “seeing the system beneath the problem.” These three practices are listed below.

2.2 Seeing the System Beneath: Evaluating behavior over time

In order to combat the common mistakes caused by event-oriented thinking, systems thinkers practice a simple, yet wholly different approach to describing problems. They describe them in terms evolving behavior over time. This means that, rather than thinking of the problem only in terms of the current state of affairs, or as something caused by someone or an event in the recent past, systems thinkers describe problems in terms of their long-term history.

One of the most powerful tools for doing this is the behavior over time graph (BOTG).  A BOTG is a plot with time on the X-axis and with one or more measures of problem severity on the Y-axis. Such a graph reveals the evolutionary history of the problem.  It shows periods when the problem was getting worse and periods when it was improving. It helps us to evaluate whether the problem is a recent development or something that has been building over time.  It also gives us a sense of how far back in time we need to go in order to understand the roots of the problem.

2.2.2   How to create a BOTG

A BOTG is made by plotting the time trajectory of a few carefully-chosen variables. These variables are chosen so as to give a reasonable picture of the status of the system at any given point in time. For example, with your friend’s car, it might be reasonable for them to keep track of some important indicators of the car’s mechanical performance. Given that they seem to be worried about oil usage, it makes sense that they would plot the number of quarts of oil added each month. They might also plot something like their car’s gas mileage every time they fill up. Notice these two variables are not chosen in order to identify the causes of the problem. They are chosen to show the status of the system (i.e., the car) over time. By looking at a plot of these two variables over time, your friend might get an idea of whether the problem is a recent thing, or something that has been going on for a while.

The BOTG gives a more complete picture of what’s going on. It shifts our attention from thinking exclusively in terms immediate causes (“My roommate messed up my car”) and opens us up to considering if there is a deeper, ongoing system that creates the time trajectory in the BOTG. If there is, then we can focus on understanding that system. Then we can diagnose the real causes of the problem. This gives us a much better chance of finding effective ways to intervene. Let’s suppose that your friend has made such a graph, and it looks like the BOTG in Figure 2.

What does the BOTG for your friend’s car problem suggest? It appears that the problem with the car didn’t “just happen” when the roommate borrowed it.  Instead, the graph shows that the car has exhibited increasing oil usage and deteriorating gas mileage for at least the last 15-20 months. The problem existed long before the roommate borrowed the car.

Now it’s time for you to get some practice making a BOTG. As you do this, make sure you follow the following best practices.

2.2.3  Augmenting the BOTG to set goals tell a story about the problem

As you’ve seen with the example about your friend’s car, the BOTG is an incredibly powerful tool to help you begin to use systems thinking when tackling a problem.

You can also use the BOTG to help your team think through your goals when tackling a problem involving a complex system. In particular, the part of the graph showing the “hopes and fears” implicitly identifies what kind of future trajectory you’d like to avoid and what you’d hope to see if your team’s work is successful.

Finally, the BOTG can be a visual aid to help you “tell the story” about the length of time over which the problem has developed and whether the problem just appeared “out of the blue” or whether it was the “tip of the iceberg” involving something deeper. The BOTG forces you to ask, “What is going on here?” It encourages you and your team to start thinking about the system underneath it all, and how that system creates the behavior you see in the graph. See, for example, the annotated BOTGs in Figures 2b and 2c show time trends of two very different problems in the U.S.:   mass shootings, and per capita cigarette consumption. Each of these graphs tells a powerful story about the problem. Figure 2a highlights the recent trend toward ever more frequent mass shootings and toward greater numbers of fatalities over the past. Figure 2b highlights the progress made from 1950 through 1995 in reducing cigarette consumption (and its related health effects.

2.3. Seeing the system beneath: Looking for feedback loops

By thinking about behavior over time and displaying that behavior in a BOTG, system modelers turn their attention to the underlying system driving that behavior. One important way of examining the system is by looking for feedback loops. A feedback loop is a circular chain of cause-effect relationships that creates a powerful force affecting how a system behaves (Ackermann et al., 2000; Arthanari, 2015) (Proceedings of the 27th International Conference of the System Dynamics society, 2009) and (Carranza & Rego, 1999).

