Mark-resighting starts from the premise that a certain number of animals are marked in some fashion and released back into a population, and in this way has common roots with capture-mark-recapture (CMR). And like CMR, abundance estimation is based on subsequent sampling of both marked and unmarked animals. However, unlike CMR, these subsequent samples do not ordinarily involve the marking of unmarked animals, so that the only animals that are marked are (usually) the initial sample of animals, typically marked and released before subsequent sessions in which observations are taken on both marked and unmarked animals.
The astute reader may recall that in fact one of our very early CMR examples in fact was an example of mark-resighting. That is, rabbits were captured, marked, and subsequently released (n1), and a second visual sample (n2) was take in which m2 rabbits were observed to be marked. The frequencies n1, n2, and m2 were then used with the Lincoln-Petersen estimator to estimate abundance (N).
Even for this simple case, one can see potential problems with mark-resighting. The biggest one perhaps is that, unlike physical capture, in observing the unmarked animals one can seldom be certain that the counts of animals captured represents n2-m individual animals, or instead represents repeated detections of some of the same individuals. Mark-resighting models typically assume that the "repeats" of the marked animals are similar to those of the unmarked, and use the information gleaned from the former to make inferences about the latter-- with the key idea being that we are trying to estimate the total number of unmarked animals in the population (U), not just the ones we happen to see (u), and from that abundance (N=U+M where M= the number of marked animals, which of course we know if the population is closed).
Basic data/ model structure
McClintock and White (2012) give a good overview of the basic types of data structures and corresponding models that can be involved in mark-resighting; see their Table 1 in particular. I will focus here on the (zero-truncated) Poisson log-normal estimator (zPNE), which is appropriate under the following circumstances:
The number of marked animals before the resighting period is either known or unknown
Sampling is either with or without replacement at an occasion, meaning that animals can be detected once only (without replacement) or multiple times
Marked animals are individually identifiable.
We focus on the "closed" version of the zPNE, in which we assume that all sampling occurs over a period of time in which there is negligible effect of entries (births, immigration) or departures (deaths, emigration) on the population so that N is constant. The following parameters are estimated, which may be indexed over time occasions for the open or "robust" version of zPNE, or by groups or other covariates:
U the number of unmarked animals in the population; when the number of marked animals M is known exactly then estimation of N follows as N= Uhat+ M, otherwise M is estimated from the data.
alpha the intercept for the Poisson distribution, giving the average count
sigma the scaling parameter for the log-normal random effect on counts.
By default these parameters are estimated on the log scale and then back transformed by exp(x) to obtain 'real' parameter values for U, alpha, and sigma.
Use of a Robust design allows flexibility in modeling longer-term situations. Where geographic closure is violated, issues arise as to what the the estimates of abundance refer to -- the population actually on the study area during sampling (N), or a "superpopulation" of animals capable of immigrating in an out of the study area (N*). The immigration-emigration logit-normal estimator (IELNE) extends the logit-normal estimator (LNE) allows for separation of N and N* but requires that the number of marks on each primary occasion is known and that sampling is without replacement (not required for zPNE) but does not require that marks be individually identifiable (required by zPNE), although estimation is improved if some marked animals are identifiable. See McClintock and White (2012) for more details.