In-class Exercise #11: Metapopulations 

Modeling metapopulations in time and space requires a tremendous amount of detailed information to parameterize potentially complex spatially explicit simulations of populations interacting as a metapopulation.  It is possible to simplify such models in a variety of ways based on real limitations in the information available.  Where the detailed information is adequate, using a model such as the metapopulation version of RAMAS allows us to explore a great variety of questions and both theoretical and management issues. 

A Windows version of RAMAS METAPOPW is located at S:\Courses\WLF448\RAMAS\METAPOPW.EXE.  Copy the entire RAMAS directory to your own network drive.

 1.  Start the program Metapopw.exe by double clicking on its icon of a map in the Ramas subdirectory after you’ve copied that subdirectory to your own network drive.

Model Menu 

 2.  Select the model of the California (Southern) Spotted Owl under the File menu by clicking Open and selecting the metapopulation model file cal-owl.mp.  When the file opens you will see a map depicting 23 spotted owl populations within the southern California metapopulation.  The size of the circle is related to the population size and the lines show which populations are connected through dispersal.  Which population is the largest?  Which population is the most isolated?

 3.  Learn about the structure of the model by exploring the description of its structure and assumptions under General Information in the Model menu.  Note that you can modify many of its assumptions and control the simulations by changing parameters in these menus.  We will use the defaults for Environmental (i.e., Normal) and Demographic stochasticity.  You can also include catastrophes based on a probably of occurrence and whether it should occur locally or regionally.  For this exercise we will not include catastrophes.  In looking at this General Information window, how would you modify the simulation to run for 50 years instead of the default of 20 years? 

4.  You can see the stage structure of the model by looking at the Stage matrix in the Model menu.  Juveniles = stage 1 and adults = stage 2.  This matrix can be interpreted as what changes between time t and t + 1, 0% juveniles stay juveniles, 30% of juveniles survive to become adults, 22% of adults produce juveniles (for example out of 100 adults 22 of them produce young that become juveniles), and 75% of adults survive.  How would you change the survival rate of adults to 80%? 

5.  Under Initial stage abundances of the Model menu the number of individuals in each stage (i.e., 1 or 2) within each of the 23 populations that makeup this metapopulation of spotted owls is shown.  Which population has the largest number of juveniles?

6.  The Stage dependent migration of the Model menu defines the dispersal rates for each stage.  The numbers are relative values with a 0 meaning that the individuals in that stage do not migrate to other populations.  A value of 1 means that the migration rate for individuals of that stage is the same as the overall migration rate for all populations.   In this model do juveniles or adults migrate? 

7.  The Catastrophe multiplier under the Model menu will not be changed since we are not including any catastrophes in our model.

8.  Populations under the Model menu shows the basic population parameters (i.e., initial abundance, growth rate, and carrying capacity) for each of the 23 populations within this metapopulation.  It also includes density dependence and catastrophe.  Note that after changing a population name, you must click in a cell in order to see the current values for that population.  You can see a graph of the 5 parameters in the View box by clicking on any of the 1-5 numbers.  If you wanted to begin the model with the same number of individuals in each population how would you do it?

9.  Under Model go to Migration and then Matrix.  The migration matrix shows the migration rate of each population (columns) to other populations (rows) at carrying capacity.  The diagonal is zero, why?  What is the migration rate between San Bernardino and San Gabriel?

10.  Under Model go to Correlation and then Matrix.  This correlation matrix shows the degree of correlation between population growth rates.  It represents the similarity of environmental fluctuations that the populations experience, which means that the growth rates among the populations are correlated through time according to this correlation matrix.  Why are all the values on the diagonal equal to 1.0?  How correlated are the growth rates between San Rafael and Santa Ynez? Why do you think their population growth rates are highly correlated?

Options Menu

11.  Now that we have looked at all the Model inputs, close the current model (File-Close).  Now, let's look at the Options menu.  If we wanted to build our own model we would choose Configuration.  You can alter the Simulation delay if you want, but it will take longer to run.  The Map feature saves the final map generated by the model in a RAMAS *.map file.  

Run Menu

12.  Click File-Open and select cal-owl.mp.  We'll run the model with the default values, so choose Run Model under the Run menu.  Choose Start when the run window appears.  Your model will begin to run 100 replications each being 20 years long. 

Results Menu

13.  When the model has completed its run, look under Results.  There are several different kinds of results to view.  Let's focus on the top 5 results (i.e., trajectory summary, population structure, final stage abundances, metapopulation occupancy, and local occupancy). Each of the results can be viewed either graphically or numerically.  Just pick the correct option in the Display Mode box before clicking on View.  Use the table below to translate population number to population name for some of the graphical results.  Note that typing ALL in the Population box (where applicable) will combine results from all populations.

Options:

Trajectory summary: shows the average (solid black line), ± 1 standard deviation (blue lines), minimum and maximum size (red diamonds) of the metapopulation (i.e. total number of individuals in all the populations included in the summation), or any given population (i.e. the number of individuals in the population). Use the drop down menu to see individual populations.

Population structure: A histogram that shows the distribution of population sizes at a specific time step. The average (green bars), ± 1 standard deviation (blue lines), minimum and maximum sizes (red diamonds) are given.  Set Reference time to 0 to view the initial population structure.

Final stage abundances: Histograms that show the average (green bar), ± 1 standard deviation (blue lines), minimum and maximum number (red diamonds) of individuals (over all replications) in each stage of a specific population, at the end of the simulation. Use the drop down menu to specify a population.

Metapopulation Occupancy: Shows the average (solid black line), ± 1 standard deviation (blue lines), minimum and maximum number (red diamonds) of extant populations (i.e. occupied patches) in the metapopulation through time.  Note how the number of populations has decreased over time.

Local Occupancy:  Histograms that show the average (green bars), ± 1 standard deviation (blue lines), minimum and maximum number (red diamonds) of time steps that each populations has remained extant (i.e. average duration each patch remained occupied).

Are the prospects for spotted owls in California over the next 20 years good or bad?  Change the duration to 50 years in Model-General information and re-run the model.  View the results.  Is your previous answer still valid?