Feedback loops are extremely important in any dynamic system. In fact, it’s because of feedback loops that the sun keeps shining, rain keeps falling, and ecosystems continue to function.  Feedback loops keep governments in power, and they fuel war.  It’s also because of feedback loops that an ocean fishery or a human society might collapse (Bueno, 2011).

Feedback loops are primal forces that dictate the behavior of systems like the one you’ve just experienced on the Kaibab plateau.  Such systems involve an interplay ― a give-and-take ― between humans, natural laws, and the struggle for survival among plants and animals. These circular chains of cause and effect exist because your actions are not independent of the other actors in the system (the stakeholders, animals, and plants). When you act, they respond, and their actions “work back” to impact your future actions ― a circle of cause and effect (see Figure 3).

These feedback dynamics are extremely powerful, but they often work under our radar. This can happen because some feedback forces take a long time to gain momentum and exert their influence. Or, we may simply be blind to other actors in the system and how our actions interact with theirs.

Recognizing the presence of feedback and learning how to identify it, describe it, and explore its role is central to your ability to understand the roots of the problem and the behavior of the overall system. The goal is to ultimately reach a point of understanding where you can more reliably predict how the future might unfold, and thereby adjust your actions with an eye on the big picture, always watching the “long game” – the long-term consequences of your actions.

2.3.1. The causal loop diagram. A tool for drawing and examining feedback

One of the tools that systems thinkers use to look for feedback loops is the causal loop diagram (or CLD).  These diagrams provide a powerful visual tool for scoping out the feedback structure in a problem. They are also useful as storytelling devices for explaining to others how the system and its accompanying feedback work to create the problem.

Figure 4 shows an example of a causal loop diagram.   The named quantities in the CLD represent system characteristics or variables that can change in value in response to one another.  These variables represent characteristics of the system that can increase or decrease over time.

The curved arrows are causal links that show the direction of causal influence. For example, the arrow from Deer population to Deer births implies that changes in the size of the deer population cause changes in the number of deer born each year.  The “+” and “-” labels on the arrows are causal link polarities that indicate how the cause-effect relationship works.

• A “+” polarity means that changes in the causal variable will cause the affected variable to move in the same direction. This means that, if the causal variable were to increase, that would cause the affected variable to be higher than it would have been without the change. Conversely, if the causal variable decreases in value, the affected variable will be lower than it would have been without the change. For example, if the Deer births per year were to increase, then the Deer population would be higher than it would have been without that change. This is why there is a causal link with “+” polarity running from Deer births per year to Deer population.
• A “-” polarity means that any changes in the causal variable will cause the affected variable to move in the opposite direction. Hence if the causal variable were to increase, then the affected variable would be lower than it would have been otherwise. Conversely, if the causal variable decreases in value, the affected variable will be higher than it would have been otherwise^[2].  For example, if the Deer deaths per year were to increase, this would cause the Deer population to be lower than it would have been without that change. Hence, there is a causal link with “-” polarity running from Deer deaths per year to Deer population.

2.3.2 Using the CLD to Explore Two Types of Feedback

The CLD in Figure 4 shows two circular chains of cause and effect, corresponding to two different feedback loops.  One loop involves the circular cause/effect relationship between the Deer Population and the Deer Births per Year.  The other feedback loop involves a circular cause/effect relationship between the Deer Population and the Deer Deaths per Year.

These two feedback loops represent the two different types of feedback that exist in complex systems: balancing feedback and reinforcing feedback.

2.3.3. Balancing Feedback – The Constraining Force Against Runaway Behavior

In Figure 4, the feedback loop involving the Deer Population and Deer Deaths per Year is an example of balancing feedback.  To see why this name makes sense, imagine what would happen if the Deer Population were to increase. This would result in more Deer Deaths per Year (as per the causal link with + polarity from the Deer Population to Deer Deaths per Year). But, if the number of deaths goes up, those increased deaths will cause the population to be lower than it would have been otherwise (note the “-” polarity on the link pointing from Deer Deaths per Year to Deer Population).  We mark balancing feedback loops with symbol (called the loop polarity).  The direction of the circular arrow provides a visual clue to the direction of the causal flow around the loop.

