Several issues come into play in properly designing a CMR study, and dealing with these depends on
Knowledge and familiarity with the basic life history of the organism (e.g., its movement and demographic rate)
Educated guesses or prior estimates of important quantities such as abundance, survival, and capture probability.
Some important questions must first be asked:
What are the study objectives?
Is it to estimate abundance?
Where and when?
Is it to estimate demographic rates?
Is it to make comparisons/model growth/ make inferences about the effects of management?
What is the time frame and spatial extent of the study?
Is the population likely to be open or closed during the study period?
Is it feasible to mark and recapture animals, and by what methods?
The answers to these questions will determine what sort of study design is appropriate, what data are likely to be available, and even whether CMR is an appropriate approach.
Closed population estimation and modeling
By closed we mean that the population is not anticipated to experience significant mortality, recruitment , or migration (in or out). By definition of course this implies that abundance (N) is a fixed constant over the course of the study. In closed population modeling we will therefore be considered mainly with modeling potential heterogeneity in capture probabilities (p) over time, in relation to previous capture, or among individual animals, although in some cases closed models will allow modeling of abundance (e.g., among age or sex groups or between geographic strata or habitats).
In designing a closed CMR study, we need to be focused on at least 2 critical points. First, we need to assure that, within a reasonable approximation, we are in fact sampling the population over a time span and area for which it is reasonable to assume closure. Thus for example it will generally be important to avoid periods when there is likely to be a great deal of mortality or migration (e.g., hunting seasons or migratory periods), or recruitment unless the recruits can be readily distinguished from adults.
Second, we need to be aware that precision of estimates will largely revolve around our ability to capture and recapture a sizable fraction of the population. it is therefore important to design sampling schemes in such a way to do accomplish this. To do so we typically (or might have) 2 factors under our control, and 1 over which we have no control but need some idea of. We of course have no control over local abundance/ density, but nevertheless its value will largely determine how large of a sample of marked and unmarked animals we can expect to obtain. We may have control over capture probability (p), at least to the extent that some methods and levels of capture effort are more likely to generate a larger fraction of the population in our marked sample (p=n/N), and consequently larger marked sample (n=pN) at each sampling occasion.
We also have control over how many sampling occasions (k) the study contains, with k=2 being the minimum (a single capture and marking period, followed by a recapture sample). Having more occasions (k= 3 or more) has 2 advantages. First, it allows for more flexible modeling of capture probabilities and relaxation of assumptions required if k=2. Second, it adds more data (kpN expected total captures), thereby increasing precision of estimates. We will use simulation approaches to investigate the effects of different CMR designs (levels of p and k) as an aid to designing improved CMR studies.
In addition to the above, often it is helpful to include in the study covariates that assist in explaining variation of capture probabilities over time and among individuals. Inclusion of covariate, however, should only be undertaken once the above basic design elements have been addressed.
Open population estimation and modeling
By contrast to closed CMR, open CMR assumes that population size may vary between capture occasions, due to demographic turnover (births or deaths), or movement (immigration and emigration). Allowing the population to be open has huge implications for CMR in that there is now the possibility both that marked animals may leave the population (mortality, emigration) and that unmarked animals many enter the population. This complicates inference, and requires the addition of additional parameters accounting for losses or gains.
So now the population state is no longer fixed, but may vary over the occasions t=1, ,,,, k as N[t], and we need to include additional parameters explicitly modeling survival , phi[t], and recruitment, f[t], under a basic state model such as N[t+1]=N[t](phi[t]+f[t]). This is actually the form of the Jolly-Seber (and related) models, which uses data on both unmarked and marked animals in the sample. However, an important class of closed models only uses marked data, and is known as Cormack-Jolly-Seber (CJS). Because CJS models do not include unmarked animals in the analysis, they cannot provide estimates of N[t] or f[t], but only of phi[t] and capture probabilities.
An additional, important point of open CMR under the simple (JS or CJS) design is that a price is paid for relaxing the closed assumption, and that is the loss of ability to model capture probabilities in a robust manner. In particular, this can result in serious biases in abundance and recruitment estimates if a JS design is used in the presence of strong capture heterogeneity. We turn to this issue under the Robust Design, below.
As with the closed design, estimator precision is influences by both capture probability and number of sampling occasions. In addition, reasonable inference on N[t], f[t] , phi[t] obviously requires more than a few time periods of data (how 'time period' is defined being dependent on the organism and how rapidly it is expected to change over time) . Proper design of an open study requires not only provisional estimates or control over p and k, but also estimates of initial abundance and rates of change (phi[t] for CJS marked only, and phi[t], f[t] for JS marked plus unmarked).
Closed-Open (Robust)
As noted above, when we stretch out sampling over longer periods we potentially gain the ability to estimate changing abundance, as well as demographic rates (survival, recruitment). But we lose the ability to properly model capture heterogeneity-- so our results (especially for abundance and recruitment) may be biased and of limited utility. Some years ago a hybrid closed-open design called the Robust Design (RD) was developed to handle this situation, by providing for short intervals of repeated, closed population sampling (over secondary periods), nested within primary periods that are spaces apart at longer intervals (when the population is assumed open). The RD potentially allows unbiased, 'robust' modeling of abundance and other parameters, and has this additional advantage of providing more data. The RD has also been adapted to other applications, some involving marked animals only and the modeling of temporary emigration. We will return to the RD later in the course.
Next: Basics of CMR modeling