Data Type
Data Type
The type of data depends on whether animals are only recaptured alive, or only recovered dead, or both, or, if the fate of each animal is known, such as radio-tracking data, or if the data are for closed captures, where survival is assumed to be 1. Additionally, whether the number of marked animals available for recovery is known, and whether multiple closely-spaced encounter occasions are available to estimate recapture probabilities determine additional models, and Model Structure. The Model Structure help document provides an overview of each of the data types in Program MARK. A complete list of the currently available data types can be generated under the Help | Data Types menu selections.
For recaptures only data, animals are only re-encountered when recaptured alive on succeeding occasions. Typically, this kind of data is from live trapping surveys. The parameter space is apparent survival (phi) and recapture probability (p). Note that apparent survival is not identical to the survival, but is the probability that the animal is alive and remains on the study area and hence is available for recapture.
For situations where multiple closely-spaced trapping occasions are available between longer periods, the robust design model applies. Individual covariates can only be used in the robust design model with the parameters associated with survival, emigration, and immigration. However, for the robust design implemented with Huggins’ estimator, individual covariates can be used with all parameters.
For recoveries only data, animals are only re-encountered when they are recovered dead, such as in waterfowl that are banded and then harvested by hunters. The parameter space is survival (S) and reporting probability (r), or the probability that a band is reported, given that the bird has died. Note that r is not the probability of a hunter reporting the mark, but rather the probability that a mark is report given that the marked animal died. Cause of death can be from either natural causes, or because of harvest, and thus cause of death affects the probability that a mark is reported.
For the special case where the number of marked animals is not known, a model that assumes the reporting probability is constant for all ages and occasions is possible. The BTO Recoveries Model should not be used when the number of animals marked is known, because the assumption of constant reporting rate should be tested.
For both, surveys with live recaptures and dead recoveries provide both kinds of re-encounter data. The parameter space is survival (S), dead reporting probability (r), live recapture probability (p), and fidelity (F), or probability that the animal remains on the study area and is available for live recapture given that it is alive.
When animals are observed alive during the survival intervals, this additional information can be used with Richard Barker’s extension to the both model. This model requires that live encounters during the survival interval are coded as a ‘2’ in the D columns of the encounter history.
For known fates data, the fate of each animal is known, usually by radio-tracking. For this model, there are no additional nuisance parameters, so that the parameter space is only survival (S). The nest survival data type allows for ragged radio-tracking data, i.e., radio-tracking data where the data were not collected in discrete occasions.
For closed captures, the parameter space is the probability of capture on an occasion if the animal has never been captured (p, the probability of capture on an occasion given that the animal has been previously captured (c), i.e., a recapture probability, and the number of animals in the population that are never captured. This value is added to the number of animals known to be in the population to provide an estimate of N, the population size. The parameters p and c are nuisance parameters, because generally N is the parameter of interest. Individual covariates are not allowed with closed captures because the cell probabilities for animals never captured cannot be computed (but see the Huggins models). Mixtures of distributions of the p‘s and c‘s are allowed in the heterogeneity closed captures models.
For the robust design, a closed captures model is used to estimate the probability of initial capture (p), the probability of recapture (c), and population size (N) for each trapping session. For the intervals between trapping sessions, probability of survival rate (S), probability of emigration (gamma”), and of remaining outside the study area (gamma’) are estimated. More details on the robust design model are provided here.
If animals are only marked once and then resightings are obtained on the marked animals and a tally of unmarked animals is made, then the mark-resight estimators can be used to estimate population size. These estimators can also be used in a robust design framework where the number of marked animals is unknown because of mortalities or emigration of marks.
For the multi-strata recaptures only model, multiple study areas (strata) are sampled. The probability of transition from one strata to another is estimated (psi), besides the survival probability (S) for each strata and the recapture probability (p) for each strata. More details on the multi-strata model are provided here. If in addition dead recoveries are available, then stratum-specific reporting rates can be estimated. For this model the data type is of the form LDLDLD… For model details, see the multi-strata model with live and dead encounters. Finally, the multi-strata data type has been extended to a robust design. All 6 of the closed captures data types are available with the closed robust design multi-strata data type.
For the Brownie et al. recoveries model, the dead recoveries model is parameterized the same as was originally done by Brownie et al. (1985). That is, probability of survival (S) and recovery probability (f) are used. The advantage of this parameterization is that there is no confounding of parameters for time-specific models. The disadvantage of this model is that the recovery probabilities (f) are a function of both survival probabilities and reporting probabilities. Thus, modeling a covariate for f is not always clear compared to the standard dead recoveries model used in MARK.
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. This model can be difficult to get numerical convergence of the parameter estimates. Also, for the population change rates to be meaningful, the study area size must not change during the study. See Population Rate of Change for more discussion of this point. Only LLLL encounter histories are required for this model.
Huggins’ model (Huggins 1989, 1991) allows estimation of closed population size (N) from initial capture probabilities (p) and recapture probabilities (c). The model conditions on the animal being captured at least once during the study, so allows individual covariates to be used to model p and c. The approach used in Huggins’ model is equivalent to the Horvitz-Thompson sampling design, where animals have unequal probability of being included in the sample. Only LLLL encounter histories are required for this model.
The robust design model has also been extended to include Huggins’ estimator for population size (N) for each trapping session. Again, individual covariates can be used to model the initial capture probabilities (p) and recapture probabilities (c) for each trapping session. Only LLLL encounter histories are required for this model.
Pradel (1996) developed a model to estimate the proportion of the population that was previously in the population. Thus, this model, labeled ‘Pradel Recruitment Only’, estimates recruitment to the population. The parameters of this model are the seniority probability, gamma (probability that an animal present at time i was already present at time i – 1), and recapture probability r. Only LLLL encounter histories are required for this model.
Pradel (1996) extended his recruitment only model to include apparent survival (phi). In MARK, this model is labeled ‘Pradel Survival and Rec.’. Parameters of the model are apparent survival (phi), recapture probability (p), and seniority probability (gamma). Gamma is defined as the probability that an animal at time i was in the population at time i-1. Only LLLL encounter histories are required for this model.
Pradel (1996) also parameterized his model with both recruitment and apparent survival to have the parameters apparent survival (phi), recapture probability (p), and rate of population change (lambda), where lambda is population size at time i+1 divided by population size at time i, or N(t+1)/N(t). This model converges quite readily compared to the equivalent Jolly-Seber model described above. Only LLLL encounter histories are required for this model.
A additional extension to the Pradel (1996) models has been parameterized with both recruitment and apparent survival to have the parameters apparent survival (phi), recapture probability (p), and fecundity rate (f), which is defined as the number of adults at time i per adult at time i-1. This model also converges quite readily compared to the equivalent Jolly-Seber model described above. Only LLLL encounter histories are required for this model.
The relationships between the parameters of the 3 models derived from Pradel (1996) are described here.
The occupancy estimation data type provides estimates of the proportion of sites (plots) occupied when the detection probability is <1. If multiple surveys are conducted, the robust design occupancy estimation model can be used to estimate the rate at which sites go extinct, and vice versa, the rate at which unoccupied sites are occupied.
Estimates of survival of dependent young from monitoring marked adults are available with the Lukacs Young Survival from Marked Adults data type.
See Encounter Histories File for details of how to enter input data for some of the data types, with the encounter histories format summarized here for each data type. Otherwise, examine the more detailed descriptions of the models for examples of encounter histories.
You can change the data type for running models within a Results Browser window with the PIM | Change Data Type menu choice, but this procedure is not recommended for most users because inconsistent ranking of models can result (i.e., the likelihoods across data types may not be consistent) and because model averaging may no longer work.