INTRODUCTION TO PROGRAM MARK
Program Mark is software written by Gary White at Colorado State University for the
analysis of capture-recapture data from marked animals. A substantial amount of
information about this software and capture-recapture in general can be found at Dr.
White’s website (http://www.cnr.colostate.edu/~gwhite/). In this lab we will learn about
the structure of input files for Mark, the basics of model construction in Mark and some
of the command structure for Mark.
1. Getting Started:
a. Mark automatically creates an output file when you open a data file so you
want to move the files you will be working with to your personal folder to prevent
the existing examples from being overwritten. Open up Windows Explorer and
move the following files to your personal folder:
BROWNIE.INP
BROWNIE.FPT
DIPPER.INP
DIPPER.FPT
The .inp files contain the data you will be working with but Mark also requires
access to the .fpt file.
b. Close (or minimize) Windows Explorer. Double-click the Mark icon to open
Program Mark. Click the spreadsheet icon in the upper left corner to open a menu
for Specifications for Mark Analysis. This menu allows you to specify the kind
of analysis you will conduct (Select Data Type). Today we will start with a data
set that includes recaptures only so be sure this Data Type is selected.
Look to the right and you will see a button: Click to Select File. Click this button
and browse to find the Dipper.inp file. Double click this file to open this file in
Program Mark. Now click the view this file button, which will allow you to see
the data file. You will see some file information at the top enclosed in //, which
tells Mark this information is not part of the data. Below, you will see encounter
histories followed by a space pairs of 1s and 0s, also separated by a space, all of
this followed by a ;. The encounter history indicates the occasions when each
individual was encountered (actually observed), indicated by a 1, or not ed,
indicated by a 0. The two columns to the right indicate the sex of each individual.
Notice that there is a column for each group and each individual has a 1 in only
one of the columns, indicating it is either a male or a female. The ; at the end
indicates the end of the record. Note that in this encounter history each individual
has its own record, which is required in this case because group membership has
to be defined for each individual. For cases with a single group, it is possible to
specify only the observed encounter histories and indicate the number of
individuals with each history.
We now have to provide Mark some information about the data. You should
provide a title for the data to keep you results organized. Below the data file
selection area you will find some buttons and counters to provide additional
information. Encounter occasions needs information about the number of
possible times an individual was encountered. Count the number of columns in
the dipper encounter history (there are 7) and enter this number for encounter
occasions. (Notice that you can also tell Mark if intervals between encounter
occasions differ in length which can be handy when individuals are sampled at
different intervals. We won’t worry about this feature today.). Mark knows thee
are two groups and you should enter labels for each group in the appropriate
location.
Once you have completed these tasks click OK; Mark has the basic information it
needs to perform an analysis.
2. Running Models:
A window will open entitled “Apparent survival Parameter (phi) males of live
recaptures”. Before we discuss this window we need to open some additional
windows. Click on the PIM button on the top toolbar, then click on “open
parameter index matrix”. Click select all then OK. Click on the Window button
on the top toolbar then click on Tile.
You should see 4 similar appearing windows all with the upper diagonal of a
matrix. Look more closely and you’ll see that the window for male survival has
numbers ranging from 1 to 6 as columns go from left to right. For female
survival, numbers range from 7 to 12. The two reencounter probability matrices
have numbers that range from 13 to 18 and 19 to 24, respectively. These numbers
specify the model structure by defining the subscripts on survival and encounter
probabilities. The model you have specified allows survival and encounter
probabilities to each differ between sexes and to vary annually. Expected
encounters of males on each occasion associated with this model would look like
the table below.
Number
Released
N1
N2
N3
N4
N5
N6
1
2
3
N1S1p13
N1S1S2p14
N2S2p14
Expected encounters on occasion i
4
5
6
N1S1S2S3p15
N2S2S3p15
N3S3p15
N1S1S2S3S4p16
N2S2S3S4p16
N3S3S4p16
N4S4p16
N1S1S2S3S4S5p17
N2S2S3S4S5p17
N3S3S4S5p17
N4S4S5p17
N5S5p17
7
N1S1S2S3S4S5S6p18
N2S2S3S4S5S6p18
N3S3S4S5S6p18
N4S4S5S6p18
N5S5S6p18
N6S6p18
We could make a similar table for females but survival subscripts would range
from 7 to 12 and reencounter subscripts would range from 19 to 24.
To run this model click on the small button with the green arrow (third from left).
Anew window will open asking for the title for the analysis and the model name.
Use dippertest or another descriptive name for the analysis. Identify the model as:
{phi(g*t),p(g*t)}, which indicates that survival and encounter probabilities can
each vary across both groups and time, independent of each other. This model is
among the most general we can run for this data set. Click OK, and a new
window will ask you if you want to use the identity matrix because no design
matrix was specified. Click yes (or OK) we’ll learn more about the design matrix
later. A new black window with scrolling text will open indicating that Mark is
doing calculations (the numerical methods to maximize the likelihood for the data
and specified model).