The balancing feedback loop works to counteract or balance the original increase in Deer population. You can see evidence of balancing feedback at work when the time BOTG shows progress toward some sort of level condition (called an  equilibrium level or a steady state). Also, if a BOTG shows an oscillating behavior around an equilibrium point, that is also an indication that a balancing feedback force is in effect. Imagine a marble in the bottom of a bowl. If the marble is moved away from its resting place at the bottom of the bowl, the force of gravity and the walls of the bowl work together to eventually force the marble back toward the center. That’s what balancing feedback does. It serves as a kind of “magnet,” trying to pull the system back to some sort of equilibrium.

Another way of saying this is that balancing feedback creates goal-seeking behavior.  It works to push the system toward some sort of stable goal. Sometimes the “goal” represents a target consciously chosen by someone who wants to push and maintain the system at that level. For example, with the Kaibab deer, you had a goal of helping the deer population grow to a level around 30-40 thousand deer and then remain steady there. Your actions and responses to the year-by-year reports comprised a balancing feedback loop that worked to push the system toward this goal.

Other times, the “goal” of a balancing feedback loop may not be consciously chosen by anyone, but it may instead be a consequence of natural laws or constraints that determine where the system is most stable. With the Kaibab deer, the natural resources on the Kaibab, the weather, soil, etc. all combine to dictate how many deer the system can sustain in the long term. That sustainable number is called a “carrying capacity” of the ecosystem. It’s not chosen by any person. It’s a product of the natural forces of nature, and the ecosystem will work to “control” the deer population to that level.

Notice that we’ve identified two different goals for the Kaibab deer population: (1) your goal of 30-40 thousand deer, and (2) nature’s goal population size based on the natural carrying capacity. These two goals are not necessarily the same.  Which goal will the system move toward? Which balancing feedback loop will ultimately “win?”  In the case of the Kaibab deer population, the answer to this question really depends on how much influence you actually have, compared to the influence that nature exerts. Of course, nature usually wins! The problem with predicting the exact outcome is that the way nature exerts its influence might be different than what you expect. Your actions to control the deer population to 30-40 thousand deer may impact the ecosystem in ways that change the natural carrying capacity. It may degrade to some lower value ― especially if you push the system to have so many deer that they over-consume the natural resources on the Kaibab!

2.3.4. Reinforcing Feedback – The Engine of Accelerating Growth

And this is only half of the story! There’s yet another kind of feedback at work in complex systems: reinforcing feedback. You can see an example of this kind of feedback in the other circular causal chain Figure 4. Notice that there is a feedback loop running from Deer population toward Deer births per year, and then back to Deer population. As the Deer population increases, this causes the Deer births per year to also be higher, which in turn causes the Deer population to increase even more.

This is a reinforcing feedback loop because it reinforces movement away from any stable condition and builds momentum toward even more change in the same direction. Reinforcing feedback creates a snowball effect that builds faster and faster movement away from equilibrium. Left unchecked, the reinforcing feedback in Figure 4 would push the Deer Population toward ever faster growth and would eventually cover the planet with mule deer! We label reinforcing feedback loops with the symbol , as in the figure. The circular arrow shows the direction of causal flow around the loop.

Feedback loops can be more complicated than the simple two-variable examples just discussed.  For example, Figure 5 adds a new feedback loop to the earlier one. This new feedback is highlighted with bold arrows to make it easier to see. The next Action Item gives you a chance to explore this feedback loop.

2.3.5 Competing Feedback Loops

Searching for feedback loops is a powerful way of looking at a problem. Instead of thinking about isolated cause/effect relationships, or looking for a single cause of a problem, we now focus our attention on the interactions between multiple factors. And those interactions show up as a contest between competing forces ― reinforcing and balancing feedback loops. Some loops work to push the system toward unfettered growth, while others try and push the system toward some sort of equilibrium. For a while, one particular feedback loop may dominate the behavior of the system.  Later, things may change so that a different feedback loop begins to assert its influence and dictate how things play out.

