CLExchange · YouTube · 4:45
This video introduces System Dynamics modeling, emphasizing that it requires identifying system connections and using basic math rather than programming. It defines key concepts: stocks (accumulations represented by boxes) and flows (rates of change represented by arrows). Using a spring-mass system and a deer population as examples, it illustrates how these components interact. The segment concludes with a demonstration in Stella Architect software, showing how to parameterize a simple deer population model by setting initial values and defining the birth rate equation as the product of the current population and a birth fraction. This video introduces system dynamics modeling using a simple deer population example in Stella Architect software. It demonstrates how to construct a stock-and-flow diagram with 'Deer' as the stock, and 'Births' and 'Deaths' as flows governed by 'Birth_fraction' and 'Lifespan' parameters. Through numerical simulations, the video illustrates sensitivity analysis: showing that when birth rates equal death rates, the population is stable; increasing lifespan leads to exponential growth; and decreasing birth fractions leads to population decline. The segment concludes by acknowledging the simplicity of this model and transitioning to a more complex framework involving food and predators. This 45-second clip concludes an introduction to system dynamics models by showing a more complex deer-population stock-flow diagram and naming possible leverage points such as regeneration time, Predators, and hunting tags. It then promotes the book Model Mysteries as a free resource for building one's own models and ends with a credit card for the Creative Learning Exchange and the STELLA software used to create the diagrams.
Use the learning inspector for key ideas and moments, or open the reading tabs for the complete notes.
Generated from the video's visuals and explanation; not verbatim speech.
The video begins by introducing System Dynamics models, explaining that they start with a structural diagram. A key point made is that users do not need to learn a new programming language; instead, they rely on identifying connections between parts and applying basic mathematical operations like addition, subtraction, multiplication, and division.
Next, the core components of the diagrams are defined. 'Stocks' or 'accumulations' are represented by boxes. These stocks change over time due to 'flows,' which act as rates of change. Inflows increase the stock, while outflows decrease it.
The narrator highlights the benefit of converting a static stock-flow diagram into a running simulation. This allows viewers to observe how accumulations evolve over time, transforming the static picture into a dynamic model akin to a moving machine or organism. An example of a spring-mass system is shown to illustrate this physical modeling capability.
A concrete example is introduced: a deer population. The population size is modeled as a stock. Two flows affect this stock: 'Births' (an inflow) and 'Deaths' (an outflow). The birth rate is determined by the current number of deer and a 'birth fraction' (the percentage giving birth annually). The death rate depends on the number of deer and their average 'lifespan'.
The scene shifts to the Stella Architect software interface to demonstrate implementation. The user sets the initial 'Deer' stock to 100. The 'Birth_fraction' parameter is set to 0.2 (representing 20%). Finally, the equation for the 'Births' flow is constructed by multiplying the current 'Deer' stock by the 'Birth_fraction', resulting in the formula `Deer * Birth_fraction`.
The video begins by defining the parameters for a basic population model. The narrator sets the 'Lifespan' of a deer to 5 years. Mathematically, this defines the outflow rate 'Deaths' as the current stock 'Deer' divided by the lifespan ().
The narrator explains the implication of this division: on average, one-fifth () of the population dies annually. This establishes the linear relationship between the stock and the outflow rate.
Before running the simulation, the viewer is asked to predict the outcome. The model includes an inflow 'Births' calculated as . With and the death rate effectively (), the inflows and outflows are balanced.
The simulation is run. The resulting graph shows a flat horizontal line, confirming that when the birth rate equals the death rate, the population size remains constant over the 20-year period.
A parameter sensitivity test is performed. The 'Lifespan' is increased to 10 years. This halves the death rate coefficient to or , while the birth rate coefficient remains at .
The second simulation run produces an upward-curving graph. The narrator explains that since fewer deer die (lower outflow) but the same proportion gives birth (unchanged inflow relative to stock), the net growth rate becomes positive, leading to exponential population growth.
A third scenario is tested. The 'Lifespan' is reset to 5 years (restoring the death coefficient), but the 'Birth_fraction' is lowered to . Now, the outflow rate exceeds the inflow rate.
