Introduction Documentation Downloading and Installation Recent Changes Reporting Problems Workshops Known Problems
Upcoming intermediate level workshop at Colorado State University, Fort Collins, Colorado, USA, 1-6 June, 2008. Registration for this workshop is CLOSED – workshop is full.
Upcoming MARK workshop associated with New Mexico State University, Las Cruces, New Mexico, USA, 6-11 April, 2008. Registration for this workshop is CLOSED – workshop is full.
The Program MARK hypertext-based online discussion forum, Analysis of Data from Marked Individuals, is found at: http://www.phidot.org/forum/index.php .
Program MARK, a Windows 95, 98, NT, 2000, or XP program, provides parameter estimates from marked animals when they are re-encountered at a later time. Re-encounters can be from dead recoveries (e.g., the animal is harvested), live recaptures (e.g. the animal is re-trapped or re-sighted), radio tracking, or from some combination of these sources of re-encounters. The time intervals between re-encounters do not have to be equal, but are assumed to be 1 time unit if not specified. More than one attribute group of animals can be modeled, e.g., treatment and control animals, and covariates specific to the group or the individual animal can be used. The basic input to program MARK is the encounter history for each animal. MARK can also provide estimates of population size for closed populations. Capture (p) and re-capture (c) probabilities for closed models can be modeled by attribute groups, and as a function of time, but not as a function of individual-specific covariates.
Parameters can be constrained to be the same across re-encounter occasions, or by age, or by group, using the parameter index matrix (PIM). A set of common models for screening data initially are provided, with time effects, group effects, time*group effects, and a null model of none of the above provided for each parameter. Besides the logit function to link the design matrix to the parameters of the model, other link functions include the log-log, complimentary log-log, sine, log, and identity.
Program MARK computes the estimates of model parameters via numerical maximum likelihood techniques. The FORTRAN program that does this computation also determines numerically the number of parameters that are estimable in the model, and reports its guess of one parameter that is not estimable if one or more parameters are not estimable. The number of estimable parameters is used to compute the quasi-likelihood AIC value (QAICc) for the model.
Outputs for various models that the user has built (fit) are stored in a database, known as the Results Database. The input data are also stored in this database, making it a complete description of the model building process. The database is viewed and manipulated in a Results Browser window.
Summaries available from the Results Browser window include viewing and printing model output (estimates, standard errors, and goodness-of-fit tests), deviance residuals from the model (including graphics and point and click capability to view the encounter history responsible for a particular residual), likelihood ratio and analysis of deviance (ANODEV) between models, and adjustments for over dispersion. Models can also be retrieved and modified to create additional models.
These capabilities are implemented in a Microsoft Windows 95 interface. Context-sensitive help screens are available with Help click buttons and the F1 key. The Shift-F1 key can also be used to investigate the function of a particular control or menu item. Help screens include hypertext links to other help screens, with the intent to provide all the necessary program documentation on-line with the Help System.
The theory and methods used in Program MARK are described in more detail in an "electronic book".
Sixteen different parameterizations of encounter data are provided in Program MARK.
Live recaptures are the basis of the standard
Cormack-Jolly-Seber. Marked animals are released into the population, often by
trapping them from the populations. Then, marked animals are encountered by catching them
alive and re-releasing them. If marked animals are released into the population on
occasion 1, then each succeeding capture occasion is one encounter occasion.
Consider the following scenario:
Release ----S(1)-----> Encounter 1
-------S(2)------> Encounter 2
Animals survive from initial release to the first re-encounter with probability S(1), and
from the first encounter occasion to the second encounter occasion with probability S(2).
The recapture probability at encounter occasion 1 is p(2), and p(3) is the
recapture probability at encounter occasion 2. At least 2 encounter occasions are
required to estimate the survival rate between the first release occasion and the first
encounter occasion, i.e., S(1). The survival rate between the last two encounter
occasions is not estimable because only the product of survival and recapture probability
for this occasion is identifiable.
Generally, the survival rates of the CJS model are labeled as phi(1),
phi(2), etc., because the quantity estimated is the probability of remaining available for
recapture. Thus, animals that emigrate from the study area are not available for
recapture, so appear to have died in this model. Thus, phi(i) = S(i)(1 - E(i)),
where E(i) is the probability of emigrating from the study area.
Lebreton et al. (1992) develop this model, and use SURGE (Pradel and Lebreton 1993)
to provide parameter estimates. MARK provides the same capabilities as SURGE, plus
additional types of models. Another program applicable to live recaptures is POPAN,
which provides for estimation of population size and recruitment with the Jolly-Seber
model. A third program is SURPH, which is
similar in its capability to MARK for live recapture and known fate data. None of
the above 3 programs will handle the band recovery models, the joint live recapture and
dead recovery models, robust design model, or the multi-strata model.
