In-class Exercise 6: Band-Recovery Analysis

WLF 448: Fish & Wildlife Population Ecology
Lab Notes 8, Fall 2004

In-class Exercise 8: Band Recovery Analysis

(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 wood ducks using some very simple models. The analysis capabilities of this program go far beyond the scope of this lab and you are encouraged to explore them.

We will working with a dataset on mallards from St. Luis Valley in Colorado.

I. Copy files from class directory to your personal directory

Use the Windows File Manager to copy all files and subdirectories from K:\WLF\448\2004\Lab2004\MARK2004 to your zip disk or personal directory on the H: drive. If you don't know how to do this, please ask for help. If you do not have enough room on your H: drive, then you will have to copy the files to a ZIP disk. As a last resort you can use the temp T: drive, but remember everything on the T: drive is erased each night!
Note: You can also obtain the program MARK from http://www.mbr-pwrc.usgs.gov/software.html.

II. Starting a project

Open MARK by double clicking on the file called Mark_Int. This should start up the MARK program.

First you need to start a new project or open an existing project. Click on the File drop down menu and then click New. You should now be in the ‘Enter Specifications for MARK Analysis' window.
Under 'Select Data Type' click on 'Recoveries Only' because we will be using band recovery data.
Enter a Title for your data set.
Now you need to tell MARK where to find the data file. Under ‘Encounter Histories File Name’, enter either the name and directory path to the file called slvm_exer.inp or select ‘Click to select file.’ Then navigate to the desired file in the directory where you saved it and select the file.
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. How many years were bands recovered? Or in other words how many columns are in the matrix of the input file? How many groups are in the data set? Or in other words how many age classes were banded and recovered? Remember these values. Close this editor when you are done (Go to File and then Exit).
Change the ‘Encounter Occasions’ to the number of years bands were recovered. It defaults to 5 but this is in no way indicative of the encounter occasions of your data set.
Change the ‘Attribute Groups’ to the appropriate number for your data set. It defaults to one but does this does not indicate the true number for your data set.
You can also click on 'Enter Group Labels' and label each age group based on your dataset (group 1 = adults, group 2 = young). Click OK.
We will not use 'Individual covariates' or 'Strata' for this exercise.
Once you have properly specified your analysis click ‘OK.’
Click ‘OK’ when the program tells you it created a dbf file.

III. Running Models

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 PIM’s. 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 PIM’s for this analysis.
To open the other 3 PIM’s click on the ‘PIM’ drop down menu and select "Open Parameter Index Matrix." Then ‘select all’ and then ‘OK.’ All 4 PIM’s should now be open. (See Program MARK Models in Lab Notes (under roman numeral XV.A.) for explanation of PIM’s.)
You can select 'Tile' under the 'Windows' menu to see all 4 PIM's at once.
Examine the PIM’s and make sure the parameter indexing is consistent with the s(g*t) r(g*t) model structure. See Lab Notes for more information regarding model structure. Remember g = group and t = time.
Then select ‘Run’ from the drop down menu and select ‘Current Model.’
You should now see the ‘Setup Numerical Estimation Run’ screen. Your model title should be the same as your entered previously.
In 'Model Name' type: s(g*t)r(g*t).
Under ‘Link Function’ click "Logit." A link function is the function that links the linear model specified in the design matrix with the survival, recapture, reporting, and fidelity parameters. Click on Help for more information.
Leave everything else set as the default and select ‘OK to Run.’
A message will pop-up asking if the identity matrix should be used. This is a matrix with 1’s on the diagonal and 0’s everywhere else. Select ‘Yes.’
The model estimation will scroll past on the screen and then the model results should appear in a 'Results Browser' window. The results will appear with a message asking if you want to append the results to the database. Select ‘Yes.’
In the ‘Results Browser’ you should see the ‘model name’, AIC_c, Delta AIC_c, AIC_c Weight, Model Likelihood, Number of parameters, and the Deviance. More on these after we have run all the models.
To view the estimates select the fourth tool bar button from the left (a series of horizontal lines) in the ‘Results Browser.’
The parameter column corresponds to the parameter number you indexed in the PIM’s. (i.e. the 1^st set of parameters estimate survival for adults for each year of recovery, the next set are survival estimates for juveniles, then the next set are recovery rates for adults, and the last set are recovery rates for juveniles.) Also note that there is a standard error and 95% confidence interval for each estimated parameter. (Note: There are 36 parameters corresponding to 36 unique values in the PIM’s.)
Close this notepad (File—Exit) (Note: You can print these estimates if you wish.)
Now you need to run 3 more models. [s(.t)r(.t)], [s(g.)r(g.)], and [s(..)r(..)]
To do this we will re-parameterize the PIM’s. You will notice that all the PIM’s are still open behind the ‘Results Browser.’
Re-parameterize the PIM’s to reflect the structure of the s(.t)r(.t) model and follow steps 4-15. (Hint: The survival PIM’s should be time dependent but should not be dependent on group. They should look identical, using the same exact numbers. See Lab Notes for an example.)
You can quickly change numbers within a PIM 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).
After running this model and viewing the results, re-parameterize the PIM’s to run the s(g.)r(g.) model and follow steps 4-15. (Hint: this model has constant survival and recovery across recovery occasions but these rates are different between groups. See Lab Notes for an example.)
After running this model and viewing the results, re-parameterize the PIM’s to run the s(..)r(..) model and follow steps 4-15. (Hint: this model has constant survival and recovery rates across all recovery occasions and groups. See Lab Notes for an example.)
Now you should have the results of 4 models in the ‘Results Browser.’
Think of how else you might parameterize a model. What are the biologically reasonable possibilities? MARK would allow you to re-parameterize this model in many more ways. You could even account for weather or environmental variables or weight the estimates by rainfall, temperature, or some other relevant variable.

IV. Interpreting the Results

Some of the 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.
Compare the order of preference of models based on AIC to their corresponding deviance. Deviance is essentially a measure of fit, or how well the estimated model compares to the data. It is possible that a model with fewer parameters could be the selected model by AIC, but have a greater deviance than other models. The likelihood of a model is the QAICc Weight for the model of interest divided by the QAICc Weight of the best model. This value is the strength of evidence of this model relative to other models in the set of models considered.
We can also compare "nested" models using likelihood ratio tests. A "nested" model is one that is constrained from a more complex situation. The null hypothesis for this test would be that the simpler model (model with fewer parameters) is as likely to explain the variation in the data as the more complex model.
To run the likelihood ratio test select ‘LR Tests’ under the ‘Tests’ drop down menu.
The 'Models Selection for Likelihood Ratio Tests' window should appear. Click ‘Select All’ to perform all likelihood ratio tests. Then click ‘OK.’ Note: Doing this may result in likelihood ratio tests that are not valid (not tests of nested models). Thus, before interpreting a test make sure it is valid. In the program this test appears as ‘reduced model’ (simplest) compared to the ‘general model’ (more complex model).
You can print these tests by selecting ‘Print’ under the File drop down menu in Notepad.
When you are done with these results exit Notepad and return to the ‘Results Browser.’
To print the ‘Results Browser’ click on the 7^th toolbar button from the left on the ‘Results Browser’ toolbar. This will open the 'Results Browser' in a Notepad where you can select ‘Print’ under the ‘File’ drop down menu.
Note: The Delta AIC is the difference in the AIC value of each model compared to the model with the lowest AIC. The AIC Weight weights the Delta AIC value for each model. This is a method for explaining how much "better" one model is compared to another.
There are many other statistical tests that MARK will perform but we will leave those for the ambitious and mathematically inclined.

Return to Lab Notes

Revised: 06 October 2004