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Statistical Methods for Estimating Abundance of Natural Resources (June 8-9, 2013)
Anchorage, Alaska, USA
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 Vista 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-encounteroccasions, 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 thisdatabase, 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 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 providedin 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), andfrom 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 forrecapture, 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-Sebermodel. A third program is SURPH, which issimilar 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-state 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 byBurnham (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 captureprobability (p) and the recapture probability (c) to estimate populationsize (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 comparisonsbetween groups and the incorporation of time-specific and/or group-specific covariatesinto the model.
Individual Covariatescannot 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 thelikelihood as part of the estimate of population size (N). Models that canincorporate individual covariates existing in the literature (Huggins 1989, 1991) havebeen 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 typewhere the statistical models are equivalent to those in Program CAPTURE. However,the ability to incorporate individual covariates makes the Huggins' models moreappropriate 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 recapturemodel 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 betweensurvival intervals, multiple (>1) capture occasions are used that are close together intime. 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 thepopulation (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 forcapture on the jth occasion given that it was not available for capture on the j-1stoccasion (gamma' (j)) are estimated. Indexing of these parameters follows thenotation 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 obtainthe "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 with the closed capture models that include N 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) are implemented in MARK, and individual covariates can be used to model the p's and c's. 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 for M0, Mt, and Mb 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-state model of Brownie et al. (1993) and Hestbeck et al.(1991) allows animals to move between states with transition probabilities. At this time, only the movement model without memory is implemented. An extension to the multi-state model to include dead recoveries is also implemented, as well as the robust-design multi-strata data types.
Additional extensions to the multi-state models include the open robust design multi-state model (Kendall and Bjorkland 2001), and multi-state models with misclassification (Kendall ).
Jolly-Seber Models (Jolly 1965; Seber 1965, 1982, 1986, 1992;Pollock et al. 1990, Schwarz and Arnason 1996) extend the CJS live recaptures models toinclude 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 ofthe 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 single-season occupancy model of Royle and Nichols (2003), plus some extensions, have been implemented. Other occupancy models include the multi-site occupancy model (Nichols et al. 2008), and single-season and multi-season occupancy models with multiple states and state uncertainty (Nichols et al. 2007, MacKenzie et al. 2009).
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 encounterhistories, 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 other special formats such as 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 Cormack-Jolly-Seber 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 File Name 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 in the Examples subdirectory. 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, nor ever will be as long as MARK continutes to be developed.
Notes concerning the theory and use of MARK from the graduate course taught 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 is the case for Program MARK. The following site provides information on how to cite electronic documents: MLA-Style Citations.
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 necessary DLL files, and put the examples distributed with the program in an Examples subdirectory under the MARK directory. If you have a recent download installed, you can update just the critical files by installing them from update.zip.
Some folks are having difficulties downloading MARK onto Windows XP operating systems. The problem concerns the setup.exe program wanting to create a file entitled TGETUP9 when 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 clockspeeds, 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 Virtual PC with Windows 98. Also able to use Microsoft Access under Virtual PC.
Recommendations: The more ram you have the better. Set your Virtual PC program's memory to as much ram as you can afford. The emulator program (Virtual PC)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 softwarein 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 MSOffice 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.
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.
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.
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.
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.
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.
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.
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".
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.
141. The Royle and Nichols (2003) single-species occupancy model with the Poisson assumption has been added. The real parameters arer 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.
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.
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.
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.
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
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.
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.
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.
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.
167. A choice under the Run menu in the Results Browser has been added to allow the user to specify columns from a design matrix as variables, and to then run all possible combinations of these variables. Details are provided in the help file.
168. An immigration-emigration version of the logit-normal mark-resight data type has been implemented.
169. A bug in the MCMC output summary was fixed. Beta estimates for columns with a scaling factor not equal to 1 (see item 121 above, February 2006) reported incorrect values of the mean and standard deviation of the posterior distribution. The median and mode were correct for these beta estates, as were the values written to the binary output file.
170. A bug was fixed for the Huggins models with dots in the encounter histories. This bug affected all of the Huggins models, including the robust design and robust design multi-state models. So, if you have been using the Huggins model with dots in the encounter histories, re-run your models.
171. The Huggins data types were modified with respect to how losses on capture and dots in the encounter history were handled. Previously, losses on capture were just added onto the estimate obtained by ignoring these individuals. The new code actually incorporates the losses on capture and individuals with dots in their encounter history into the calculation of p and c, then also into the calculation of N.