With dead recoveries, marked animals are released into the population, and re-encountered as dead animals, typically harvested. This theory has been developed by Brownie et al. (1985). Parameters estimated are survival rate, S(i), and band reporting rate, r(i), following Seber (1970). The primary model used by MARK differs somewhat from the parameterization of Brownie et al. (1985) because the f(i) of Brownie et al. are reparameterized as (1 - S(i))r(i). The primary parameterization of MARK results in better numerical estimation properties, plus, makes the band recovery models consistent with the parameterization of the CJS models. In particular, the use of covariates with the S(i) and r(i) is reasonable, because each parameter represents a particular process in the the overall band recovery process (unlike the f(i) parameter of the Brownie et al. model). However, the last S(i) and r(i) are confounded. In addition, with the S(i) and r(i) parameterization, S(i) is always estimated between zero and one. However, when the estimate of S(i) is at the boundary, i.e., close to or equal to one, the standard error is not estimated correctly. An equivalent situation occurs with the binomial distribution when either no successes occur in the data, or all successes occur in the data, and the standard error is estimated as zero. Both the S(i), r(i) and S(i), f(i) parmeterizations of the band recovery model are included in MARK.
The joint live and dead model is based on theory developed by Burnham (1993). The parameter space consists of survival rates [S(i)], recapture rates [p(i)], reporting rates [r(i)], and fidelity [F(i)]. An extension developed by Barker (1997) that allows live resightings during the interval between live recaptures is also available. Barker's model extends the capability of Burnham's model, plus allows for the option of no dead recoveries and live recaptures and live resightings.
Known fate data assumes that there are no nuisance parameters
involved with animal captures or resightings. The data derive from radio-tracking studies,
although some radio-tracking studies fail to follow all the marked animals and so would
not meet the assumptions of this model. A diagram illustrating this scenario is
Release -----S(1)----> Encounter 2 -----S(2)----> Encounter 3 -----S(3)---->
Encounter 4 ...
where the probability of encounter on each occasion is 1 if the animal is alive or dead.
The closed captures models allow the modeling of the initial capture
probability (p) and the recapture probability (c) to estimate population
size (N). This data type is the same as is analyzed with Program CAPTURE
(White et al. 1982). All the likelihood models in CAPTURE can be duplicated in MARK.
However, MARK allows additional models not available in CAPTURE, plus comparisons
between groups and the incorporation of time-specific and/or group-specific covariates
into the model.
Individual Covariates
cannot be used with the closed captures data type because animals that were never captured
(and hence, whose individual covariates could never be measured) are incorporated into the
likelihood as part of the estimate of population size (N). Models that can
incorporate individual covariates existing in the literature (Huggins 1989, 1991) have
been implemented in MARK. Estimates of population size are given for the Huggins'
models, but these estimates are not quite as efficient as the closed captures data type
where the statistical models are equivalent to those in Program CAPTURE. However,
the ability to incorporate individual covariates makes the Huggins' models more
appropriate if individual heterogeneity exists in the data. Further, the
Huggins models seem to provide more reasonable estimates of N when nearly
all the population has been captured. The Huggins models provide
the population size as a derived parameter, and MARK allows these derived
parameters to be used in model averaging and variance components analyses.
In addition, the Pledger(2000) models using mixtures of p values to model individual heterogeneity have been incorporated into all the closed capture models available in MARK. Thus, there are a total of 6 different different data types that can be used to estimate population size.
Robust Design Models are a combination of the CJS live recapture model and the closed capture models, and are described in detail by Kendall et al. (1997, 1995) and Kendall and Nichols (1995). Instead of just 1 capture occasion between survival intervals, multiple (>1) capture occasions are used that are close together in time. These closely-spaced encounter occasions are termed "sessions".
For each trapping session (j), the probability of first capture
(p(ji)) and the probability of recapture (c(ji)) are estimated (where i indexes the number
of trapping occasions within the session), along with the number of animals in the
population (N(j)). For the intervals between sessions, the probability of survival
(S(j)), the probability of emigration from the study area or more precisely, the
probability of the animal not being available for capture on the jth occasion given that
it was available on the j-1st occasion (gamma' ' (j)), and the probability of
staying away from the study area or the probability of an animal not being available for
capture on the jth occasion given that it was not available for capture on the j-1st
occasion (gamma' (j)) are estimated. Indexing of these parameters follows the
notation of Kendall et al. (1997). Thus, gamma' '(2) applies to the second trapping
session, and gamma' (2) is not estimated because there are no marked animals outside the
study area at that time. To provide identifiability of the parameters for the
Markovian emigration model, Kendall et al. (1997) suggest setting gamma' ' (k-1) = gamma'
'(k) and gamma'(k-1) = gamma'(k), where k is the number of trapping sessions. To obtain
the "No Emigration" model, set all the gamma parameters to zero. To obtain the
"Random Emigration" model, set gamma'(i) = gamma' '(i).