The third simulation shows a downward sloping curve. The narrator observes that the population declines because fewer deer are born each year than die, eventually approaching zero.
The video concludes this section by stating the model is 'very limited.' It transitions visually to a title card 'A MORE COMPLEX MODEL OF THE DEER POPULATION,' introducing a dense diagram with additional stocks like 'Food' and 'Predators' to address real-world ecological constraints missing from the simple exponential model.
The clip opens on a stock-flow diagram titled A MORE COMPLEX MODEL OF THE DEER POPULATION. Three main stocks are visible: Food, Deer, and Predators. Around them are labeled flows such as regeneration, consumption, deer births, deer starvation, deer hunting per yr, deer predation per yr, predator births, and predator deaths, plus auxiliary variables including regeneration time, amount per deer, fraction starving, hunting tags, kills per predator, deer birth fraction, predator birth fraction, and predator death fraction.
As the narrator says to consider leverage to improve the situation, blue arrows successively highlight regeneration time, then Predators, then hunting tags. This visually connects the spoken idea of leverage to concrete parts of the model: a parameter affecting food inflow, a population stock, and a management-related auxiliary variable affecting hunting.
The diagram gives way to a promotional slide for the book Model Mysteries. The cover subtitle reads An Exploration of Vampires, Zombies and Other Fantastic Scenarios to Make the World a Better Place. On-screen text says Build your own models using fun, step-by-step instructions. Available for free on the Creative Learning Exchange website. The URL shown is http://www.clexchange.org/curriculum/modelmysteries/.
The final card reads INTRODUCTION TO SYSTEM DYNAMICS MODELS* and Brought to you by CREATIVE LEARNING EXCHANGE Making Thinking Visible. A footnote states *STELLA® Software by isee systems, Inc. used to create stock/flow diagrams and models. Additional text directs viewers to See the website at clexchange.org for additional resources.
System dynamics modeling focuses on mapping the structure of a system using diagrams. It utilizes basic arithmetic functions (add, subtract, multiply, divide) to define relationships, eliminating the need for traditional programming languages.
Stocks (represented by boxes) are accumulations within the system that can rise or fall. Flows (represented by arrows with valves) are the rates of change that add to (inflows) or subtract from (outflows) the stocks.
Running a system dynamics model transforms a static diagram into a dynamic simulation. This allows users to visualize how stocks accumulate or deplete over time, revealing the system's behavior like a moving machine.
In this example, 'Deer' is the stock. 'Births' is the inflow, dependent on the deer count and birth fraction. 'Deaths' is the outflow, dependent on the deer count and lifespan. This creates a feedback loop governing population size.
Using software like Stella Architect, abstract concepts are given values. For the deer model: Initial Stock = 100, Birth Fraction = 0.2. The Births flow equation is defined as `Deer * Birth_fraction`.
In system dynamics, a 'Stock' (rectangle) accumulates quantities over time, like the Deer population. 'Flows' (pipes) represent rates of change entering or leaving the stock. 'Births' is an inflow, and 'Deaths' is an outflow.
Flows are often calculated using auxiliary variables (circles). Here, 'Births' depends on 'Birth_fraction' and 'Deaths' depends on 'Lifespan'. The equations are and .
When the rate of input equals the rate of output, the stock does not change. In the first run, with a birth fraction of 0.2 and a lifespan of 5 (death fraction 0.2), the population stays constant.
Increasing the lifespan reduces the death rate. If births remain proportional to the population, a lower death rate creates a positive net growth, causing the population to rise exponentially, as seen in Run 2.
Lowering the birth fraction reduces the inflow. If the outflow (deaths) remains higher than the inflow, the population shrinks over time, eventually dying out, as shown in Run 3.
Simple linear models assume unlimited resources and constant rates. Real populations are limited by factors like food availability and predation, requiring more complex feedback loops.
The video shows a system dynamics stock-flow diagram for a deer population. Rectangular boxes represent the stocks Food, Deer, and Predators. Pipes with valves represent flows such as regeneration, consumption, deer births, deer starvation, deer hunting per yr, deer predation per yr, predator births, and predator deaths. Auxiliary variables such as amount per deer, fraction starving, kills per predator, and several birth/death fractions link stocks and flows, illustrating how the model encodes interactions in the ecosystem.
