k-sample model exercise

This exercise is designed to show how to run programs CAPTURE and MARK to compute Capture-probability and abundance estimates from 'capture-recapture' data.

Input data consists of capture-histories of individual animals or Summarized frequencies of capture-histories. Program CAPTURE also requires a file of instructions or commands.

Running program MARK

Program MARK may also be used to estimate capture-probability and abundance from these data. Here are the steps to run MARK on this input file:

Start MARK by clicking 'Start' button (lower left corner usually), 'Programs', 'MARK 4.2', then 'MARK'. Or, double-click the MARK icon on the desktop.

When the form appears, go to the 'File' menu and select 'New'.

A dialog window will appear where you can specify the data type, title, filename, and occasion. For this example, click 'Closed Captures' under 'Select Data Type', and 'Huggins closed captures' from the list of model sub-types. Click in the textbox under 'Title for this set of data', and type:'k-sample model exercise'. Next, click the button labelled 'Click to select file'.

The program will present a dialog box asking for the name of the input file. Find the folder containing the sample input file (chap14.inp), then click on the filename (chap14.inp), then click 'Open'.

Click 'OK' and the program will create a database file containing the results for this data.

Once MARK gathers the necessary information about the input, it is ready to run the first model. By default, the first model is one where each parameter varies over time. For 'Closed captures', there are two sets of parameters: capture-probabilities(p) and recapture-probabilities (c). With five capture occasions, the parameters which can be estimated are p(1)..p(5) and c(2)..c(5). Initially, only the PIM for p is shown. To show the PIM for c, go to the 'PIM' menu, select 'Open parameter index matrix', and click 'Select all'. MARK will then show a window for p and c.

For this example, we want to run a few different models. It's best to start with the simplest models and work up to the more complicated ones. So, the first model to run will be one where all p's and c's are equal. To do this, click 'Window', then 'Tile' so all PIM windows are visible. Next, click on the window containing the PIM for p (labelled 'Capture Probability (p) Group 1', then click 'Initial', then 'Constant'. This will automatically change all of the numbers in the window to '1'. Next, click on the window containing the PIM for c (labelled 'Recapture Probability (c) Group 1', then click the textbox containing '6'. Change the '6' to a '1', then click 'Initial' and 'Constant'. Click the 'Close' button on each of the PIM windows.

Our model is now specified where all p's and c's are numbered parameter number 1. Run this model by going to the 'Run' menu and clicking 'Current model'.

A dialog box will appear allowing you to enter a model name and other information. Enter 'p(.)' in the 'Model Name' textbox, click the 'List Data' checkbox, then click 'OK to Run'.

After clicking 'Run', a window will appear briefly, then disappear. Then, a results dialog box will appear. Click 'Yes' to include the output from the model you just ran in the database file.

The MARK results browser window will now contain a line with the name of the model you just ran (p(.)) with some statistics. To view the parameter estimates for this model, click the fourth button from the left (the first button is the trash can).

A notepad window will open with the parameter estimates, standard errors and confidence limits.

The second model to run is one where recapture probability is different from capture probability. First, close any open MARK or NOTEPAD windows except for the MARK program window. Next, open the PIM windows, 'PIM', 'Open parameter index matrix', and click 'Select all'.

Make all PIM windows visible ('Window', 'Tile'), then click the first '1' in the recapture probability (c) PIM window. Click the '+' button to increment the numbers. Close all PIM windows.

Click 'Run', 'Current Model', and enter 'p(.),c(.)' for the model name.

Click 'OK to run, then 'Yes' when asked to append model results to the database file. Parameter estimates can be viewed by clicking the fourth button from the left in the 'Results Browser' window.

The third model to run is one where capture probability is time-specific, and recapture probability equals capture probability. First, close any open MARK or NOTEPAD windows except for the MARK program window. Next, open the PIM windows, 'PIM', 'Open parameter index matrix', and click 'Select all'.

Make all PIM windows visible ('Window', 'Tile'), then click the first '1' in the capture probability (p) PIM window. Click 'Initial', then 'Time' and you should see the numbers change to '1,2,3,4,5'.

Click in the recapture probability (c) PIM window, then click 'Initial', then 'Time'.

Close all PIM windows and run this model, naming it 'p(t)'.

Click 'OK to run, then 'Yes' when asked to append model results to the database file. Parameter estimates can be viewed by clicking the fourth button from the left in the 'Results Browser' window.

Running CAPTURE from MARK

You can run CAPTURE on this input by going to the 'Tests' menu and selecting 'Program CAPTURE'. When the run-dialog box appears, select 'appropriate', then click 'OK'. A notepad window will appear with the CAPTURE output. See below for what to look for. Click 'File', and 'Exit' to exit the program.

Program CAPTURE is an old MSDOS program where instructions and data are read from text files. A user-friendly interface named 2CAPTURE was written some time ago, but does not work with Windows XP. I've written a new user-friendly interface named 'CAPTURE2' to replace it.

Run program CAPTURE2 by double-clicking it from Windows Explorer. Change the title to:
'Nichols MP data, Females, month 10 adults (21+g) only'
Click the 'Input file:' button and select the 'chap14.inp' file. Click the 'View file' button to see what the file looks like.

Next, change the number of occasions to 5 and select the 'MARK' input-type option.

Run the analysis by clicking 'Run/CAPTURE' from the menu. After a few seconds, a notepad window should appear containing the output from CAPTURE.

Program Output

In the output, look for the 'closure test' to see if the data indicates rejection of a closed model.

Test for closure procedure.  See this section of the Monograph for details.



               Overall test results --
               z-value                                 -0.430
               Probability of a smaller value         0.33355

Next, look for the model selection summary:

 Model selection criteria.  Model selected has maximum value.
 
 Model     M(o)     M(h)     M(b)     M(bh)    M(t)     M(th)    M(tb)   M(tbh)
 Criteria  0.65     1.00     0.23     0.37     0.00     0.29     0.24     0.44
 
 
 Appropriate model probably is  M(h)
 Suggested estimator is jackknife.

Then, look for the results from the best model - M(h):

 Population estimation with variable probability of capture by animal.
 See model M(h) of the Monograph for details.
 
 
 
 Number of trapping occasions was            5
 Number of animals captured, M(t+1), was    52
 Total number of captures, n., was         121
 
 Frequencies of capture, f(i)
    i=   1   2   3   4   5
 f(i)=  18  15   8   6   5
 
           Computed jackknife coefficients
 
           N(1)      N(2)      N(3)      N(4)      N(5)
      1  1.800     2.400     2.800     3.000     3.000
      2  1.000     0.550     0.050    -0.250    -0.250
      3  1.000     1.000     1.133     1.250     1.250
      4  1.000     1.000     1.000     0.992     0.992
      5  1.000     1.000     1.000     1.000     1.000
 
           The results of the jackknife computations
 
   i       N(i)    SE(i)     .95 Conf. Limits      Test of N(i+1) vs. N(i)
   0      52                                         Chi-square (1 d.f.)
   1      66.4      5.09      56.4      76.4          1.748
   2      70.4      7.53      55.7      85.2          0.085
   3      71.2      9.55      52.5      89.9          0.000
   4      71.2     10.73      50.2      92.2          0.000
   5      71.2     10.73      50.2      92.2          0.000
 
 Average p-hat = 0.3723
 
 Interpolated population estimate is         65 with standard error     5.6978
 
 Approximate 95 percent confidence interval        58 to         81

Can you do it?

Suppose it rained on days 1 and 3 of sampling and you expect the capture probabilities to be the same value for those days, but a different value for the other 3 days. Also, recapture probabilities on each day are the same as capture probabilities. How would you run this model?