Individual Covariates can be used to model the parameters S, gamma' ', and gamma' in the
Robust Design data type. Individual Covariates cannot be used with the Robust Design data
type for the p's, c's, and N's because animals that were never captured (and hence, whose
individual covariates could never be measured) are incorporated into the likelihood as
part of the estimate of population size (N). Models that can incorporate individual
covariates existing in the literature (Huggins 1989, 1991) have been implemented in
MARK. Estimates of population size are given for the Huggins' models, but these
estimates are not quite as efficient as the closed captures data type where the
statistical models are equivalent to those in Program CAPTURE. However, the ability
to incorporate individual covariates makes the Huggins' models more appropriate if
individual heterogeneity exists in the data. The Pledger (2001) models are
also available to model individual heterogeneity in capture probabilities.
The multi-strata model of Brownie et al. (1993) and Hestbeck et al. (1991) allows animals to move between strata with transition probabilities. At this time, only the movement model without memory is implemented. An extension to the multi-strata model to include dead recoveries is also implemented, as well as the robust-design multi-strata data types.
Jolly-Seber Models (Jolly 1965; Seber 1965, 1982, 1986, 1992; Pollock et al. 1990, Schwarz and Arnason 1996) extend the CJS live recaptures models to include recruitment into the populations. In addition to the apparent survival and recapture probabilities of the Cormack-Jolly-Seber model (recaptures only model), the Jolly-Seber model allows estimation of the population size (N) at the start of the study, plus the rate of population change (lambda) for each interval. Also included in MARK are the 3 models developed by Pradel (1996) where only recruitment is estimated, both recruitment and apparent survival are estimated, and apparent survival and rate of population change are estimated. The POPAN model is also available in MARK for the Jolly-Seber situation.
Estimation of nest survival has been a problem of interest since the Mayfield estimator. The nest survival model implemented into MARK allows estimation of daily nest survival rates as a function of both time of season and age of nest (Dinsmore et al. 2002). The nest survival model is also useful for "ragged" radio-tracking datasets, where all animals in the radioed population are not checked simultaneously, as required for the known fate model.
Estimation of the proportion of sites occupied is a common problem in ecology. MacKenzie et al. (2002) have formalized the model to incorporate the probability of detection of a species at a site. MacKenzie et al.'s model, plus a robust-design extension, (MacKenzie et al. 2003) have both been implemented into MARK. In addition, the Royle and Nichols (2003), plus some extensions, have been implemented.
Estimation of population size when marks are only applied once can be performed with the models in the NOREMARK software. However, Brett McClintock has developed likelihood-based models that provide improvements over the NOREMARK models, plus with being implemented in MARK, allow model selection with AICc, model averaging of population estimates, and variance components analysis.
The Encounter Histories File is the file that contains the encounter
histories, i.e., the raw data needed by Program MARK. Format of the file depends on the
data type and examples are given in the help file. The convention of Program Mark is that
this file name must end in the INP suffix. The root part of the file name dictates the
name of the dBASE file used to hold model results. For example, the input file
MULEDEER.INP would produce a Results File with the name MULEDEER.DBF and 2 additional
files (MULEDEER.FPT and MULEDEER.CDX) that would contain the memo fields and index
orderings, respectively. MULEDEER.CDX will be erased upon exit from MARK.
Encounter Histories Files do not contain any PROC statements, but only
encounter histories or recovery matrices. You can have group label statements and comment
statements in the input file, just to help you remember what the file contains. The
interactive interface adds the necessary program statements to produce parameter estimates
with the numerical algorithm based on the model specified.
Once the encounter histories file is created with an ASCII text editor,
the next step is to execute the program and select File, New. You then enter the number of
Encounter Occasions, number of Groups, and the Data Type. After this input is provided,
the Parameter Matrices are created, one for each parameter and group. These matrices
default to Time matrices, which you can then modify to other possibilities using menu
options. If you don't need any additional constraints, which can be specified via the
Design Matrix, then choose the Run menu option to produce the numerical estimates. The Run
Window has additional requests for input, including the Run Title, Model Name, Time
Intervals, and Encounter Histories File Name. When you click the OK button to run compute
the numerical estimates, you must wait for this process to complete before proceeding. At
that time, a Results data base will be created (if you request it), and the output stored
in the data base for comparison with other models you may provide.
The input file for the example data from American Fisheries Monograph No. 5 (Burnham et al. 1987) is provided as AFSMONGR.INP. This data set has 5 re-encounter occasions, 2 groups, and is live recapture data. Specify these values when you start the program from the File | New menu choices. In the Run Dialog Window, select the AFSMONGR.INP file as the Encounter Histories Input File. Alternatively, the results database for this example is also included with the program. Use the File | Open menu choices to open this file, and review the model results provided.