While the narrator discusses using leverage to improve the situation, the video highlights three example elements in sequence: regeneration time, Predators, and hunting tags. These correspond respectively to a food-regeneration parameter, a population stock, and a management-related auxiliary variable that affects deer hunting per yr. The clip presents them as examples of places in the model where intervention may change system behavior.
After the model example, the clip promotes the book Model Mysteries as a resource for building one's own models. The narration says it includes fun, step-by-step instructions and examples throughout. The on-screen text adds that it is available for free on the Creative Learning Exchange website and displays the URL http://www.clexchange.org/curriculum/modelmysteries/.
The ending card identifies the series as INTRODUCTION TO SYSTEM DYNAMICS MODELS and credits the Creative Learning Exchange. A footnote states that STELLA® Software by isee systems, Inc. was used to create the stock/flow diagrams and models. The card also directs viewers to clexchange.org for additional resources.
Explore conditions, steps and evidence. Supplementary explanations are labeled separately from content shown in the video.
A red rectangle labeled 'Key accumulation' or 'Deer'.
Stock
Represents an accumulation in a system that can go up and down based on flows.
Non-negative real numbers (implied by context).
Blue arrows with valve symbols labeled 'Inflow', 'Outflow', 'Births', 'Deaths'.
Flow
Represents the rate of change of a stock.
Real numbers (can be positive or negative depending on direction).
Green circle labeled 'Birth fraction' connected to the 'Births' flow.
The narrator defines it as the percentage of deer that will give birth in any given year.
Birth fraction
The proportion of the total population that gives birth in a given time period.
Dimensionless fraction between 0 and 1.
Green circle labeled 'Lifespan' connected to the 'Deaths' flow.
The narrator mentions it as a factor determining how many die.
The exact mathematical formula for deaths using lifespan is not explicitly shown in the software interface within this clip, though the variable is introduced.
Lifespan
The average duration of life for an individual in the population.
Time (e.g., years).
In the Stella Architect software, the equation for the 'Deer' stock is set to '100'.
Narrator says, 'let's say that we'll have 100 deer to start'.
Deer (initial)
The starting population size of the deer.
Integer >= 0.
In the Stella Architect software, the equation for 'Birth_fraction' is set to '.2'.
Narrator says, 'birth fraction will be about 20% ... .2'.
Birth_fraction
The numerical value assigned to the birth fraction parameter.
Real number (0.2).
In the Stella Architect software, the equation for 'Births' is typed as 'Deer*Birth_fraction'.
Narrator says, 'we multiply the number of deer by the birth fraction'.
Births
The rate of new individuals entering the population.
Real number >= 0.
Red rectangular box labeled 'Deer' in the center of the stock and flow diagram.
Narrator refers to the 'deer population' and 'how many deer we have'.
Deer
The stock variable representing the total number of deer in the population at any given time.
Non-negative real numbers (representing a count of individuals).
Blue pipe with an arrow pointing into the 'Deer' stock, labeled 'Births'.
Equation panel shows 'Births = Deer*Birth_fraction'.
Births
The inflow rate variable representing the number of new deer added to the population per unit of time.
Non-negative real numbers (rate of change).
Blue pipe with an arrow pointing out of the 'Deer' stock, labeled 'Deaths'.
Equation panel shows 'Deaths = Deer/Lifespan'.
Deaths
The outflow rate variable representing the number of deer removed from the population per unit of time due to natural causes.
Non-negative real numbers (rate of change).
Green circular auxiliary variable labeled 'Birth fraction' connected by an arrow to the 'Births' flow.
Equation panel shows 'Birth_fraction = .2' initially, later changed to '.1'.
Narrator mentions 'birth fraction'.
Birth_fraction
A dimensionless parameter representing the proportion of the current deer population that gives birth in a given time period.
Real numbers between 0 and 1.
Green circular auxiliary variable labeled 'Lifespan' connected by an arrow to the 'Deaths' flow.