You can often see evidence of this tug-of-war between balancing and reinforcing feedback by examining the BOTG for your problem. Reinforcing feedback creates rapid, exponential growth, while balancing feedback creates movement toward some sort of equilibrium (either a “flat line” equilibrium or oscillation around an equilibrium).

For example, imagine that there was an abundant food supply for the Kaibab deer and very few predators. Under those conditions, we’d expect the reinforcing feedback loop in Figure 5 (Deer Population ↔ Deer Births per Year) to dominate the system. The deer would flourish, produce offspring, and grow rapidly. Of course, the deer population would eventually get so large that there would be too many deer for the ecosystem to support them. At that point, more deer would starve and deaths would mount. During that period, other feedback loops would begin to dominate the system, pushing the Deer Population back toward some sort of equilibrium.

2.3.6. Using Causal Loop Diagrams – Identifying Polarity in Feedback Loops

In this section you will get some more practice in reading and interpreting causal loop diagrams. The goal is for you to become proficient in assigning polarities to causal links and in finding feedback loops in the system.  The causal loop diagrams in the Modeling Challenge below represent the mental models of the authors.  You should feel comfortable changing the variable names or adding intervening variables that represent your mental models.  Also, for significant delays in the system, you can add a hash mark.

2.3.7. More Practice with Causal Loop Diagrams – Telling Systems Stories

Everyone loves a good story. In fact, stories are one of the most powerful tools we have for exploring complex ideas involving multiple characters and competing interests. Think about the series of Star Wars movies. These have spawned a whole line of books, a religious movement (“May the force be with you!”), and several acting careers. Such is the power of stories.

When trying to understand how a feedback-rich system impacts a problem like the collapse of a deer population, or the spread of an infectious disease the use of stories is one of the best strategies a systems thinker can use. Every story has one or more main characters. In the case of a system story, the main characters are those feedback loops that you believe are important to the problem. Think of a system story as something like a crime mystery. A crime has been committed, and the detective has to figure out who did it and how.  In the case of a system story, the “crime” is represented by the BOTG. That graph shows the evolution of a undesirable situation. That time trajectory is the “crime.”  We also know that the crime was not committed by a single actor, but instead by a collection of actors working together.

Who are the actors? The feedback loops in the system comprise the “crime syndicate” that has created the problem in the BOTG. You, the system modeler, have to figure out just how those feedback loops have conspired to bring about this undesirable situation.

So, a system story is a story about what you consider to be the important feedback loops impacting the problem. The purpose of the story is to explain just how those feedback loops have worked (sometimes in competition with one another; sometimes in concert) to bring about the situation we see in the BOTG.

To illustrate how this works, consider the imaginary case study introduced in the box that follows^[3].

2.4. Seeing the System Beneath: Identifying Stocks and Flows

It’s fairly easy to think about how a simple system involving only one or two feedback loops might behave over time. What if we were faced with a system involving three, four…or many more feedback loops. In order to understand how things actually work in such a system, we have to build computer models that give life to these feedback loops and that help us explore how things might play out.  We’ll start working toward this goal by applying the third practice used by system modelers: Looking for stocks and flows.

You’ve hopefully seen that feedback loops have a huge impact on the behavior of complex systems. The reason feedback loops exert so much power is because they represent the forces that affect how important populations and resources in the system change over time.

System modelers use stocks to represent these critical populations and resources. Stocks refer to quantities in the system that accumulate (or deplete) over time. Flows are those processes by which the accumulation or depletion occurs.  The purpose of this section is to introduce the concept of stocks and flows and to help you learn to identify those stocks and flows that are important to the problem at hand.

2.4.1. Introducing Stocks and Flows

Think of a stock as the collection of all of a particular population or resource pool that is currently available in the system. The “contents” or size of the population or resource in the stock can accumulate or be drained over time.  This happens through the flows of material, animals, etc. into or out of the stock.