No paper documentation is available for MARK. Electronic
documentation is provided in the Windows help file that accompanies the program and
available here as HTML files. Open up the Help
document with the program, and read some of the documentation, or check out the HTML
version. You can print any of this material if you really want hard copy.
A reasonably complete description of Program MARK was developed for the
Euring 97 conference, available as a PDF file. I consider
this paper as the primary citation for Program MARK:
White, G.C. and K. P. Burnham. 1999. Program MARK: Survival estimation from populations of marked animals. Bird Study 46 Supplement, 120-138.
An electronic book, Program MARK A Gentle Introduction, is being developed by Evan Cooch at Cornell University. For the complete novice, this is the place to start to learn how to run MARK. This guide is a work in progress, so is not complete just yet.
Notes concerning the theory and use of MARK from the graduate course that David Anderson and Gary White teach at Colorado State University: FW663, Analysis of Vertebrate Populations, are available. This is the same material provided as "Technical Background" from Evan's site referenced in the preceding paragraph.
A set of slides that illustrate the concepts of MARK is available for viewing. These slides give a general overview, and portions of them are used in the slide talks listed below.
A one day workshop on Program MARK was given at the Second International Wildlife Management Congress in Gödölló, Hungary, July 2, 1999. The following are the slide talks given:
 | Introduction to Program MARK -- Gary C. White |
| Exploring Ecological Relationships in Survival and Estimating Rates of Population Change Using Program MARK -- Alan B. Franklin |
| The Robust Design for Capture-Recapture Studies: Analysis using Program MARK -- William L. Kendall |
| Jointly Analyzing Live and Dead Encounters using MARK -- Richard J. Barker |
| Advanced Features of Program MARK -- Gary C. White |
In addition, the following papers were published from this workshop.
| First Steps with Program MARK: Linear Models -- Evan Cooch |
| Exploring Ecological Relationships in Survival and Estimating Rates of Population Change Using Program MARK -- Alan B. Franklin |
| The Robust Design for Capture-Recapture Studies: Analysis using Program MARK -- William L. Kendall |
| Jointly Analyzing Live and Dead Encounters using MARK -- Richard J. Barker and Gary C. White |
| Advanced Features of Program MARK -- Gary C. White, Kenneth P. Burnham, and David R. Anderson |
One of the problems with obtaining software from the Web is that hard copy documentation is not available, such as is the case for Program MARK. The following sites provide information on how to cite electronic documents: MLA-Style Citations of Electronic Sources and Electronic Sources: APA Style of Citation .
I developed a new version of the MARK interface (Version 5.0) with a new Visual Objects compiler (Version 2.8) on 18 December, 2007. To use this new version, you must download the 13Mb setup.exe file and install in a separate subdirectory from previous versions of MARK. A common error that occurs when you have mixed versions of the code (i.e., the DLL files are not completely compatible with the EXE file) is an error from Kernal32.DLL. To prevent problems, uninstall your old version of MARK, and then install the new version, or else select a different subdirectory for the new version. The splash screen for the new version is a grizzly sow with 2 cubs, with the MARK logo superimposed. To uninstall MARK, go to Control Panel, Add and Remove Software, and remove MARK. There are no new features in the code, but execution times should be improved, and better memory management should be realized. Let me know of issues you encounter with this new version.
Copy the single setup.exe file to your hard disk, and execute it to install MARK. This setup file should place a MARK icon on your desktop, register the graphics package, and put the examples distributed with the program in an Examples subdirectory under the Mark directory. If you have difficulty copying a single large file, the setup has been broken down into 10 pieces: setup.exe, setup.2, setup.3, setup.4, setup.5, setup.6, setup.7, setup.8, setup.9 and setup.10. Copy down these pieces and install MARK by executing the setup.exe file.
Note that any of the setup files, are available via anonymous ftp from ftp.cnr.colostate.edu in the pub/mark subdirectory, in case you are having problems with your browser copying down the files. The single large file is in the cdrom/disk1 subdirectory, the 10-part setup files are in 144mb/disk1 through 144mb/disk10. If you are using WIndows XP and are unable to download MARK from this ftp site, you should uncheck "Use passive FTP" on their Internet Explorer browser settings and then try to download again.
If you have a recent download installed, you can update just the critical files by installing them from update.zip.
The version of MARK since 14 July 2004 can have problems with large analyses. The program will generate models and work fine as long as it is not closed. However, once the program is closed, you are unable to open up the DBF and FPT files. There is some kind of bug in the Visual Objects code that causes this, but the company has not been willing to fix this problem. So, one option is to use the old version of MARK that will open up the files. You can download the setup.exe file, and install the old version in a different subdirectory. Because the setup file was generated with an expiration date, you will have to set the year on your computer back several years to get this setup file to run.