Equation panel shows 'Lifespan = 5' initially, later changed to '10'.
Narrator states 'the lifespan of a deer will be about five years'.
Lifespan
A parameter representing the average duration of life for a deer, measured in years. It determines the rate at which the population dies off.
Positive real numbers.
Narrator explains that system dynamics models start with a diagram showing structure and use basic math functions like adding, subtracting, multiplying, dividing.
Title slide 'Introduction to System Dynamics Models' with a spring-mass diagram and a stock-flow diagram.
System dynamics modeling is a method for understanding the behavior of complex systems over time. It involves identifying how parts are connected and inputting basic mathematical functions rather than learning a new programming language.
Requires identification of system components and connections.
Uses basic arithmetic operations.
Narrator states, 'Key stocks or accumulations are identified with a box.'
Red rectangle labeled 'Key accumulation' appears.
In a system dynamics diagram, stocks represent accumulations of resources, information, or physical entities. They are visually represented by rectangles (boxes). Stocks change over time based on inflows and outflows.
Represented by boxes/rectangles in diagrams.
Can increase or decrease.
Narrator states, 'These stocks can go up and down based on their flows or rates of change.'
Arrows labeled 'Inflow' and 'Outflow' connect to the stock box.
Flows represent the rate at which a stock changes. Inflows add to the stock, while outflows subtract from it. They are visually represented by arrows with valves.
Represented by arrows with valves.
Determine the rate of change of stocks.
Narrator explains the advantage of moving to a running model is seeing accumulations over time, making the diagram dynamic like a moving machine.
A graph of 'Key accumulation' vs 'Years' updates dynamically as the simulation runs.
Moving from a static stock-flow diagram to a running simulation allows observers to see how accumulations (stocks) change over time. This transforms the static picture into a dynamic representation of the system's behavior.
Requires a simulation engine (like Stella Architect).
Diagram shows 'Deer' stock with 'Births' inflow and 'Deaths' outflow. Auxiliary variables 'Birth fraction' and 'Lifespan' are added.
Narrator describes the example: deer population as a stock, births adding, deaths subtracting. Births depend on deer count and birth fraction. Deaths depend on deer count and lifespan.
A basic system dynamics model for a deer population where 'Deer' is the stock. 'Births' is the inflow determined by the current population and a birth fraction. 'Deaths' is the outflow determined by the current population and average lifespan.
Assumes closed population (no migration).
Births proportional to population.
Deaths proportional to population and inverse of lifespan (implied).
Stella Architect software interface is shown. User inputs '100' for Deer initial value, '.2' for Birth_fraction, and 'Deer*Birth_fraction' for Births equation.
Narrator guides through setting initial values and equations: '100 deer to start', 'birth fraction... .2', 'multiply the number of deer by the birth fraction'.
The process of assigning specific numerical values and mathematical equations to the variables in the system dynamics diagram using simulation software (Stella Architect). This includes setting initial stock levels, parameter constants, and flow equations.
Access to simulation software.
Defined units and dimensions.
Visual representation using rectangles (stocks), pipes with arrows (flows), and circles (auxiliary variables) connected by lines.
A visual modeling language used in system dynamics. Rectangles represent stocks (accumulations), pipes represent flows (rates of change into or out of stocks), and circles represent auxiliary variables or parameters that influence the flows.
Rectangles denote state variables.
Pipes denote rate variables.
Circles denote auxiliary variables or constants.
Equations visible in the software interface: 'Births = Deer*Birth_fraction' and 'Deaths = Deer/Lifespan'.
Narrator explains dividing the number of deer by the lifespan to find deaths.
The model is defined by a differential equation for the stock 'Deer', where the rate of change is the difference between inflows and outflows. The inflow 'Births' is proportional to the current stock, and the outflow 'Deaths' is inversely proportional to the 'Lifespan'.
Time is continuous.
Parameters are constant over the simulation period.
The narrator says, "and consider leverage to improve the situation."
The slide title reads A MORE COMPLEX MODEL OF THE DEER POPULATION and shows a stock-flow diagram with stocks, flows, and auxiliary variables.