When Mark is finished a new window will open asking you if you want to append
the model to the database. Click yes and a new table (The Results Browser) will
open. The model is identified on the left based on the notation you provided,
AIC, AIC weight, number of parameters and deviances are all reported. We’ll
learn more about AIC later. For now view AIC as a ranking of the quality of the
models from best (low AIC) to worst (high AIC). Deviance is a measure of how
well the model fits the data.
Retile all of your windows (the Results Browser will also appear now). Use the
minus button to reduce the numbers in survival windows to 1 for both males and
females and 2 for the both the windows for encounter probabilities (for the latter
reduce all matrix entries to 1 then use the plus button to increase them to 2). Use
the green arrow to run this model and follow the same procedure as for the earlier
model to run this model. Identify the model as {phi(.),p(.)}, which indicates that
both parameters are constant across both groups and time. This is the simplest
model we can run for these data. Again, use the identity matrix and append the
results to the Results Browser. The “dot” model performs better (lower AIC) and
has fewer parameters so it is the best of the two models run so far.
3. Examining Parameter Estimates:
To examine parameter estimates click on the model, then move the curser to the top
tool bar and click on Retrieve. Then click on current model. To see the parameter
estimates for the retrieved model return the curser to the Results Browser and click
the fourth icon from the left (the third minipage from the left). A text file will open
with a list of parameters and their estimates. For the dot model you will only see one
survival estimate and one encounter probability because you specified that both
parameters would be constant across groups and time.
Now retrieve the {phi(g*t),p(g*t)} model and examine parameter estimates for this
model. You will se 12 survival estimates and 12 estimates for detection probability,
six of each for each group. These are indexed using the numbers you provided in the
PIMs. Notice that the 6th and 12th estimates for both phi and p have standard error
that are either very large or zero. These are the estimates for the last survival and
encounter probability for each group, which cannot be estimated; only their product
can be estimated.
4. Examination of models:
To save time we will examine a number of models of the dipper data that have
already been run. Click on the File button, then Open File. Select the Dipper.dbf file
from the Examples subdirectory in the Mark Directory. A new Results Browser will
open with the results from a number of pre-run models. When you do a complete
analysis of a capture-recapture data set this is approximately what the Results
Browser will look like. Notice that most combinations of model parameters have
been considered.
Each model represents a specific hypothesis about the nature of the variation in either
survival or encounter probability. One illustrative example is the model with a
“flood” term for survival. Biologists studying the dipper population hypothesized
that years with exceptionally high water might negatively affect survival of dippers.
Using the PIM they created a model in which survival in flood years differed from
that in non-flood years but was constant between sexes and across years of either
type. Notice that a model with a flood term for survival and constant encounter
probability performed best based on AIC. Retrieve this model and open the PIM.
You can see that survival was classified as having two values, one for flood years and
one for non-flood years. Encounter probability was constant across sexes and years.
5. Other issues:
You have just several models to capture-recapture data using maximum-likelihood
approaches to parameter estimation (remember the binomial coin toss example).
Mark provides an extremely powerful tool for model selection (more about that later)
and parameter estimation for studies of marked animals.
You now have a new set of tools for population analysis. There are a number of
issues we have not yet addressed, however, that are necessary for the proper
application of theses tools. We will address these issues in future lectures and labs.
You need a clearer understanding of AIC and what it means. We have not discussed
measures of goodness-of-fit and how these impact conclusions about the best model
and parameter estimates.
6. An introduction to band recovery data:
a. Structure of the data:
We are going to briefly explore one other type of data from marked animals today:
recoveries of banded birds by hunters. In band recovery data individuals are
encountered only twice, once when they are initially captured and banded and again
when they are shot by a hunter and their band reported. The data have a structure
similar to that for capture-recapture data except we estimate survival and recovery
probabilities.
Number
Released
N1
N2
N3
N4
N5
N6
1
2
3
N1S1f2
N1S1S2 f3
N2S2 f3
Expected recoveries on occasion i
4
5
6
N1S1S2S3f4
N2S2S3f4
N3S3f4
N1S1S2S3S4f5
N2S2S3S4f5
N3S3S4f5
N4S4f5
N1S1S2S3S4S5f6
N2S2S3S4S5f6
N3S3S4S5f6
N4S4S5f6
N5S5f6
7
N1S1S2S3S4S5S6f7
N2S2S3S4S5S6f7
N3S3S4S5S6f7
N4S4S5S6f7
N5S5S6f7
N6S6f7
b. Getting started:
Copy the files Brownie.fpt and Brownie.inp from the Examples subdirectory of Mark to
your personal folder. Then click on the spreadsheet icon in the upper left corner of Mark
to open the menu for specifications for Mark analysis. Click to select file and browse to
find Brownie.inp. Double click to select. Look at the structure of the data file. Do you
notice differences form the capture histories we were just working with? Tell mark how
many encounter occasions and groups there are in your analysis, then click OK.
c. Analysis:
Open the Pim and select all then tile these so you can see them all. The model specified
allows both survival and recovery rates to vary across years independently for groups
banded initially as young or adults. Given that ducks reach maturity by one year of age
this model is overly general. Wouldn’t it make more sense to constrain survival and
recovery rates of the two groups to be the same after those banded as young reach one
year old? Make the appropriate adjustments to the Pim and run the resulting model. Are
there other models you should try?