Before you can successfully create and run models in either MARK or RMark, you must have a basic understanding of certain issues that will determine (1) what models you can (or should) run, (2) the parameters that you can expect to be able to estimate.
Data structure/ model types
Data structure refers to the type and dimension of the CMR data you have, as well as to the assumptions that it was collected under. Examples of some data structures are:
Captures and recaptures for closed populations
Live captures and recaptures for open populations
Resighting of marked animals (open or closed populations)
Dead recoveries for open populations
Combined data for open populations (live and dead data, recapture and re-sighting data)
Robust design (combined closed and open sampling periods)
The data structure in turn determines the type of models that you can expect to be able to use,e.g.:
Close abundance estimation including modeling of capture heterogeneity
Survival estimation (CJS models) from live recaptures and resighting
Survival estimation (Seber and Brownie models) from dead recoveries
Estimation of survival and fidelity from joint live/data data (Burnham model)
Estimation of survival, abundance and temporary emigration (Robust Design temporary emigration models)
Parameter types
Once you have determined the basic data structure and type of model, you should know what to expect in terms of the model parameters that are potentially involved. I will illustrate with 2 very common examples: CJS (live recapture) models, and closed abundance models.
CJS models - These typically have 2 parameter types: the survival (or apparent survival) parameter, Phi, and the recapture parameter (p). Phi is the probability of surviving an interval between recapture occasions, and p is the probability that a marked animal is recaptured if it survives to a particular interval. As noted below, both of these may vary over occasions, among groups, or with respect to factors such as covariates.
Closed abundance models- These usually have 3 and sometimes 4 parameter types: capture probability (p): the probability that an animal is captured (or recaptured); recapture probability (c), the probability of recapture, which can be different than p if previous capture affects recapture; and abundance (N). p and c may vary over sampling occasions and potentially among individuals, whereas N by definition is constant over time (closed assumption) but may differ among groups (if we have stratified the data by area, sex, age, or other attribute). An additional parameter pi is sometimes invoked in these models to allow modeling of capture heterogeneity by finite mixture models.
Group and time effects
The number of groups (if >1) and the number of capture-recapture occasions jointly determine the numbers of the various parameters. I illustrate with CJS and closed data structures.
CJS - Generally if there are k occasions there will be up to k-1 survival (1 for each interval) and k-1 recapture parameters (one for each occasion after the first) for each group in the usual (non-cohort) CJS model. So for example if there are 7 occasions and 2 groups, we would have 12 Phi values and 12 p values.
Conventionally, both MARK and RMark number these within parameter type, first for Phi then for p, then group within type, then occasion withing group. So in this example the parameters would be:
1-6: Phi group 1
7-12: Phi group 2
13-18: p group 1
19-24: p group 2
As we will see later, this ordering/ numbering scheme becomes the basis for the Parameter Index Matrices (PIMS).
Closed abundance - For non-mixture models, if there are k occasions there will be up to k capture probabilities (one for each occasion), k-1 recapture parameters (one for each occasion after the first), and a 1 abundance parameter for each group. So for example if there are 7 occasions and 2 groups, we would have 14 p values, 12 c values, and 2 N values. Conventionally, both MARK and RMark first for p then for c, then for N, then group within type, then occasion withing group. So in this example the parameters would be:
1-7: p group 1
8-14: p group 2
15-20: c group 1
21-26: c group 2
27: N group 1
28: N group 2
For mixture models the group/specific mixture probability(ies) precedes the other parameters. Again, this ordering/ numbering scheme becomes the basis for the PIMS used later in model construction.