This clip presents a system dynamics model as a stock-flow diagram for a deer population. The diagram uses rectangular boxes for stocks (Food, Deer, Predators), pipes with valves for flows (such as deer births, deer starvation, deer hunting per yr, deer predation per yr, predator births, and predator deaths), and auxiliary links for variables such as amount per deer, fraction starving, hunting tags, and kills per predator. The narration frames these elements as parts of a model that can be used to consider leverage to improve the situation.
The model is presented visually as a stock-flow diagram.
The narration explicitly mentions food for the deer, predators, and more.
The narrator says, "and consider leverage to improve the situation."
Blue arrows point first to regeneration time, then to Predators, then to hunting tags.
The video identifies leverage as a way to improve the modeled situation. The highlighted examples are regeneration time, Predators, and hunting tags. In the diagram, these correspond respectively to a parameter affecting food inflow, a stock in the ecosystem, and an auxiliary control variable affecting deer hunting per yr. The visual emphasis suggests that changing these elements can alter system behavior.
The clip does not provide equations showing how each lever changes outcomes.
The identification of leverage points is conveyed by narration plus arrow highlights.
The narrator says, "To create some of your own models, check out the book Model Mysteries that includes fun, step-by-step instructions and examples throughout."
A book cover titled Model Mysteries appears with the subtitle An Exploration of Vampires, Zombies and Other Fantastic Scenarios to Make the World a Better Place.
On-screen text reads Build your own models using fun, step-by-step instructions. Available for free on the Creative Learning Exchange website. http://www.clexchange.org/curriculum/modelmysteries/
The clip promotes the book Model Mysteries as a resource for building one's own models. The narration describes it as including fun, step-by-step instructions and examples throughout. The on-screen text adds that it is available for free on the Creative Learning Exchange website.
This item is a resource reference rather than a mathematical derivation.
The clip does not show any worked example from the book.
Narrator says, 'You don't need to learn a new programming language, you just need to identify how the parts are connected and input some basic math functions such as adding, subtracting, multiplying and dividing.'
System dynamics modeling does not require learning a new programming language; it relies on identifying connections and using basic arithmetic functions.
User understands basic arithmetic.
User can identify system components.
Universal for the context of introductory modeling.
Narrator says, 'So the diagram isn't just a static picture of a system, but rather it becomes dynamic, like a moving machine or organism.'
Running a system dynamics model transforms the static diagram into a dynamic representation that shows changes over time.
The model is executed/simulated.
The system has stocks that change via flows.
Existential (for any valid SD model).
The narrator says, "These might include elements like food for the deer, predators, and more."
Arrows highlight regeneration time, Predators, and hunting tags in sequence.
The clip does not state whether these are the only possible leverage points or merely examples.
In this deer-population model, elements that may serve as leverage to improve the situation include food-related factors, predators, and additional components such as hunting tags.
The system is represented by the displayed stock-flow model.
The narrator is discussing ways to improve the modeled situation.
existential
Narrator explains: 'To figure out the number of births in any given year, we multiply the number of deer by the birth fraction.'
Equation 'Deer*Birth_fraction' is typed into the software for the 'Births' flow.
The number of births depends on how many deer there are.
Stated dependency in audio.
The number of births also depends on the fraction of deer giving birth.
Stated dependency in audio.
Combining the dependencies multiplicatively gives the flow equation.
Narrator instruction and software input.
The inflow 'Births' is calculated as the product of the current stock 'Deer' and the parameter 'Birth_fraction'.
Graph updates showing different curves (Run 1, Run 2, Run 3) as parameters are changed in the software.
Narrator asks 'What do you think will happen...' and then explains the result of changing lifespan and birth fraction.
Initial state where inflow equals outflow.
Observation of Run 1 graph being flat.
Increasing lifespan decreases the death rate ().
Mathematical relationship defined in the model.
With lower deaths and unchanged births, the net rate of change becomes positive.
Subtraction of rates.
The graph for Run 2 shows an upward curve.
Observation of simulation result.
Decreasing birth fraction lowers the birth rate while restoring the original death rate.
Parameter modification.
With lower births and higher deaths, the net rate of change becomes negative.