172. The mis-identification models were modified to compute the confidence interval on N from a lognormal distribution.
173. The individual covariate plot was fixed to properly handle values of the over-dispersion parameter c > 1.
174. The Kendall robust design data types were modified to make the gamma parameters a function of the time interval. This was done to make them consistent with the Barker robust design data types. So, if you have been running the Kendall robust design data type with unequal time intervals between primary sessions, your results will now differ from your previous runs. Note that an alternative to the Kendall robust design data type is to use the robust design multi-state data types with an unobserved state. For multi-state data types, the psi parameters are not a function of the time interval between primary sessions because the transitions are assumed to take place at the end of the interval. Further, I discovered that the gamma parameters in the Barker robust design data types are actually complements of the gamma parameters of the Kendall robust design. I thought this would be easy to correct, but it turns out to not be so. Hence, for the present, recognize that the estimates from the Barker robust design data type correspond to the F and F' of the Barker live-dead data type.
175. The Lukacs et al. (2004) model was implemented to estimate survival of young from marked adults. Counts of young are entered as pairs of digits in the encounter history -- see the help file for details. Lukacs, P. M., V. J. Dreitz, F. L. Knopf, and K. P. Burnham. 2004. Estimating survival probabilities of unmarked dependent young when detection is imperfect. Condor 106:926-931.
176. A bug was fixed that caused incorrect effective sample sizes when a new results file was created, and only saved structures were put into the file.
177. Bugs were fixed with running CAPTURE and RELEASE from MARK when there were blanks in the subdirectory or file names.
178. Simulation capability was added for the Lukacs et al. (2004) model of young survival from marked adults.
179. The Subsets of Models capability was modified to allowthe user to modify variable names, and to specify the maximum number of variables to be included in models in addition to variables specified to be always in the models. For example, a maximum variables per model value of 1 with 3 variables and anintercept that is specified to always be included would result in 4 models beingrun.
180. Appropriate confidence limits were added to the median c-hat calculation. Two-sided confidence limits are picked off the logistic regression line for 2.5% and 97.5%, and a one-sided bound is reported for 95%. The SE reported represents the sampling variation from the Monte Carlo sampling process, whereas these confidence bounds represent the uncertainty from the data. To generate "good" estimates of the confidence bounds, you may have to prescribe more simulations for these tail areas. Because the lower bound on c is 1, the lower bound is not particularly useful.
181. MARK has the capability to import data/output from RMark. A new function export.MARK is now included in RMark that writes out a .Rinp file with the necessary parameters to define the model to MARK, the .inp file (encounter histories file) with the data and optionally any output files that should be imported into MARK. The .DBF and .FPT files (Results File) will be created in the same subdirectory as the .Rinp file is located. The RMark import capability should prevent the problems where folks have unknowingly changed the group structure or other aspects of the problem in creating the MARK project to import the RMark results. This caused some folks to get discrepancies. With this export/import facility the data/model structures will match between MARK and RMark. Also, it will import a whole set of model results rather than importing them one at a time with MARK. Note that you do need to delete the .tmp files manually after importing them into MARK. The RMark Import menu choice is under the File menu.
182. Effective sample size calculation was changed for the logit-normal and immigration-emigration logit-normal mark-resight estimators.
183. The multi-site occupancy model was installed, along with the ability to simulate this data type. Details are provided in the help file under the "Occupancy Estimation Multi-site" and in the article: Nichols, J. D., L. L. Bailey, A. F. O'Connell, N. W. Talancy, E. H. C. Grant, A. T. Gilbert, E. M. Annand, T. P. Husband, and J. E. Hines. 2008. Multi-scale occupancy estimation and modelling using multiple detection methods. Journal of Applied Ecology 45:1321-1329.
January, 2010, Version 6.0
184. Version 6.0 is now the production version. In this version, the graphics package has been replaced with simpler code to reduce problems with installation. A 64-bit version of the mark.exe file is available upon request for those of you with VERY large jobs that require addditional memory.
