FW364 Ecological Problem Solving
Lab 4: Blue Whale Population Variation
[Ramas Lab]

Log onto computers please
Download files from Website for today’s lab

Computer Lob Logistics
Feel free to use your own laptops instead of lab computers
BUT…
We are using the Ramas software-
Ramas 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’ , N
0
, # 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!
Download Ramas software from website:
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)
Comments: “Muskox simulation Exercise 2.2”
Can list parameter values in comment box
Comments will be the header on any results you print out
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
Select “Population” from Model menu
 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
Select “Run” from Simulation menu
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:
N t+1
= N t

 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

Exercise 2.2 – Checking Answer
Note: We can check the deterministic result with a calculator using:
N t
= N
0
 t where N
0
= 31 , 
= 1.148
, t = 12
N t
=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

Exercise 2.2 – Adding Stochasticity
Now let’s try adding stochasticity
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)

Exercise 2.2 – Adding Stochasticity
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)
Select “Population” from Model menu
Keep Initial abundance = 31
Keep Growth rate (R) = 1.148
Set Survival rate (s) = 0.921
We now have a 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: N t+1
= N t
( λ ± error t
)

Exercise 2.2 – Running Stochastic Simulation
Select “Run” from Simulation menu
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
( N
C
) 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 (N
C
) 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
( N
C
) 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 ( N
C
) 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 (N
C
) or larger during the 12 year trajectory
(based on the maximum population
…
 Pest species management
Can easily determine the probability of the population exploding above threshold sizes ( N
C
) 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
General Comments
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
General Comments
For reports:
You will be making most figures in Excel
There is one figure (trajectory summary) you will get directly from Ramas
Remember axis labels on figures
Need to use tables to summarize results
Report DUE October 8
Don’t forget to think about the assumptions you are making…
 You are making an assumption regarding whether demographic stochasticity is important (through your modeling choice)