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Program MARK: Survival Estimation from Populations of Marked Animals


Gary C. White, Department of Fishery and Wildlife Biology, Colorado State University, Fort Collins, CO 80523 USA, and Kenneth P. Burnham, Colorado Cooperative Fish and Wildlife Research Unit, Colorado State University, Fort Collins, CO 80523 USA

Program MARK, a Windows 95 program, provides survival 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), from live recaptures (e.g. the animal is re-trapped or re-sighted), or from radio tracking. 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. The user can use a summarized form of the encounter histories when multiple animals have the same history and no individual covariates. In addition, program MARK can 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 individual-specific covariates.

Parameters (Φ, S, N, or encounter probabilities) 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, with all possible combinations across all parameters. Open models can include covariates, specific to the individual animal or to the encounter occasion. The Design Matrix provides this capability. Examples are the weight of the animal at the time of marking, or the average temperature over the survival interval. 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 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 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-F 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.

Additional information and the program are available from http://www.cnr.colostate.edu/~gwhite/mark/mark.htm .


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