### Powerpoint Slides - Sara Parr Syswerda

```FW364 Ecological Problem Solving
Lab 4: Blue Whale Population Variation
[Ramas Lab]
Computer Lob Logistics
BUT…
We are using the Ramas softwareRamas will not work on Macs
Outline for Today
Example of population growth modeling of muskox using Ramas
1. Introduce Ramas software
2. Illustrate how to run deterministic vs.
stochastic models
• Exercise 2.2 in text
Lab 4: Blue whale population growth given uncertainty
1. Practice modeling population growth using software
2. Understand how uncertainty (demographic and environmental
stochasticity) affects:
• Predictions of future population size
• Risk of extinction
Introduction to Ramas
Ramas is a simple software program used for simulation modeling
Ramas does not allow us to write our own equations
Equations are pre-packaged in modules designed to illustrate
basic principles in applied ecology
However, users can specify:
Parameter values:
λ ± SD, s’, N0, # time steps (duration), # trials
Stochasticity: environmental and/or demographic
Growth model: exponential, scramble or contest density dependence
Introduction to Ramas
Ramas can readily create useful figures….
Growth trajectories
Extinction Risk Curves
Explosion Risk Curves
…with associated data in tables
Introduction to Ramas
Let‘s get started!
SETUP.EXE
 Ramas program file
REpatch2.exe
 Patch file for Ramas
Save both of these files someplace (P: drive, pendrive)
You need to re-install Ramas every time you use the program
STEP 1: Install SETUP.EXE  Click through defaults
Do not open Ramas yet (just install)
STEP 2: Install REpatch2.exe
BE PATIENT!! (it takes > minute to search for Ramas)
Introduction to Ramas
Let‘s get started!
STEP 3: Start RAMAS EcoLab software
STEP 4: Click Population Growth (single population models)
Take a minute to browse the program... e.g., look at toolbars
Introduction to Ramas
General Process for RAMAS:
Set up model:
Enter parameter values
Specify functions
Run
simulation
Get
results
Exercise 2.2 – Setting General Information
Muskox Population Growth – Simulation Modeling
Select “General Information” from Model menu
Title: Your name (for finding output from printer)
Can list parameter values in comment box
Replications = 0
 Zero specifies deterministic simulation
Duration = 12 (time steps = years in this case)
Note the demographic stochasticity box (currently dimmed)
Check this box when you want to have demographic stochasticity
We cannot check for this example because deterministic simulation
Exercise 2.2 – Setting Population Parameters
 This is the window where we enter parameter values
Set Initial abundance = 31
Set Growth rate (R) = 1.148  Equivalent to λ
Note that Survival rate (s) is dimmed because deterministic model
Likewise, SD of R is dimmed because deterministic model
Density dependence type: (Keep) Exponential
(Scramble and Contest available for density dependence labs)
Note that Carrying capacity (K) is dimmed because no density
dependence
Click “OK”
The model is now created!
Exercise 2.2 – Running the Simulation
There is a tone when complete
Says Simulation complete in lower right corner of window
We now have results!
Close Simulation window (don’t worry – you will not lose the simulation)
Click the X to close window
The model we are using is:
Nt+1 = Nt
 Ramas is doing a numerical simulation (forecasting year-to-year)
like we did in Excel in Lab 3
Exercise 2.2 – Viewing Results
Now let’s examine results
Select “Trajectory summary” from Results menu
Only one trajectory  shows exponential increase
Exercise 2.2 – Viewing Results
Now let’s examine results
Select “Trajectory summary” from Results menu
Only one trajectory  shows exponential increase
You can copy figure to paste into another document and also print
To get actual numbers,
click on Show numbers icon
Can also Copy or Print numbers
Show numbers
Print
Copy
Note that SD = 0
 All columns equal the Abundance average
Ramas presents actual values for average ± 1 SD
To obtain SD, subtract the Abundance average from +1 S.D. value
OR subtract the -1 S.D. value from the Abundance average
Note: We can check the deterministic result with a calculator using:
N t = N 0 t
where N0 = 31,  = 1.148, t = 12
Nt =162 muskox
Why is our calculated result ( = 162 muskox)
different from Ramas (= 163 muskox)?