Problems encountered when installing and running MARK with Microsoft Vista (thanks to Paul Doherty).
The MARK help file does not work.
a. The MARK Help file was written with the Windows Help (WinHlp32.exe) program. This program is no longer included in Windows operating systems starting with Vista. To get this program go to: http://www.microsoft.com/downloads/details.aspx?FamilyID=6ebcfad9-d3f5-4365-8070-334cd175d4bb&DisplayLang=en
b. Click “Continue” – Validation Required
c. Scroll down to “Files in This Download” and download the appropriate file.
MARK is not able to find temporary results files “The mrk****z.tmp cannot be found.”
a. Navigate to the Mark_Int.exe file and right click (probably under C:/Program Files/Mark/ or right click on the MARK icon) On the ”Compatibility” tab and under “Privilege Level” click “Run this program as an Administrator.”
MARK is not able to write results directly to Excel.
a. Go to Preferences in MARK and click the appropriate Excel version. Even in Excel 2007, Excel 2003 might still work in compatibility mode. You may have to experiment with this option.
Some folks are having difficulties downloading MARK onto Windows ME and XP operating systems. The problem concerns the setup.exe program wanting to create a file entitled TGETUP9 when ME or XP already has one. Here's the work around from Jon Runge:
1. Through Window Explorer go to Tools: Folder Options: View. Check the "show hidden files and folder" box and uncheck the "hide protected operating system files" box.
2. Go to the folder C:\WINDOWS:\TEMP. Rename TGSETUP9.TMP to something like TGSETUP~9.TMP.
3. Run Setup.exe for MARK.
4. When done, go back and restore TGSETP9's original name.
To run MARK on a Mac (from Evan Cooch):
Equipment Tested: Macintosh PowerBook G3 (Lombard) 333 MHz with 192 MB of ram (note that Mac clock speed numbers are NOT the same as Windows/Intel clock speeds, i.e., a 333 MHz Mac is faster than a comparable WinTel machine).
Software: Virtual PC version 3.0.3 with Windows 98. Able to use MARK under VirtualPC with Windows 98. Also able to use Microsoft Access under VirtualPC.
Recommendations: The more ram you have the better. Set your VirtualPC program's memory to as much ram as you can afford. The emulator program (VirtualPC) actually runs Windows using the amount of ram that you set aside for the emulator. I set the Virtual PC to use 69MB of memory and find that this allows Windows/Dos software to run as fast as a real contemporary WinTel machine. Also, I've had best results running the Mac OS with an abbreviated set of Extensions. You can easily do this by creating a reduced Extension set with the Extension Manager (this is a Control Panel).
Update (2/3/06) from Martin Renner:
Equipment tested: 800 Mhz G4 Dual Processor, Mac OX 10.3.9, Virtual PC 6 running Windows 98 and MARK version 4.10.
While not really fast, this configuration is perfectly usable. Allocating more RAM helps.
When preparing .inp files on the Macintosh it seems to be important to
convert the end-of-line character from mac <CR> or unix <LF> to dos/windows
<CR/LF>. This can be easily done in BBedit, a number of free utilities, or by
opening and saving the file in WordPad.
To run MARK on a Linux machine (from Len Thomas):
Software: VMWare -- a BIOS emulator for both Linux and WinNT that effectively lets you run one or more "virtual computers" inside your current operating system. So, for example, you can open a Win95 window from your linux box, and everything within that window thinks its in Windows 95. Of course you do need a Win95 license for this, but at least it gets around the problem of wanting to run linux for most things, but having some legacy software in windows.
Many people use VMWare because they do most things in linux (SPlus, C++, F90), but then some people want or have to use MS Office for their word processing, for example. I use it the other way around: I do most things in WinNT (Visual Basic, etc), but need to be able to test my programs in "vanilla" Windows NT, 98, 95, 2000 systems, so I can run these inside my main machine.
Communication between virtual computers is via virtual networking.
At this time MARK has never been tested under VMWare in linux, but MS Office works, so MARK is expected to work.
Older changes are stored here. Recent changes include the following:
February, 2006, Version 4.3
120. A message asking the user if they really want to exit out of MARK has been added because some users are accidentally clicking the red exit box in the upper right corner of the MARK application. If you feel this message is not needed, you can turn it off in the File | Preferences menu. Personally, I recommend you look before you click!
121. The design matrix is now scaled internally so that you do not have to use the "Standardize Individual Covariates" to scale covariates to obtain numerical convergence. Hence, the only reason to use the standardize option is to have the mean of the covariates equal to zero.