185. The multiple state occupancy model with imperfect detecion single season model (Nichols, J. D., J. E. Hines, D. I. MacKenzie, M. E. Seamans, and R. J. Gutierrez. 2007. Occupancy estimation and modeling with multile states and state uncertainty. Ecology 88:1395-1400.) and the robust design moddel (MacKenzie, D. J., J. D. Nichols, M. E. Seamans, and R. J. Gutierrez. 2009. Modeling species occurrence dynamics with multiple states and imperfect detection. Ecology 90:823-835.) are now implemented. Both the general parameterization and the conditional binomial parameterization were implemented for the robust design data type. Details on how to use these data types are in the MARK help file under Occupancy Estimation Multiple States Robust Design.
186. An estimator of density from trapping grids that uses radio-tracking data has been added. The estimator is a modification of the Huggins closed population estimator. See the help file ("Density Estimation") for more details.
187. The capability to include a Pledger mixture model to account for unmodeled heterogeneity has been included for the Cormack-Jolly-Seber data type, the Pradel data types, and the Link-Barker data type. For the Pradel (1996) and Link-Barker (2005) data types, the mixture can only be used with the detection probabilities (p), but the implementation for the CJS data type follows the original Pledger et al. (2003) paper. You obtain access to these new data types through the PIM | Change Data Type menu choices from one of your existing CJS or Pradel MARK files.
188. Numerical integration via the Gauss-Hermite quadrature (GHQ) can be efficiently used to approximate the capture–recapture model likelihood with individual random effects. This technique has been employed for the Cormack-Jolly-Seber data type (Gimenez, O., and R. Choquet. 2010. Individual heterogeneity in studies on marked animals using numerical integration: capture-recapture mixed models. Ecology 91:951-957.), and the Link-Barker data type. For each basic parameter, an additional parameter is addded to specify the standard deviation (sigma) of the normal distribution You obtain access to these new data types through the PIM | Change Data Type menu choices from one of your existing CJS or Pradel MARK files. The mark-resight models had already incorporated this technique to model individual heterogeneity.
189. An additional 2-species occupancy model (Richmond et al. 2010) has been added to supplement the McKenzie et al. (2006) model. The McKenzie parametrization does not handle covariates well, whereas the new conditional occupancy model does successfully incorporate covariates, and is nmerically more stable.
190. The robust design multi-state data type with open primary sessions and mis-classification of states is now working correctly. More details are provided in the help file.
191. Data cloning is implemented as an option in the Results Browser under the Output | Specific Model Output menu choice. Data cloning is useful for determining estimability of parameters. Output from the analysis is presented in an Excel spreadsheeet.
192. A model name is now displayed in the caption heading of the design matrix, along with a menu choice (included in the right click button pop-up menu) for the user to change the model name.
193. A bug in the robust design Pradel models that included N was fixed. The first c parameter of the last primary session was getting set to a log link instead of the value specified for the PIM (i.e., the first c parameter was treated as an N parameter which gets the log link by default). This bug only appeared in models that included N in the likelihood, not the Huggins parameterizations that do not include N.
194. An option from the Results Browser | File menu was added to replace the encounter histories file and rerun all of the existing models. If you replace the input data with a different data set, you have to rerun all of the models because chaning the data means that none of the results in the Results Browser are now correct.
195. An option to view the encounter histories file in the editor was provided under the Results Browser | Output menu choice. Note that the input data summary procedure is also available in the same menu.
196. The odds ratio estimator of lambda for multi-season occupancy models (labeled lambda' on page 200 of the MacKenzie et al. occupancy book) was added as a derived parameter for parameterizations of the multi-season occupancy models.
197. The numerical output from the random effects model that is placed in the Results Browser when an AICc value is calculated is now stored in the Model Notes field of the Results Browser.
198. The data bootstrap estimator was modified to fix 2 issues. First, encounter histories files with aggregated frequency counts are now de-aggregated so that individual encounter histories are sampled, although specifying a covariate to cluster the encounter histories still works correctly. Second, the number of encounter histories in the original data for each group is used to determine the number of bootstrap samples to include, rather than the number of clusters as was what previously was done. Third, specification of a c (over-dispersion) parameter >1 in the simulation input window means that this value will be applied during the resampling. As an example a value of c = 1.5 means that approximately 1/2 of the encounter histories sampled will get a frequency count of 1 and the other 1/2 a value of 2. However, the total number of encounter histories will remain approximately the same as the original data for each group.