Subtraction of rates.
The graph for Run 3 shows a downward curve approaching zero.
Observation of simulation result.
Small changes in parameters like lifespan and birth fraction significantly alter the long-term behavior of the population, shifting it from stability to exponential growth or decline.
Visual construction of the deer population model in slides and then in Stella Architect software.
Narrator walks through the example step-by-step.
Construct and parameterize a system dynamics model for a deer population with births and deaths.
Initial Deer population = 100
Birth fraction = 0.2 (20%)
Deaths depend on Lifespan (value not entered in this clip)
Define the stocks, flows, and auxiliary variables, and write the equation for the Births flow.
Identify the accumulation (population) as a stock.
Standard SD modeling practice.
Identify the addition to population as a flow.
Biological process of reproduction.
Identify the subtraction from population as a flow.
Biological process of mortality.
Define the parameter for birth rate.
Given in problem statement/narration.
Write the formula for the inflow rate.
Derived from dependencies.
The model consists of a 'Deer' stock initialized to 100, a 'Births' inflow calculated as 'Deer * 0.2', and a 'Deaths' outflow dependent on 'Lifespan'.
The software interface shows the correct equations entered. The logic matches the narrator's explanation.
The entire video segment focuses on building and running this specific model in Stella Architect software.
Narrator walks through setting values and interpreting the graph.
Simulate the deer population over 20 years under different parameter settings for birth fraction and lifespan.
Initial Deer population (implied non-zero, likely 100 based on graph scale).
Base equations: Births = Deer * Birth_fraction, Deaths = Deer / Lifespan.
Simulation time: 0 to 20 years.
Observe the trajectory of the Deer stock variable.
Configure the model for equilibrium.
Narrator instruction.
Execute the model.
Software action.
Result: Population stays constant.
Graph visual.
Modify parameter to test sensitivity.
Narrator instruction.
Execute updated model.
Software action.
Result: Population grows.
Graph visual.
Modify parameters for decline scenario.
Narrator instruction.
Execute updated model.
Software action.
Result: Population declines.
Graph visual.
The population remains stable when Birth_fraction = 1/Lifespan. It grows when Lifespan increases (holding birth fraction constant) and declines when Birth_fraction decreases (holding lifespan constant).
Visual inspection of the plotted graphs for Runs 1, 2, and 3 confirms the theoretical predictions derived from the rate equations.
The slide shows A MORE COMPLEX MODEL OF THE DEER POPULATION with stocks Food, Deer, and Predators and multiple labeled flows and auxiliary variables.
The narrator discusses considering leverage to improve the situation and names food for the deer and predators as example elements.
No numerical values, equations, or simulation outputs are shown in this clip.
Illustrate how a more complex system dynamics model represents interactions among food, deer, and predators and where leverage might be considered.
Stocks: Food, Deer, Predators.
Flows shown in the diagram: regeneration, consumption, deer births, deer starvation, deer hunting per yr, deer predation per yr, predator births, predator deaths.
Auxiliary variables shown: regeneration time, amount per deer, fraction starving, hunting tags, kills per predator, deer birth fraction, predator birth fraction, predator death fraction.
Identify the structure of the model and the elements highlighted as possible leverage points.
Read the diagram as a stock-flow model with three main stocks: Food, Deer, and Predators.
The rectangular boxes are labeled Food, Deer, and Predators in the displayed diagram.
Trace the flows into and out of each stock, such as regeneration into Food, consumption out of Food, deer births into Deer, and deer starvation, hunting, and predation out of Deer.
These labels are visible on the pipes and valves of the stock-flow diagram.
Note auxiliary relationships such as amount per deer feeding fraction starving, and kills per predator feeding deer predation per yr and predator births.
The diagram shows arrows from auxiliary variables to flows and other variables.
Use the narration and highlighted arrows to identify example leverage points: regeneration time, Predators, and hunting tags.
The narrator says to consider leverage to improve the situation, and blue arrows point to these elements in sequence.
The clip presents a deer-population system dynamics model with interacting food, deer, and predator stocks, and it highlights regeneration time, Predators, and hunting tags as example leverage elements.