122. The revised variance formula is now the default for model averaging, i.e., this box is checked when you start the model averaging dialog. If you want the original equation, uncheck this box.
123. The absolute value link function has been added to the list of possible link functions. The absolute value link is handy for closed captures models when the estimated population size is close to M(t+1) because the parameter is counted as being estimated. In contrast, the default log link will not count such parameters as being estimated because the beta value is approaching negative infinity. The absolute value link function works particularly well with the Coulombe closed captures example distributed with MARK. To access the absolute value link function for population estimation, you must use the "Parm. Specific" link option.
March, 2006
124. Robust-design Pradel models were added for the closed model situations with no mis-identification for a total of 18 new models. These models do not include the gamma'' and gamma' parameters (temporary emigration), so the Pradel robust design models assume no temporary emigration. Also turns out that the mis-identification models do not work well with Pradel models, so these 18 additional models are on hold. The File | New dialog page now only shows one entry for Pradel models, but when you click on this entry, a list of the possible models comes up. Then, if you select a robust design model, you are asked to select from the possible closed models.
125. An option has been added to the File | Preferences dialog to specify the location of the editor you want to use to view MARK text files. The default is NotePad, but you can change this default to WordPad or another editor of your choice.
April, 2006
126. Simulation capability for the robust-design Pradel models for the 6 types of closed models times the 3 types of Pradel models (gamma, lambda, f) has been added so that power analyses can be conducted to design surveys.
July, 2006
127. An option was added under the Adjustments menu of the Results Browser to specify the effective sample size for computing AICc and QAICc. The reason for this adjustment is the different types of parameters in the robust design capture-recapture and also robust design occupancy data types. Parameters related to primary occasions can be considered to have different sample sizes than parameters related to secondary occasions within primary occasions. The effective sample size is now stored in the data file so that all models in the results browser will have used the same effective sample size to compute AICc or QAICc. The default value is still the value computed by the MARK numerical routine.
128. Effective sample size calculations for the robust design occupancy data types were changed to be the sum of the number of sites sampled in each primary occasion, rather than just the number of sites sampled in the first primary occasion. The effective sample size for the regular occupancy data type is still the number of sites visited.
129. A bug with the specification of the Burnham Jolly-Seber data type was fixed. However, this model is still not recommended for general use. Rather, use the Pradel, Link-Barker, or POPAN data types. The Burnham Jolly-Seber data type often does not converge to the maximum likelihood estimates, whereas the other models usually do. Note, however, that the Pradel lambda (λ) data type does not enforce the constraint that lambda(i) >= phi(i), so you can get nonsensical answers from this parameterization. Hence, I generally recommend use of the Pradel recruitment (f) data type.
September, 2006
130. The capability to increment or decrement the font size in the design matrix and the results browser was implemented. Buttons were added to the task bar to make this task quick to implement.
131. Calculation of profile likelihood confidence intervals was modified to include c-hat for data sets where overdispersion (c-hat > 1) is specified. When c-hat > 1, the profile intervals are only available in the full output window because the user can change the value of c-hat and the profile intervals would not be automatically changed. More details are provided in the help file in the Profile Likelihood Confidence Intervals entry.
January, 2007
132. Mixture models were added to the occupancy data type and the robust design occupancy data type. You can access these models from the "Change Data Type" choice under the PIM menu when you open up the basic data types.
April, 2007
133. I've discovered a problem with the Huggins-Pledger mixture models, where the conditioning on the never-seen category was done independently for each mixture rather than jointly. The new code corrects this problem, but is going to change estimates of pi and the derived population estimates. In most cases, the estimates of the p's are the same under both the old and new parameterizations, with changes only in estimates of pi and the derived N. But, I have also found datasets where the new parameterization does not converge to reasonable values, e.g., the either of the Carothers taxicab datasets distributed with the program.
May, 2007
134. Four additional functions were added to the list of design matrix functions. The max and min functions return the maximum or minimum of the 2 arguments. As an example with the individual covariate Length, max(5,Length) entered into the design matrix cell will return a value of 5 or the value of Length if >5. The log and exp functions only use a single argument, and return the natural logarithm or the exponential of the argument.
135. The Reorder Columns command to reorder the columns of the design matrix has been added to the Appearance menu, but also remains in the popup menu that you get by right-clicking the design matrix.
136. Options to use the alternate optimization method (simulated annealing) for estimation have been added to the simulation and the median c-hat procedures.
137. The capability to bootstrap data (encounter histories) has been added to the simulation menu. To make this useful, you need an individual covariate that "blocks" sets of encounter histories. Details on the use of this procedure are in the help file under "Bootstrap Data".
June, 2007
138. The help file was updated to include R code for diagnostic analysis of the MCMC.BIN file, with the MARK output including parameter specification for the R code.