199. The psiB (occupancy of species B) and psiAB (joint occupancy of both species) parameters were added as derived parameters for the 2-species conditional occupancy model of Richmond, O. M. W., J. E. Hines, and S. R. Beissinger. 2010. Two-species occupancy models: a new parameterization applied to co-occurrence of secretive rails. Ecological Applications 20:2036-2046.
200. A bug in the robust design occupancy models with heterogeneity (mixtures for p) was fixed in all three parameterizations.
201. Simulators were added for the CJS Pleder, CJS random effects, single-season multiple state occupancy, and multiple-season multiple state occupancy data types.
202. An option was added to the Help menu choice to list out all of the data types available in MARK.
203. Code was added to check the true model when specified in the simlation module to see if a simulator is actually available for the specifiedd data type. Plus, you can list all of the data types that can be simulated with an option under the Simulation menu choice.
204. The Barker robust design model was updated to a proper definition of the temporary emigration parameters: the gamma's were changed to a's (availability) to properly reflect their meaning. Also, this data type now properly handles unequal time intervals (L) between primary sessions. S and F are corrected as S^L and F^L, and the R and R' parameters are corrected as 1 - (1 - R)^L and 1 - (1 - R')^L. The a'' and a' parameters cannot be corrected for unequal time intervals, so must remain time-specific. No correction is needed for r because no matter how long the time interval, an animal can only die once.
205. The Barker model was updated to correctly handle unequal time intervals (L). S is corrected as S^L, and the R and R' parameters are corrected as 1 - (1 - R)^L and 1 - (1 - R')^L. The F and F' parameters cannot be corrected for unequal time intervals, so must remain time-specific. No correction is needed for r because no matter how long the time interval, an animal can only die once.
206. The regular robust design model was updated to change the effect of unequal time intervals (L) between primary sessions. S is still corrected as S^L. However, because the gamma'' and gamma' parameters cannot be corrected for unequal time intervals, they must remain time-specific to accommodate unequal intervals. For the case where time intervals are multiples, e.g., L = 1 and L = 2, a dummy primary session can be used with all values equal to dots (.). However, you better understand which parameters remain estimable and which will become unidentifiable when doing this.
207. A bug with dots in the encounter history was fixed in the Huggins robust design data types, so that the estimate of N is now correctly computed. In addition, the robust design data types with N in in the likelihood were changed to not allow dots in the encounter history because N cannot be correctly estimated in these data types when dots are in the encounter histories.
208. The multi-season occupancy models with gamma (colonization) and epsilon (extinction) were updated to not correct for unequal time intervals using L as a power. This change was made because the previous correction did not work correctly.
May, 2012 (Version 6.2)
209. Two versions of the FORTRAN numerical estimation code are now supplied with MARK in the setup.exe file, with both now generated with the gfortran compiler. Depending on whether you are running a 32-bit or 64-bit version of the operating system, either the 32-bit or 64-bit version of the mark.exe file is used for numerical estimation. Both include parallel processing using multiple threads You can specify the number of threads to use for parallel processing in the File | Preferences menu choice. The number of threads used and the maximum available are reported at the top of the full output text file.
210. The Pledger and Schwarz (2002) mixture model for the Seber (1970) band recovery model was added, available from the "Change Data Type" menu from either the Seber or Brownie dead recoveries data type.
211. The individual heterogeneity random effects model for the Seber (1970) band recovery model was added, available from the "Change Data Type" menu from either the Seber or Brownie dead recoveries data type. Although both sigmaS and sigmar are included in the model, the sigmar parameter is not identifiable.
February, 2013 Presto (Piping) Plover Version (Version 7.1)
212. The Richmond et al. (2010) 2-species occupancy model was extended to a multi-season model using the transition matrix described in Miller et al.(2012). The help file is titled "Occupancy Estimation Robust Design 2 Species".
213. Simmulation capability for the single-season Richmond et al. (2010) 2-species occupancy model was added.
214. Simmulation capability for the multi-season Richmond et al. (2010) 2-species occupancy model was added.
215. Two bugs with the specification of threads were fixed, so that multiple threads now run as specified.
216. The data type names for the closed captures data types were changed to be more informative. This also changes the names of all robust design data types.
217. The dead recoveries data types were consolidated into a single entry on the new data analysis screen. These data types were the Seber, Brownie et al. and the BTO dead recoveries.
218. A bug that was apparently introduced in December, 2012, concerning retrieval of PIMs that were fully specified was fixed.
219. Added the derived parameter of survival over all occasions to the data type Lukacs survival of young with a marked adult.