The answer matches both the visible diagram labels and the narrated examples of elements that might be used to improve the situation.
A complex stock-flow diagram representing a spring-mass system is shown alongside an animation of a bouncing spring.
Spring
Mass
Stocks (Position, Momentum)
Flows (Velocity, Force)
Auxiliary variables (Mass, Spring constant, Equilibrium position)
Animation of spring compressing and extending.
Highlighting of different parts of the diagram corresponding to physical quantities.
Structure of the diagram remains constant while animation plays.
Illustrates that system dynamics can model physical systems, not just abstract ones. Shows mapping between physical concepts (position, momentum) and SD elements (stocks, flows).
Screen recording of Stella Architect software showing the deer model being built.
Model diagram canvas
Property inspector panel
Graph window
Toolbar
Cursor moves to select elements.
Values are typed into equation fields (100, .2, Deer*Birth_fraction).
Warning triangle appears on Deer stock before initialization.
The overall layout of the software interface.
Demonstrates the practical application of the theoretical concepts discussed, showing how to implement the model in a standard tool.
The graph window updates in real-time or upon clicking 'Run', drawing blue, red, and purple lines corresponding to different simulation runs.
Graph axes (Years vs Deer)
Plot lines (Run 1, Run 2, Run 3)
Purple text boxes with arrows pointing to trends
Lines are drawn sequentially as time progresses.
New lines appear in different colors for new runs.
Text annotations appear to explain the trend (e.g., 'There's no change...', 'Deer population is growing...').
X-axis scale (0-20 years).
Y-axis scale (0-800 deer).
Model structure diagram remains static above the graph.
The visual changes directly map parameter adjustments to system behavior, illustrating the concept of dynamic response in a differential equation model.
A blue arrow points to regeneration time around 00:04–00:06.
A blue arrow points to Predators around 00:07–00:09.
A blue arrow points to hunting tags around 00:10–00:11.
regeneration time
Predators
hunting tags
stock-flow diagram
Arrow moves from regeneration time to Predators to hunting tags.
Each target is emphasized in turn while the rest of the diagram remains visible.
The underlying stock-flow diagram remains on screen.
The slide title A MORE COMPLEX MODEL OF THE DEER POPULATION remains visible.
The animation visually marks example components of the model that the narrator associates with leverage for improving the situation.
The deer diagram disappears and a book cover for Model Mysteries slides in.
Text appears promoting the book and its free availability on the Creative Learning Exchange website.
Model Mysteries book cover
promotional text
URL
The model diagram is replaced by a book cover and promotional text.
The URL http://www.clexchange.org/curriculum/modelmysteries/ becomes visible.
The clip remains within the same introductory presentation context.
This visual transition shifts from the example model to a resource for building one's own models.
The final card reads INTRODUCTION TO SYSTEM DYNAMICS MODELS* and Brought to you by CREATIVE LEARNING EXCHANGE Making Thinking Visible.
Footer text states *STELLA® Software by isee systems, Inc. used to create stock/flow diagrams and models.
Additional text reads See the website at clexchange.org for additional resources.
title text
Creative Learning Exchange logo
software footnote
website text
The book promotion is replaced by a static closing card with credits and website information.
No new mathematical content is introduced after the closing card appears.
The ending identifies the series title, sponsoring organization, software used for the diagrams, and where to find more resources.
Narrator explicitly addresses this: 'You don't need to learn a new programming language...'
Users might believe that building system dynamics models requires expertise in computer programming.
The video clarifies that only basic math functions (add, subtract, multiply, divide) and logical connection of parts are needed, making it accessible without coding skills.
Narrator says 'Yet this model is very limited... We can add other aspects...' followed by a transition to a complex diagram.
Transition from simple 3-variable diagram to a complex multi-variable diagram at 01:47.
Believing that a simple linear birth/death model accurately represents real-world ecological systems without limitations.
The video explicitly transitions to a 'MORE COMPLEX MODEL' to show that real systems involve feedback loops (food, predators) not captured by the simple exponential model.
Linking SD modeling to basic math functions.
System dynamics modeling applies basic mathematical operations to define relationships between system components.