One way to visualize the concept of a stock and its flows is to think of a bathtub of water with a faucet feeding water into it and with a drain through which water is removed (Figure 6).  In this figure, the bathtub is the stock of water in the system. The faucet is a flow of water into the system (i.e. an inflow). The drain is a flow of water out of the system (i.e. an outflow).  If only the faucet is open and operating, then the water level in the tub will rise according to the rate of inflow through the faucet. If only the drain is open and operating, then water flows out of the tub, while none is being added.  Then the water level will drop according to the rate of outflow through the drain. If both the faucet and the drain are open so that water is simultaneously flowing in through the faucet and out through the drain, the net difference between the inflow and outflow rates will determine if the water level in the tub rises or falls.

2.4.2. Stock and Flow Diagrams: Visually Showing Stocks and their Flows

Let’s now apply the idea of stocks and flows to show how this changes the way we visualize and think about the feedback structure in a causal loop diagram.  Figure 7 shows a causal loop diagram, along with a corresponding diagram using stocks and flows.  These two diagrams are, for our purposes, equivalent, but the stock and flow diagram emphasizes which part of the system is a critical accumulating resource (the Deer Population).

The Deer population is shown as a rectangle, designating it as a stock (i.e. as the collection of all the deer on the Kaibab). The Deer births per year is shown as a flow, symbolized as a pipe with a valve (i.e. ) flowing into the stock. That is, the Deer Births per Year is an inflow: it adds deer to the population. The Deer Deaths per Year is also shown as a flow, but it points out of the stock because it removes deer from the population. Hence, the Deer Deaths per Year is an outflow.  The two causal links and their polarities pointing from the stock to the two flows have the same meaning as in the original CLD in Figure 4. That is, each link tells us that the the stock affects the two flows with a + polarity: an increase in the Deer Population causes a corresponding increase in each of the flows.

The diagram in Figure 7 is called a stock and flow diagram. Stock and flow diagrams^[5] give a more complete picture of the system structure than what we see in a simple causal loop diagram like Figure 4.  Stock and flow diagrams also provide the basic building blocks for creating working simulators that you can use to explore the problem.

Notice that the right side diagram in Figure 7 also shows the same two feedback loops as in the original CLD. But something doesn’t seem right. In the original CLD, there are two additional causal links: one running from the Deer births per year into the Deer population and another from the Deer deaths per year into the Deer population. Why don’t we see those same causal links in the stock and flow version of that diagram?  The reason for this is because those causal links are already implied by the presence of the flows themselves. That is, including the links in the stock and flow diagram would be redundant.  In order to more explicitly emphasize that the flows do in fact have a causal influence on the flow, we attached polarities to those flows to indicate the type of influence.  See Figure 8.

2.4.3. Specifying Units for Measuring Stocks and Flows

Units for Measuring Stocks

In a system dynamics simulator, the stocks and flows have numeric values that specify their status. These values can change over time as the system evolves.  At any point in time, the numeric value associated with a stock specifies how much “stuff” is contained in the stock at that moment. The nature of the “stuff” depends on what the stock represents. For example, a stock of deer contains deer. A stock of water in a lake contains water. At any point in time, the numeric value of these stocks tells us how many deer or how much water is in the stock.  For example, Figure 9 shows two stocks and several flows associated with a lake and a population of beavers that live around it.  During a simulation run, the contents of the Water in the Lake stock will be a expressed as a numeric value that specifies how much water is in the lake at each moment. This value will change as the simulation progresses. But a numeric value (like, say, 50,000) has no meaning unless we know the units in which that value is expressed. Do we mean 50,000 ounces of water? 50,000 gallons? 50,000 cubic meters? 50,000 liters? What?  There are many possible choices for the stock units, but a choice must be made, and this choice affects how the rest of the model is set up and how we interpret the simulation results. For the sake of illustration, let’s use cubic meters as the unit for expressing the contents of the Water in the Lake.  Based on that decision, a stock value of 50,000 means that the lake contains 50,000 cubic meters of water.

What about the Beavers stock in Figure 9? If the numeric contents is, say, 100, then this stands for 100 what?  Clearly the most logical unit for this stock is beavers. So that a numeric value of 100 means the stock contains 100 beavers.