 Ramas rounds off at each time step to integers
 Ramas gives a population size as opposed to density
Environmental:  varies for population (“random lambda”)
Like good and bad years for growth
In Ramas: fill in SD of R in “Population” window
Demographic:
Modeling of individuals
Chance of each individual surviving is, e.g., 0.4,
rather than 0.4 of population survives
No error in lambda, just randomization due to modeling of
individuals
In Ramas: check box Use demographic stochasticity in
“General Information” window
 Ramas can look at effects of each type of uncertainty independently
Note: When including stochasticity, we now need a Survival rate (s)
Continuing with Exercise 2.2
Let’s specify simulation with environmental stochasticity
Select “General information” from Model menu
Set Replications to 100
Keep Duration = 12
Do not check Use demographic stochasticity
(no demographic stochasticity this time)
Keep Initial abundance = 31
Keep Growth rate (R) = 1.148
We now have a
Set Survival rate (s) = 0.921
distribution for λ
Set Standard deviation of R = 0.075
(note that in this case  is now an average value, rather than a constant)
Keep Density dependence type as exponential
Model we are now using is:
Nt+1 = Nt ( λ ± errort )
Exercise 2.2 – Running Stochastic Simulation
Note that program executes the specified number of trials automatically
(trials are replicates, the same parameter values multiple times)
We can watch the
simulations run!
Note “Simulation complete”
when finished
Exercise 2.2 – Stochastic Trajectory Summary
Select “Trajectory summary” from Results menu
Dashed (blue) line:
Average trajectory of
model trials
Vertical lines:
1 SD above and below the
mean trajectory
Diamonds:
Max and min of all trials
Exercise 2.2 – Stochastic Trajectory Summary
Select Show numbers icon
What are some final
population sizes?
Did anyone have a
maximum population size
above 400 muskox?
Did anyone have a
minimum population size
below 10 muskox?
To obtain SD, subtract the Abundance average from +1 S.D. value
OR subtract the -1 S.D. value from the Abundance average
Exercise 2.2 – Stochastic Extinction
Select “Extinction / Decline” from Results menu
This is an extinction risk curve
 Can determine the probability of the population falling
below critical (threshold) population sizes we determine
Exercise 2.2 – Stochastic Extinction
Select Show numbers icon
Can easily determine the
probability of the population
falling below threshold sizes
(NC) from table
E.g., The probability of the
muskox population falling to
31 muskox or less during the
12 years is 0.04 (4%)
 Extinction risk
What are some probability for
decline to 31 muskox or less?
Exercise 2.2 – Stochastic Extinction
Select Show numbers icon
Extinction risk is calculated by
counting the number of trials in
which the population fell to a
particular population size (NC) or
smaller during the 12 year trajectory
(based on the minimum population
size during a trial)
 Endangered species management
Can easily determine the
probability of the population
falling below threshold sizes
(NC) from table
E.g., The probability of the
muskox population falling to
31 muskox or less during the
12 years is 0.04 (4%)
 Extinction risk
What are some probability for
decline to 31 muskox or less?
Exercise 2.2 – Stochastic Explosion
Select “Explosion / Increase” from Results menu
This is an explosion risk curve
 Can determine the probability of the population exploding
above critical population sizes we determine
Exercise 2.2 – Stochastic Explosion
Select Show numbers icon
Can easily determine the
probability of the population
exploding above threshold
sizes (NC) from table
…
…
E.g., The probability of the
muskox population exploding
to 337 muskox or more during
the 12 years is 0.01 (1%)
 Explosion risk
Exercise 2.2 – Stochastic Explosion
Select Show numbers icon
Explosion risk is calculated by
counting the number of trials in
which the population rose to a
particular population size (NC) or
larger during the 12 year trajectory
(based on the maximum population
size
… during a trial)
…
 Pest species management
Can easily determine the
probability of the population
exploding above threshold
sizes (NC) from table
E.g., The probability of the
muskox population exploding
to 337 muskox or more during
the 12 years is 0.01 (1%)
 Explosion risk
Lab 4 – Blue Whales
Follow up to blue whales exercise from Lab 3
(We are not looking at harvest this week)
Lab 4: Blue whale population growth given uncertainty
1. Practice modeling population growth using software
2. Understand how uncertainty (demographic and environmental
stochasticity) affects:
• Predictions of future population size
• Risk of extinction
Lab 4 – Blue Whales
Read through the Lab 4 handout carefully!
 Lab manual walks through the exercise thoroughly
Part A: Investigating effect of uncertainty in λ on population growth
and risk of decline
Part B: Investigating the effect of duration (simulation time) on risk of
decline
Part C: Investigating the effect of demographic stochasticity and
population size on risk
Lab 4 – Blue Whales