WLF 448: Fish & Wildlife Population Ecology
Lab 13, Fall 2011

In-class Exercise #13:

Band Recovery (Survival Estimation)

 

We will be using a program called MARK for this exercise. MARK is a very powerful program that utilizes current modeling techniques and model selection procedures. This program can handle most types of marking data. Survival estimation is the main focus of the program although it does have the capabilities to perform population estimation. For this exercise we will analyze a band recovery data set on mallards (Anas platyrhynchos) from the San Luis Valley of Colorado using some very simple models. The analysis capabilities of this program go far beyond the scope of this lab.

I. Copy the input files from the class directory to your personal directory:

The file you need to copy for the in-class exercise and homework problem set is in the directory at S:\Courses\WLF448\MARK\ and is called slvm_exer.inp.  I also suggest you copy the entire MARK directory to your personal workspace to avoid problems.  If you encounter problems in the early stages of the exercise, you may find that copying the entire MARK folder from the S: drive to your workspace alleviates the problems.

II. Starting a project:

              To begin:  Open MARK by clicking Start - UI Software - Programs - Analytical - MARK.

    1. Start a new project or open an existing project. Click on the
      2. File drop-down menu and then click New. You should now be in the Specifications Window.
    2. Select the Data Type. We will be using band recovery data so select
      3. Dead Recoveries (Seber).
    3. Enter a Title for your data set.
    4. Under Encounter Histories File Name: either type the directory and filename or select Click to select file. Navigate to slvm_exer.inp in the directory where you saved it and select it.
    5. Once you have selected the file, view it by clicking View File. Go through the recovery matrix and be sure you understand the structure of the file. The numbers recovered each year are shown in the matrix, followed by the total number banded each year.  Note the groups (adult and young) and number of recovery events (9).  You will need this info in the next steps.  Close the editor when you are done (File - Exit or click the red X).
    6. Change the Encounter Occasions to the appropriate number for your data set. It defaults to 5 but this is in no way indicative of the encounter occasions of your data set. How many years were bands recovered?  (Hint: There are 9 columns in the matrices in the input file).
    7. Change the Attribute Groups to the appropriate number for your data set. The default is 1, but this does not indicate the true number for your data set.  How many groups do you have? (Hint: There are 2 classes--adults and young--in the input matrices.)  Although not required, labeling your groups (Enter Group Labels) at this stage will help clarify the groups for later in the exercise.
    8. We will not deal with individual covariates or strata for this exercise.
    9. Once you have properly specified your analysis click OK.
    10. Click OK when the program tells you it created a dbf (database) file.

III. Running Models

    1. You should now see the parameter index matrix (PIM) for the survival parameters of the first group. We need to look at all of the PIMs. There will be one PIM for survival for each group and one PIM for recovery for each group. Thus, we will have a total of 4 PIMs for this analysis.
    2. To open the other 3 PIMs click on the PIM drop-down menu and select Open Parameter Index Matrix.  Then Select all and then OK.  All 4 PIMs should now be open.
    3. See the lab notes for an explanation of PIM structure.  Examine the PIMs and make sure the parameter indexing is consistent with the [s(g t) r(g t)] model structure.
    4. Then select Run from the drop-down menu and select Current Model.
    5. You should now see the Setup Numerical Estimation Run screen.
    6. Type in the Model Name: [s(g t) r(g t)].
    7. Change the Link Function to Logit. The link functions transform the data for the numerical estimation procedure. We will only use Logit.
    8. Leave everything else set to default values and select OK to Run.
    9. A message will pop-up asking if the identity matrix should be used. This is a matrix with 1s on the diagonal and 0s everywhere else. Select Yes.
    10. The model estimation will scroll past on the screen and then the model results will appear as a tab at the bottom of the screen. Select the results file by clicking on the ‘Results’ tab at the bottom of the screen.
    11. The results will appear with a message asking if you want to append the results to the database. Select Yes.
    12. In the Results Browser you should see the Model name, AICc, Delta AICc, and other parameters listed.
    13. To view the parameter estimates, select the 4th tool bar button from the left in the Results Browser window.
    14. The parameter column corresponds to the parameter number you indexed in the PIMs (i.e., the 1st set of parameters estimates survival for adults for each year of recovery, the 2nd set is survival estimates for juveniles, the 3rd set is band recovery rates for adults, and the 4th set is the recovery rates for juveniles).  Also note that there is a standard error and 95% confidence interval for each estimated parameter. There should be 36 parameters corresponding to 36 unique values in the PIMs.
    15. Close this Notepad file (File - Exit).  Note: you could print these estimates if desired.
    16. Now you need to run 3 more models: [s(. t) r(. t)], [s(g .) r(g .)], and [s(. .) r(. .)]
    17. To do this you need to re-parameterize the PIMs. You will notice that all the PIMs are still open behind the Results Browser.
    18. Re-parameterize the PIMs to reflect the structure of the [s(. t) r(. t)] model.  Consult the lab notes to see an example matrix for this model type (as well as other types).
    19. You can quickly change numbers in the PIMs by changing the first cell in the PIM to the desired number. Then go to the Initial drop-down menu and select either Time (to get time specific variation) or Constant (to get constant rates across recovery periods).
    20. Follow steps 4-15, above, to run this model and view the results. 
    21. Re-parameterize the PIMs and follow steps 4-15 again to run the remaining 2 models: {[s(g .) r(g .)] and [s(. .) r(. .)]}.
    22. Now you should have the results of 4 models in the Results Browser.
    23. How else might you parameterize a model?  What are the biologically reasonable possibilities?  MARK allows you to re-parameterize models in many more ways.  You even could account for weather or other environmental variables or weight the estimates by rainfall, temperature, or some other relevant variable.

IV. Interpreting the Results

    1. Current statistical theory would suggest that you can select the most applicable model based on information criteria (AIC). Thus, the most appropriate model of those that you just ran would be the one with the lowest AIC.
    2. What are the parameter estimates (survival and recovery) with the AIC best-fit model?  Hint: see step 13 in the "Running Models" section, above.
    3. The Delta AIC is the difference in the AIC value of each model compared to the model with the lowest AIC.
    4. There are many other statistical tests that MARK will perform, but we will leave them for those of you that are ambitious and statistically inclined.

Revised: 28 November 2011