Multi-strata Open model exercise

This exercise is designed to show how to run program MARK to compute survival, movement, and capture-probabilities from 'capture-recapture' data.

Background

Data for this example came from the trapping of meadow voles, Microtus pennsylvanicus, of mass >=22g, at Patuxent Wildlife Research Center, Laurel, MD from September 1991 through May 1992. A sample grid consisted of a 7 x 15 retangle of trapping stations with adjacent stations within each row or column separated by 7.6m (25ft.) The rectangle was divided into two square strata. Stratum 1 was defined by trapping rows 1-7 and stratum 2 was defined by trapping rows 9-15. Because the overall grid contained seven columns of traps, both strata were squares with 7 x 7 trapping stations. The grid was one of four replicates that received a "fragmentation" treatment. During primary sampling periods 1-4, the grid was continuous, and between periods 4 and 5, it was plowed and disced [see Nichols and Coffman (1999) and Coffman et al. (2001) for illustration of grids]. This "fragmentation" occurred between the two grid halves andaround the periphery of the grids, and involved a 7.6-m strip of bare, plowed ground. Sampling periods 5-11 were thus viewed as posttreatment. The two grid halves were the patches of interest and movement occurred when an animal present on one half in one sampling period was present on the other half in the next smapling period.

Primary sampling occurred every 8 weeks, and five secondary periods (consecutive days) were trapped during each primary period.

Data input

Input data consists of summarized frequencies of capture-histories.

The example we'll use for this model contains 2 groups of animals: Males and females. So, each capture-history will have 2 frequencies following the capture-history. The input file has allready been created and is named: 'multistrata.inp'.

Here are the steps to run MARK on this input file:

Start MARK by clicking 'Start' button (lower left corner usually), 'Programs', 'MARK 4.3', 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 'Multi-strata Recaptures only' under 'Select Data Type'. Click in the textbox under 'Title for this set of data', and type:'Multi-strata open 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 (multistrata.inp), then click on the file (multistrata.inp), then click 'Open'.

Change the number of encounter occasions to 11. Change the number of groups to 2, and click the 'Enter group labels' button. When the dialog box appears, change the name of group 1 from 'Group 1' to 'Males'. Change the name of group 2 from 'Group 2' to 'Females'. Then, click OK.

Click the 'Enter strata names' button. When the dialog box appears, change the first strata-code from 'A' to '1', and change the second strata-code from 'B' to '2'. Click 'OK' to close the dialog box.

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

Model S(.),psi(.),p(.)

For the 'Multi-strata' models, there 3 sets of parameters: survival, movement, and capture probability. Once the database file is created, MARK will open one PIM window for you. Since there are a lot of PIM's, we'll create the simplest model the PIM chart. Close the parameter index window and click the PIM chart button.

The parameter index chart is a graphical representation of the parameters. The blue box in the lower-left corner means that parameters 1-10 on the horizontal axis are associated with survival for males in strata 1 (S1:Strata 1 m). To make survival constant over time for this group, right-click on the blue box, and select 'Constant' from the pop-up menu. The box will be modified so that only parameter number 1 is associated with strata-1-male survival.

Right-click on all of the other boxes and select 'Constant' for each of them.

At this point, parameters 2-9, 11-19, 21-29,... are undefined (ie. not associated with survival, movement, or capture probability). The parameters must be renumbered to eliminate these 'gaps'. To do this, right-click anywhere in the chart, and select 'Renumber with overlap'.

Currently, survival is constant, but strata and sex specific. To make survival equal amoung stata and sexes, left-click on the second box from the left, hold the left-button down and move the box to the left until it is on top of the leftmost box. Repeat for the other two survival boxes. Now, all four sets of survival parameters are parameter number 1.

Make capture-probability equal amoung the sexes and strata by 'dragging' three of the boxes on top of the box for the first p (p 1:strata 1 m). All capture probabilities are parameter number 5 now.

Make all movement rates equal by dragging three of the boxes on top of the first movement rate box (psi 1 to 2 m).

Get rid of the gaps again by right-clicking on the chart and selecting 'Renumber with overlap'. We now have a 3-parameter model - S(.),psi(.),p(.).

Click the 'Close' button, then click 'Run', then 'Current model'.

When the dialog box appears, enter 'S(.),psi(.),p(.)' for the model name, click the 'List data' checkbox, then click 'OK to Run'. Click 'Yes' when asked about appending the model output to the database. View the output by clicking the fourth button from the left in the Results Browser, then close the notepad window.

Model S(t),psi(t),p(t)

The next model to run with this example is: S(t),psi(t),p(t) [ survival time-specific, but equal amoung strata and sex, same for movement(psi) and capture probability(p)].

Start by going to the 'PIM' menu and selecting 'Parameter Index Chart'. Right-click in the lower-left box and select 'Time'. You'll see that one of the original four boxes has been expanded to fill columns 1-10. Right-click the other original boxes and select 'Time' to expand them.

Next, move the capture probability boxes to the far right until they are over columns 11. Then, right-click on each one and select 'Time'.

Repeat for the movement probabilities, first moving the boxes to column 21, then make time-specific.

Click 'Close', then click the 'run' button.

By default, MARK will use the name of the last run model for the model name. Make sure to change this or you will have two models with the same name, and worse, the model name will not reflect the actual structure of the model. Change the model name to 'S(t),psi(t),p(t)', then click 'Fix Parameters'.

When the dialog box appears, click in the textbox next to number 20, enter '1', then click 'OK'. The reason for setting parameter number 20 to 1 is because under a time-specific survival and time-specific capture-probability model, the last estimated survival and last estimated capture probability cannot be estimated separately. Only their product can be estimated, so if we set the parameter 20 (the last p) to 1, then parameter 10 (the last S) will actually be the product of S(last)*p(last).

Next, click the 'List data' box to deselect it, then click 'OK to run'

Model S(t),psi(1-4,5-10),p(t)

For this experiment, there was a treatment applied to the trapping area after occasion 4. So, we would like to try a model where movement is constant for occasions 1-4 and constant (but different) for occasions 5-10.

This type of model cannot be specified in the Parameter Index Chart, so go to the PIM menu and select 'Open parameter index matrix', and click on each of the transition parameters and click the 'Open' button.

Next, click somewhere in the 'Transition (psi) 1 to 2 m' window to make it fully visible. Go to the 'Initial' menu, and click 'Constant'. Next, change the '21' to '22' in the first 4 rows and first 4 columns of the matrix.

Next, go to the 'Initial' menu, then select 'Copy a PIM to 1 or more PIMs'. When the dialog box appears asking which PIM you want to copy, select 'Transition (Psi) 1 to 2 m'. Then, click 'OK'. When the dialog box appears asking which PIM to copy to, select the other 3 transitions ('1 to 2 f', '2 to 1 m', and '2 to 1 f'. Then, click 'OK'.

Close the matrix windows and run the model by clicking the second-from-right button (containing green triangle), change the model name to 's(t),psi(1-4,5-10),p(t)', and click 'OK to Run'. Then, click 'Yes' to append the model output to the database, and click the 'view parameter output' button (4th button from left).

Model S(t),psi(s*1-4,5-10),p(t)

The last model to try is like the previous model except that males and females have different movement rates before the treatment. So, we need one additinal parameter in the model. We need to change the parameter number for pre- treatment movement for males (or females) to a different parameter index number. So, let's open the parameter index matrices for movement 1-2 and movement 2-1 for females, and change the 22's to 23. Then, run the model and view the estimates for effects of treatment on movement. Click 'File', and 'Exit' to exit the program.