220. The product of columns menu choice was modified to use the design matrix product function for columns containing individual covariates.
221. We have made the following change to the multistate robust design (open and closed) with state uncertainty (3 data types). We have reparameterized the mixture parameters for the first primary period, so that pi1^s = w1^s*p1^*s / sum[w1^s*p1^*s] (see Kendall et al. 2012 Ecology). Therefore pi1 no longer exists as a parameter in the likelihood, and there are now K-2 parameters in the pi PIMs, where K is the number of primary periods. The first parameter listed is for primary period 2, and the last pi is for primary period K-1. There is a pi estimate only for the first S - 1 states, where S is the number of states. The pi for the last state is obtained by subtraction. We made this change because for the common case where a given state is never known with certainty, pi1 and therefore the survival and transition probabilities for primary period 1 for that state were not estimable.
222. The ability to "lasso" blocks in the PIM Chart was extended so that once you have lassoed a set of blocks, as shown by changing to green instead of blue, you can right click and use the Constant, Time, Age, or All Different pop-up menu choices to make the selected change to the lassoed blocks. Note that to lasso a block, you only need to include the lower left corner inside the lasso rectangle. You lasso blocks by holding down the shift key and then the left mouse button and draging out the resulting rectangle to capture blocks.
223. The pent parameter of the data types (1) Open Robust Design Multi-state, and (2) Open Robust Design Multi-state with classification uncertainty, has been changed to obtain the last value by substraction, rather than the first as was originally programmed. This change makes it easier to fit linear and quadratic models to the probability of entry parameter in these models.
224. The Open Robust Design Multi-state with State Uncertainty data type was extended to create a new data type that allows seasonality. The idea is that the attribute that allows determination of the state may not be identifiable, so that an additional set of parameters, alpha (PIM for each primary session and each state) to allow the attribute to become identifiable has been added. In addition, the attribute may go away, so yet another set of parameters, c (again with a PIM for each primary occasion and state) was added to allow the attribute to cease. See the updated help file for more details on these models.
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: Gary.White at 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., Larissa Bailey, and William Kendall 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, 2010, beginning mid-January and ending early April.
Another intermediate level workshop is scheduled for June 3-8, 2012, 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 of Vertebrate Populations, co-taught by Paul F. Doherty, Jr. Larissa Bailey, and William Kendall. The course meets from mid-January until the last week of March, MWF from 8-12. The class will next be taught spring semester, 2010. We strongly encourage students from outside Colorado State University to participate in this course.
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Barker, R. J. 1999. Joint analysis of mark-recapture, resighting and ring-recovery data with age-dependence and marking-effect. Bird Study 46 Supplement:82-91.
Barker, R. J., and G. C. White. 2001. Joint analysis of live and dead encounters of marked animals. Pages 361-367 in R. Field, R. J. Warren, H. Okarma, and P. R. Sievert, editors. Wildlife, land, and people: priorities for the 21st century. Proceedings of the Second International Wildlife Management Congress. The Wildlife Society, Bethesda, Maryland, USA.
Barker, R. J., G. C. White, and M. McDougal. 2005. Movement of paradise shelduck between molt sites: a joint multistate-dead recovery mark recapture model. Journal of Wildlife Management 69:1194-1201.
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Brownie, C., J. E. Hines, J. D. Nichols, K. H. Pollock, and J. B. Hestbeck. 1993. Capture-recapture studies for multiple strata including non-Markovian transitions. Biometrics 49:1173-1187.
Burnham, K. P., D. R. Anderson, G. C. White, C. Brownie, and K. H. Pollock. 1987. Design and analysis methods for fish survival experiments based on release-recapture. American Fisheries Society Monograph No. 5. Bethesda, Maryland, USA. 437pp.
Burnham, K. P. 1993. A theory for combined analysis of ring recovery and recapture data. Pages 199-213 in J.-D. Lebreton and P. M. North, editors. Marked individuals in the study of bird population. Birkhauser Verlag, Basel, Switzerland.
Dinsmore, S. J., G. C. White, and F. L. Knopf. 2002. Advanced techniques for modeling avian nest survival. Ecology 83:3476-3488.
Hestbeck, J. B., J. D. Nichols, and R. A. Malecki. 1991. Estimates of movement and site fidelity using mark-resight data of wintering Canada geese. Ecology 72:523-533.