Units for Measuring Flows and Accounting for the Passing of Time

In a similar way, we have to make some decisions about units of measurement for the numeric values of the flows connected to a stock.  Flows represent the rate at which “stock stuff” flows into/out of the stock – or, equivalently, the amount of “stock stuff” added to or removed from the stock in one unit of time.  For example, because the Water in the Lake stock is measured in cubic meters, the three flows attached to that stock represent the number of cubic meters added to or removed from the lake during a single unit of time.

But what constitutes “a single unit of time?”  Again, there are many possible choices: one second, one hour, one day, one year, etc.  How do we choose the time unit?  The time unit should be chosen to be short enough to allow us to model the kinds of behaviors we are interested in studying, but not any shorter than necessary. For example, suppose we are interested in modeling the long-term seasonal behavior of the lake/beaver system across multiple years, without concerning ourselves with short-term fluctuations created by rain events or short dry spells of several days. Using a time unit of one second is too short for this purpose because seasonal fluctuations in the amount of water in the lake or of the beaver population happen over a matter of weeks or months, not seconds. In addition, using a time unit of 1 second would require us to simulate millions of seconds just to simulate a few years of time. This would correspond to even greater millions and billions of computations by the simulation software. Because we wish to model behaviors that take weeks, months, and years to play out, it is more reasonable and efficient to use a time unit of 1 week or possibly 1 month (assuming changes that occur over less than 1 month are not of interest to us).

Once the time unit is specified, this affects the numeric values we use for the flows. Consider the inflow called Water flowing in (Figure 9). Supposed that we know that water enters the lake via a feeder stream at the rate of 6,000 cubic meters per day. If we wanted to use a time unit of 1 day, then the 6,000 figure is the correct value to use for this flow. What if we wanted to use a time scale of 1 week (7 days). Then the flow rate would be 42,000 m3/week (6,000 m3/day times 7 days/week). If we wanted to use a time scale of 1 month (30 days), then the flow rate would be 180,000 m3/week (6,000 m3/day * 30 days/month = 180,000 m3/month).

Unit consistency: Making sure stocks and flows contain the same “stuff”

It is very important that we specify the units of a stock and it attending flows in such a way that those units are compatible. This is done by following three basic rules.

Making sure that these three conditions are met will assure that, as time progresses, the contents of the stock will represent the amount of stuff accumulated up to any given point in time.  Failure to pay careful attention to unit consistency between stocks and flows is a common mistake made by novice modelers.  For example, see Figure 10, where a stock of People is affected by three flows:  Births/Year, Deaths/Year, and Food Harvested/Year. The stock is expressed in “people units,” so that a value of, say, 1000 means “there are 1000 people right now.”  Suppose that the time unit is 1 year.  All of the flows must have numeric values representing the number of people flowing into out of the stock per year.

The units of a stock and its associated flows must be compatible (i.e. they must contain the same “stuff”).  In Figure 10, the Food harvest inflow is incompatible with the People stock because the flow contains food, while the stock contains people.  The Births and Deaths flows are compatible because they both contain people.

Can you see the problem with Figure 10?  The Birth and Death flows can easily be expressed in terms of people per year. On the other hand, the Food harvest inflow is confusing. Since it flows into the People stock it has to represent some number of people added per year. But that does not appear to be the case.  The name of this flow suggests that it represents the size of a crop harvest (probably measured in something like “bushels per year”). But “bushels” are not the same thing as “people,” so the units of this flow and its associated stock are not compatible.  In fact, the logic of this model is suspect because food does not directly create people (as if “12 bushels of corn per year converts into 1 person”).

It is true that the size of a crop harvest will undoubtedly affect the size of the population, but not in way shown in Figure 10.  Instead, the effect of food on the People stock is indirect; the food probably affects the stock of people by affecting either the birth or death rates (or both!). Later we’ll learn how to account for indirect effects such as this. For now, the important point to remember is that the units of a stock and its associated flows must be compatible. The flows must contain the same “stuff” that is stored in the stock.