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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 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! 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: 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 Exercise 2.2 – Checking Answer 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 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 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 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 (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 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)