Huggins, R. M. 1989. On the statistical analysis of capture-recapture experiments. Biometrika 76:133-140.
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Kendall, W. L. 1999. Robustness of closed capture-recapture methods to violations of the closure assumption. Ecology 80:2517-2525.
Kendall, W. L., and J. D. Nichols. 1995. On the use of secondary capture-recapture samples to estimate temporary emigration and breeding proportions. Journal of Applied Statistics 22:751-762.
Kendall, W. L., K. H. Pollock, and C. Brownie. 1995. A likelihood-based approach to capture-recapture estimation of demographic parameters under the robust design. Biometrics 51:293-308.
Kendall, W. L., J. D. Nichols, and J. E. Hines. 1997. Estimating temporary emigration using capture-recapture data with Pollock's robust design. Ecology 78:563-578.
Kendall, W.L. and R. Bjorkland. 2001. Using open robust design models to estimate temporary emigration from ca pture-recapture data. Biometrics 57(4): 1113-1122.
Kendall, W. L. and J. D. Nichols. 2002. Estimating state-transition probabilities for unobservable states using capture-recapture/resighting data. Ecology 83:3276-3284.
Lebreton, J-D., K. P. Burnham, J. Clobert, and D. R. Anderson. 1992. Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs. 62:67-118.
Link, W. A., and R. J. Barker. 2005. Modeling association among demographic parameters in analysis of open population capture-recapture data. Biometrics 61:46–54.
Lukacs, P. M., V. J. Dreitz, F. L. Knopf, and K. P. Burnham. 2004. Estimating survival probabilities of unmarked dependent young when detection is imperfect. Condor 106:926-931.
Lukacs, P. M., and K. P. Burnham. 2005. Estimating population size from DNA-based closed capture-recapture data incorporating genotyping error. Journal of Wildlife Management 69:396-403.
MacKenzie, D. I., J. D. Nichols, G. B. Lachman, S. Droege, J. A. Royle, and C. A. Langtimm. 2002. Estimating site occupancy when detection probabilities are less than one. Ecology 83:2248-2255.
MacKenzie, D. I., J. D. Nichols, J. E. Hines, M. G. Knutson, and A. B. Franklin. 2003. Estimating site occupancy, colonization and local extinction probabilities when a species is not detected with certainty. Ecology 84:2200-22078.
MacKenzie, D. I., L. L. Bailey, and J. D. Nichols. 2004. Investigating species co-occurrence patterns when species are detected imperfectly. Journal of Animal Ecology 73:546.
MacKenzie, D. I., J. D. Nichols, M. E. Seamans, and R. J. Gutierrez. 2009. Modeling species occurrence dynamics with multiple states and imperfect detection. Ecology 90:823-835.
McClintock, B. T. and G. C. White. 2009. A less field-intensive robust design for estimating demographic parameters with mark-resight data. Ecology 90:313-320.
McClintock, B. T., G. C. White, M. F. Antolin, and D. W. Tripp. 2009a. Estimating abundance using mark-resight when sampling is with replacement or the number of marked individuals is unknown. Biometrics 65:237-246.
McClintock, B. T., G. C. White, K. P. Burnham, and M. A. Pryde. 2009b. A generalized mixed effects model of abundance for mark-resight data when sampling is without replacement. Pages 271-289 in D. L. Thomson, E. G. Cooch, and M. J. Conroy, editors. Modeling Demographic Processes in Marked Individuals. Springer, New York, USA.
Nichols, J. D., J. E. Hines, D. I. MacKenzie, M. E. Seamans, and R. J. Gutierrez. 2007. Occupancy estimation and modeling with multiple states and state uncertainty. Ecology 88:1395-1400.
Nichols, J. D. L. L. Bailey, A. F. O'Connell, N. W. Talancy, E. H. C. Grant, A. T. Gilbert, E. M. Annand, T. P.Husband, and J. E. Hines. 2008. Multi-scale occupancy estimation and modelling using multiple detection methods. Journal of Applied Ecology 45:1321-1329.
Pledger, S. 2000. Unified maximum likelihood estimates for closed capture-recapture models using mixtures. Biometrics 56:434-442.
Pledger, S., K. H. Pollock, and J. L. Norris. 2003. Open capture-recapture models with heterogeneity: I. Cormack-Jolly-Seber model. Biometrics 59:786-794.
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