Stella v8.1.1

1
Stella v8.1.1
2
What is Stella?

• Graphical modelling environment
• Simplifies the modelling process w/o compromising
  rigor
• Processes reflected through structure of Stella
  models
• Designed around (but not limited to) dynamic
  modelling

3
Not a toy
Carbon cycle model (Univ. of North Carolina)
4
Four basic building blocks

• Stocks
• Flows
• Converters
• Connectors

5
Example Population Growth (approximately from
Hannon and Ruth 1997)
6
Stocks

• Act as state variables
• Also called a reservoir in Stella
• In this example, the reservoir Population Size
  is updated with each time step (dt) during
  execution of the model
• State variables must be seeded by the modeller
  with an initial value (Stella puts a ? inside
  symbols that have not been initialized)

7
Flows

• Add reproduction as a control variable or flow
  (controls the value of the stock)
• Flows
• Uniflow (or inflow) adds to the stock (arrow
  points into the stock)
• Biflow adds or subtracts from the stock
  depending on whether the flow generates a
  positive or negative number (arrow points both
  ways more on this later)
• Reproduction is always positive uniflow

8
Converters

• What influences reproduction?
• (Reproductive rate)
• Expressed as a proportion, this transforming
  variable is called a converter.

9
Connectors

• Connectors pass information between variables in
  a model
• Here, reproduction is determined by the size of
  the population and what proportion (or rate) is
  reproducing.
• That reproduction is then added through the flow
  to the population size.

10
Initializing and running the model
Initialize Population size (N) 10 Reproductive
Rate (r) 0.4 Reproduction Nr Number of
iterations and time base and of model are set
under RunRun Specs Here, 25 iterations, one
each year. Pink graph icon is not part of model
but a means of monitoring output as a graph.
11
Population growth model output
As expected, population growth progresses
exponentially without negative feedback on
reproductive rate.
12
Adding negative feedback on reproductive rate

• Reproductive rate should decrease as population
  size increases
• Add that connection
• In the Reproductive Rate converter, draw the
  function that relates population size to
  reproductive rate where rate decreases as we
  approach 1000 individuals (carrying capacity).

13
Population growth model output
Characteristic Sigmoid appears as population
nears carrying capacity (1000).
14
Population growth model output (cont)
Can monitor changes in all variables through time.
15
Example Population Growth II (doing the math)

• Previous example Stella allows users to graph
  relationships where the math is unknown or poorly
  understood
• Lets try it with the math.classic logistic
  growth
• where ?N is change in population size, Ni is
  population size, r is the population growth rate,
  K is carrying capacity

16
Population Growth II (cont)

• Remove graphical feedback relationship between
  Population Size and Reproductive Rate, and rename
  variables to reflect more general behavior.
• Initialize
• Insert Carrying Capacity (K) as a converter and
  set to 1000 individuals.
• Ni 10
• r 0.4

17
Population Growth II (cont)
18
Population Growth II (cont)
19
Population Growth II functions
Stella offers a number of functions that
influence how a variable changes through
successive iterations
The result of clicking on the carrying capacity
converter
20
Population Growth II functions (cont)
e.g. sinusoidal variation in carrying capacity
21
Population Growth II functions (cont)
e.g. random variation in carrying capacity
22
Population Growth II sensitivity analysis
e.g. incremental variation in population growth
rate
Under Run Sensi Specs, Stella allows
parameters for the sensitivity analysis to
be specified.
23
Lotka-Volterra predator-prey interactions --
one of the simplest predator-prey interaction
models --
where H is prey population size L is
predator population size r is the intrinsic
population growth rate for prey a is the
predation rate b is the reproduction rate
for predators per prey m is the predator
mortality rate
24
Prey

• Model is structured similar to the equation
• population increasing parameters (inflow) are on
  the left
• population decreasing parameters (outflow) are
  on the right

25
Predator
Predator populations driven by similar forces.
26
Lotka-Volterra Predator-Prey Model
27
Lotka-Volterra Predator-Prey Model
28
Brief aside
Double click graph
29
Sectors segregate model components
30
Ghosts
(Stella version of an alias. Gives submodels
structural independence.)
31
The Interface Level (an exploratory tool)
32
Can add pictures for a little flair
33
Cellular Automata (e.g. Stella ifs, ghosts, and
animation)

• John von Neumann develops simple models of
  reproducing machines
• Spawned research in use of simple rules to govern
  replication
• Models collectively known as cellular automata
• Definition A regular spatial lattice of
  "cells", each of which can have any one of a
  finite number of states. The state of all cells
  in the lattice are updated simultaneously and the
  state of the entire lattice advances in discrete
  time steps. The state of each cell in the lattice
  is updated according to a local rule which may
  depend on the state of the cell and its neighbors
  at the previous time step. (Dictionary of
  Computing 2000)

34
Cellular Automata (cont)

• Most popular version is the Game of Life by
  John Conway (Professor of Mathematics,
  Princeton). In a sufficiently large lattice,
  automata appear vaguely as organisms that move,
  interact, replicate, etc.
• Stephen Wolfram of Mathematica fame
• Uses
• usually treated as a novelty or curiosity
• Behavior of fluids
• Sediment transport
• Spread of forest fires
• Can explore different behaviors by varying simple
  rules

35
Conways Game of Life - rules

• Each cell on the grid can only take on two
  characteristics (e.g. black and white).
• If for a cell the number of alive neighbors is
  exactly two, the value of the square does not
  change at the next time step.
• If the number of black neighbors is three, the
  square will be black in the next step.
• If the number of black neighbors is neither two
  or three, the square will be white at the next
  time step.

36
How it works in Stella
IF (A1A2A3B1B3C1C2C3)BIRTH_ AND B20
THEN 1 ELSE IF (A1A2A3B1B3C1C2C3)_MIN OR (A1A2A3B1B3C1C2C3)NEIGHBOR_MAX
AND B21 THEN -1 ELSE 0
37
How it works in Stella
Under Model Model Prefs
Each cell in the cellular automata is represented
as the ghost of its corresponding reservoir.
Ghosts are aligned in a 2D grid and set to
animate - or flicker depending on whether its
value is 1 or 0.
38
Game of life cellular automata in Stella (Hannon
and Ruth 1997)