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 software2. Illustrate how to run deterministic vs.

stochastic models• Exercise 2.2 in text

Lab 4: Blue whale population growth given uncertainty

3. Practice modeling population growth using software4. 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 equationsEquations 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….

…with associated data in tables

Growth trajectories

Extinction Risk Curves

Explosion Risk Curves

Introduction to Ramas

Download Ramas software from website:SETUP.EXE Ramas program fileREpatch2.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)

Let‘s get started!

Introduction to Ramas

STEP 3: Start RAMAS EcoLab software

STEP 4: Click Population Growth (single population models)

Let‘s get started!

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

Runsimulation

Getresults

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 boxComments 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 stochasticityWe 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 modelLikewise, 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 menuThere is a tone when completeSays Simulation complete in lower right corner of window

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

We now have results!

Exercise 2.2 – Viewing Results

Now let’s examine results

Select “Trajectory summary” from Results menuOnly one trajectory shows exponential increase

Exercise 2.2 – Viewing Results

Now let’s examine results

Select “Trajectory summary” from Results menuOnly 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

Note that SD = 0 All columns equal the Abundance averageRamas presents actual values for average ± 1 SDTo obtain SD, subtract the Abundance average from +1 S.D. valueOR subtract the -1 S.D. value from the Abundance average

Show numbers PrintCopy

Exercise 2.2 – Checking Answer

Note: We can check the deterministic result with a calculator using:

Nt = N0t

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

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 individualsChance of each individual surviving is, e.g., 0.4,rather than 0.4 of population survivesNo error in lambda, just randomization due to modeling ofindividuals

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

Exercise 2.2 – Adding Stochasticity

Continuing with Exercise 2.2

Let’s specify simulation with environmental stochasticity

Select “General information” from Model menuSet Replications to 100Keep Duration = 12Do not check Use demographic stochasticity

(no demographic stochasticity this time)

Select “Population” from Model menuKeep Initial abundance = 31Keep Growth rate (R) = 1.148Set Survival rate (s) = 0.921Set 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 )

We now have a distribution for λ

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 ofmodel trials

Vertical lines:1 SD above and below the mean trajectory

Diamonds:Max and min of all trials

Select Show numbers icon

What are some finalpopulation sizes?

Did anyone have amaximum population sizeabove 400 muskox?

Did anyone have aminimum population sizebelow 10 muskox?

To obtain SD, subtract the Abundance average from +1 S.D. valueOR subtract the -1 S.D. value from the Abundance average

Exercise 2.2 – Stochastic Trajectory Summary

Exercise 2.2 – Stochastic Extinction

Select “Extinction / Decline” from Results menu

This is an extinction risk curve Can determine the probability of the population fallingbelow critical (threshold) population sizes we determine

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 the12 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

Exercise 2.2 – Stochastic Extinction

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 the12 years is 0.04 (4%) Extinction risk

What are some probability for decline to 31 muskox or less?

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 inwhich 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

Exercise 2.2 – Stochastic Explosion

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

(We are not looking at harvest this week)

Lab 4 – Blue Whales

Follow up to blue whales exercise from Lab 3

Lab 4: Blue whale population growth given uncertainty

1. Practice modeling population growth using software2. Understand how uncertainty (demographic and environmental

stochasticity) affects:• Predictions of future population size• Risk of extinction

Read through the Lab 4 handout carefully! Lab manual walks through the exercise thoroughly

Part A: Investigating effect of uncertainty in λ on population growthand risk of decline

Part B: Investigating the effect of duration (simulation time) on risk ofdecline

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 RamasRemember 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)

Lab 4 – Blue Whales

General Comments