Visual depiction of stocks connected by flows.
The concept of a system structure contains both stocks (accumulations) and flows (rates of change) as fundamental components.
Narrator introduces the deer example to illustrate the concepts.
The deer population model is a specific application (special case) of the general stock-accumulation concept.
Transition from slide diagram to software interface.
The parameterization method is applied to instantiate the specific deer population model structure.
Screen wipes from the simple 'Deer' model to a title card 'A MORE COMPLEX MODEL OF THE DEER POPULATION' and then a dense diagram.
The simple model serves as a foundational example of stock-flow structures, which are then generalized into a more complex network involving multiple interacting stocks (Food, Predators) in the subsequent scene.
The narrator discusses leverage while the deer-population stock-flow diagram is on screen.
Arrows point to specific elements within that diagram.
The idea of leverage is applied directly to the displayed deer-population model by highlighting specific model elements that could be changed to improve the situation.
The narrator says, "To create some of your own models, check out the book Model Mysteries..."
The book cover and promotional text appear after the model diagram.
The promoted book is presented as a resource for creating models like the deer-population system dynamics model shown earlier.
Detailed walkthrough of deer population modeling.
Definitions of stocks and flows provided sequentially.
Equation 'Deer*Birth_fraction' shown.
Narrator states no new programming language is needed.
Births = Deer * 0.2 and Deaths = Deer / 5 imply Births = Deaths.
'Notice that the deer population stays exactly the same...'
Changing Lifespan from 5 to 10 causes the graph to curve upwards.
The slide title and stock-flow diagram are visible.
The narrator mentions leverage to improve the situation.
Arrows highlight regeneration time, Predators, and hunting tags.
The narrator recommends the book Model Mysteries.
The book title and website information are shown on screen.
Covered · Introduction to System Dynamics and accessibility.
Covered · Explanation of stocks, flows, and dynamic simulation benefits.
Covered · Introduction of the deer population example and its structure.
Covered · Implementing the model in Stella Architect software.
Covered · Detailed analysis of the simple deer population model construction, parameterization, and simulation results.
Covered · Transition to a more complex model, highlighting the limitations of the simple exponential growth/decay assumption.
Covered · Narration about leverage and the deer-population stock-flow diagram with highlighted example elements.
Covered · Promotion of the book Model Mysteries with on-screen text and website URL.
Covered · Closing credit card with series title, Creative Learning Exchange branding, STELLA software footnote, and website text; no new mathematical content.
Reviewed subject paths
Increasing the average lifespan decreases the death rate (since ). If the birth rate remains constant, the inflow exceeds the outflow, resulting in a positive net growth rate and exponential population growth.
Conditions: The birth fraction parameter remains unchanged.; The lifespan parameter is increased.; The model follows the equation .
In system dynamics diagrams, stocks (also called accumulations) represent quantities that build up or deplete over time and are depicted as rectangles. Flows represent the rates of change that add to or subtract from these stocks and are depicted as arrows with valves.
Conditions: The context is introductory system dynamics modeling.; The model uses standard stock-and-flow diagram notation.
The simple model assumes unlimited resources and constant birth/death rates, ignoring feedback loops from food availability and predation. Real-world ecosystems have carrying capacities and complex interactions that constrain population growth.
Conditions: The comparison is between the simple exponential/linear model and realistic ecological systems.; The simple model includes only births and deaths dependent on population size.
The deer population remains constant when the inflow (births) equals the outflow (deaths). Given the equations and , this occurs when .
Conditions: The model uses the specific equations and .; Parameters are constant over the simulation period.
The video highlights regeneration time, Predators, and hunting tags as example leverage points. These correspond to a parameter affecting food inflow, a population stock, and a management-related auxiliary variable affecting deer hunting.
Conditions: The context is the complex deer-population stock-flow diagram.; Leverage points are identified by visual highlighting and narration.
The births flow is calculated by multiplying the current deer population (stock) by the birth fraction parameter. Mathematically, this is expressed as .
Conditions: The model assumes births are proportional to the current population.; The birth fraction is a constant parameter representing the proportion of the population giving birth per time period.
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