139. Cormack-Jolly-Seber (Live Captures) encounter histories will now allow dots (".") in the encounter history to identify occasions in the encounter history where no survey was conducted.
140. Huggins closed captures models will also allow dots (".") in the encounter history to identify occasions where no survey was conducted. However, dots do not work with the regular closed-captures models with N in the likelihood, because there is no way to estimate a probability of the all zero encounter history when some of the animals never captured may not have actually been surveyed.
August, 2007
141. The Royle and Nichols (2003) single-species occupancy model with the Poisson assumption has been added. The real parameters are r and lambda, and psi and E(p) are computed as derived parameters. To allow model averaging, psi has been added as a derived parameter for the other single-species occupancy models. The negative binomial version of the Royle and Nichols model has also been added to MARK, where the r and lambda parameters are the same as for the Poisson model. The third real parameter is the amount of variance (VarAdd) that is increased over the mean density. Thus, if you run the negative binomial model and fix VarAdd to equal zero, you get back the same estimates as you would from the Poisson model. My main purpose in adding these data types is to account for heterogeneity across the sites, rather than produce an estimate of density. I'm quite skeptical about the usefulness of the density estimate in most scenarios.
September, 2007
142. A bug was fixed with almost all of the robust design models that caused an array bounds error when the last primary session had the most secondary occasions.
143. A bug was fixed in the Pradel f parameterizations for datasets with time intervals between occasions unequal to 1. The f parameterization now produces estimates consistent with the gamma and lambda parameterizations for unequal time intervals.
October, 2007
144. Previously, I had build in a kluge in MARK to try to detect whether you were running Excel 2003 or Excel 2007 by checking the path to your Excel executable. However, it turns out that Excel 2007 can be run in a compatibility mode that makes it look like Excel 2003 to MARK. Therefore, I set an option in the File | Preferences window for the user to select Excel 2007 as your spreadsheet. If writing to an Excel file does not work on your system, try specifying the Excel 2007 option.
145. The mark-resight models that Brett McClintock has developed for his Ph.D. work have been implemented. Details on running these models in MARK are contained in a PDF file here.
146. The multiple-state occupancy model of Nichols et al. (2007) has been implemented. In addition, the other occupancy models (basic, Pledger heterogeneity, Royle-Nichols) have been modified to treat the "2" in encounter histories as a "1", so that the multiple-state occupancy model is available from the "Change Data Type" menu choice in the PIM menu.
147. The Poisson and Negative Binomial Count models of Royle (2004) have been implemented. The data for these two data types requires that counts be entered in the encounter histories using the 2 characters of the LD pair to enter integers from 00 to 99. Therefore, these two data types are not compatible with the other occupancy models, but you still select these models from the Occupancy button on the new analyses page. Two examples are provided through the help file. Royle, J. A. 2004. N-mixture models for estimating population size from spatially replicated counts. Biometrics 60:108-115.
December, 2007
148. When the Visual Objects compiler was upgraded to version 2.7, users with "large" data sets encountered difficulties with re-opening a MARK DBF file that contained model results. I've fought with this bug ever since, and I think I figured out the solution (i.e., what was changed when the new compiler was used). So, try the new version posted on the web and see if you can now open your DBF files with it, and not have to use the pre-2.7 version of MARK.
149. Version 5.0 of MARK is now available as a test version. This version has been compiled with a new Visual Objects compiler, version 2.8. See the section above for details.
February, 2008
150. Version 5.0 of MARK is now the production version. You should uninstall your old versions, or else install this new version in a different subdirectory.
April, 2008 Version 5.1
151. Design matrix functions (add, product, power, min, max, log, exp, lt gt, le, ge, eq) can now be called recursively. So, an entry in the design matrix such as
log(add(age,30))
will now work. The price of this recursion is that the "COLx" capability to refer to a prior column in the design matrix had to be removed. See the help file on design matrix functions for full details.
152. The ability to enter missing encounter history data with a dot ('.') has been extended to the robust design and multi-state closed robust design data types. This capability was already available for the Cormack-Jolly-Seber (see # 139 above) and the multi-state data types.
153. The Pradel seniority (γ) and Pradel recruitment (f) data types now produce the full variance-covariance matrix of the derived lambda parameters. Therefore, variance components on lambda can now be conducted with these lambda estimates.
154. Four additional variables have been added to the Results File: BIC (Bayesian Information Criterion), -2log(Likelihood), a Time Stamp, and a memo field to contain notes about the model. To see these variables in the Results Browser window, you have to go to File | Preferences and click on the appropriate checkboxes. If you select BIC, then AICc will not be displayed, and the model weights and model likelihood values will reflect BIC values, instead of AICc values. The Results Browser can be ordered (sorted) by BIC. I should have included -2log(Likelihood) in the Results File from the beginning, but at the time, Deviance seemed adequate. However, with the inclusion of many data types in MARK where the computation of Deviance is not clear, -2log(Likelihood) seems necessary. The Time Stamp is included so that you can see when the model was run. The format is YY:MM:DD:HH:MM:SS, i.e., last 2 digits of year, month, day, hour, minute, and seconds. The Results Browser can be ordered (sorted) on the Time Stamp. Model Notes can be included to describe some details about the model. An icon is on the tool bar, or a menu choice is available under the Adjustments menu. The conversion of old files to the new format that includes these four additional variables should be seamless, but just to be safe, you may want to back up your old Results File (both the DBF and FPT files) before opening the Results File with the new version. The MARK Help File has been updated to describe these new capabilities.
155. The capability to add notes about the entire analysis is now included. The File Notes menu choice is under the Output menu choice in the Results Browser, or available with an icon on the tool bar.
156. A bug was fixed so that the mean value of an individual covariate is now correctly computed when the encounter history frequency is >1.
157. The capability to plot the real parameter estimate as a function of individual covariate values has been implemented. An icon on the Toolbar and a menu entry in the Results Browser under Output | Specific Model Output | Individual Covariate Plot provide access to this capability. A plot of the function and 95% confidence intervals are provided, with the capability to set other individual covariates to specified values. The values can also be downloaded to Excel to produce publication quality plots, or more complex plots. See the help file "Individual Covariate Plot" for details.
May, 2008
158. The Poisson log-normal mark-resight model was modified to produce an estimate of the unmarked population size as a real parameter (U), and the estimate of the entire population size (N) as a derived parameter. This change fixed a bug that caused the estimate of N to be too small for cases where the number of marked animals was unknown. In addition, the mean resighting rate for this model was added as a second derived parameter.
158. Mark-resight models were modified to correctly estimate population size when individual covariates were used in the model.
June, 2008
159. The capability to "lasso" PIM boxes in the PIM Chart has been added. Hold down the Shift key, then hold down the left mouse button and drag the cursor to "lasso" multiple PIM boxes. A dashed-line rectangle will enclose the lassoed boxes. The lower left corner of the box (the "origin") must be in the lasso to be collected. Then, release the left mouse button and then the Shift key, and the collected boxes will be colored green. This collection can now be moved to the desired location.
160. A bug in the PIM Chart was fixed that allowed users to generate negative values in the PIM by dragging a box to the left of parameter 1.
161. The width of design matrix columns are now set wide enough to display the labels at the top of the columns.
162. The median c-hat and parametric bootstrap procedures were modified to use the real parameter values with an identity link to specify the model to be simulated. This change means that individual covariates cannot be used, but they couldn't anyway. The reason for the change was to eliminate the need to handle link functions in the specification of the model to be simulated.
163. Columns in the design matrix are automatically reordered when a model is run if the user has changed the order.
164. A short-hand version of constant PIMs (PIMs with all values the same) was implemented to reduce the size of the input and output files, and to speed up the processing of the output file.
July, 2008
165. A short-hand version of time PIMs (PIMs with a time structure, as described in the help file) was implemented to reduce the size of the input and output files, and to speed up the processing of the output file.
166. The help file was converted to the html (*.chm) format, so that now MARK is more compatible with Windows Vista.
For questions or to let me know about problems you have encountered, send email. Please try to provide as much documentation as possible to help me duplicate your problem. In particular, I would like to have the input file that caused the problem, and the values you entered for the number of occasions, the number of groups, and the data type. Further, if you have created a results file, please send these via a zipped attachment. Both the *.DBF and *.FPT files must be forwarded -- both are needed to see the models you have built.
Email: gwhite at cnr.colostate.edu
An alternative to a week-long workshop is to take FW663, Analysis of Vertebrate Populations, a 5-credit graduate course taught by Paul F. Doherty Jr. and Gary C. White in alternate spring semesters at Colorado State. Out-of-state tuition for the course is approximately $2,700, and cheaper for Colorado residents. The class meets MWF from 8-12 from mid-January until the first of April. The class will next be taught spring semester, 2007, beginning mid-January and ending early April.
Another intermediate level workshop is scheduled for June 1-6, 2008, in Fort Collins, Colorado.
Individuals desiring a comprehensive treatment of the background material of Program MARK, and gaining a familiarity with using the program, are encouraged to take the course FW663, Sampling and Analysis and of Vertebrate Populations, co-taught by Paul F. Doherty, Jr. and Gary C. White. The course meets from mid-January until the last week of March, MWF from 8-12. The class will next be taught spring semester, 2007, beginning January 24 and ending April 6. We strongly encourage students from outside Colorado State University to participate in this course.
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