What is mark-recapture?
Mark- recapture (also termed mark-release-recapture, capture-recapture, tag-recapture or band recovery) is where a number of individuals are marked such they can be identified subsequently, and then released back into the population. The population is subsequently resampled, and inferences are drawn about the population from the recapture of marked individuals.
Marking can be unique to each individual, or to a batch of individuals sampled on the same date. Traditionally such marks have been applied by the researcher using paint, dye, fluorescent powder, external tags, branding or mutilation. Radio-active isotopes or rare earths have also been used. Radio-tags can also be used for mark-release-recapture, but are more commonly used to study behavioural aspects such as home range size. More recently non-invasive mark-recapture techniques have been increasingly used in which some characteristic of the animal is used to identify it. These include photographs of unique visual features of the animal. For example, Kawanishi & Sunquist (2004) estimated the size of tiger populations by mark-recapture using self-activating, remote-camera systems equipped with an infrared sensor. Another approach is use DNA analysis of some product of the animal, for example hairs or faeces. For example, Boulanger et al. (2004) estimated the size of grizzly bear populations has been estimated using arrays of barbed wire hair traps set around a bait. The barbed wire captures hair which can then be identified using DNA analysis.
Why do mark-recapture?
There are two main reasons for marking individuals.
- To identify a cohort for subsequent studies on the behaviour and/or survival of members of that cohort. Behavioural studies may include long range migration, foraging, territoriality, kinship groups, or mate selection.
- To estimate population parameters. In particular:
- The absolute population size - that is the total number of individuals in a population, as opposed to relative population estimates, such as catch per trap per day, or number of tracks observed.
- The population gain rate (births + immigration) and the population loss rate (deaths + emigration).
The second of these comprises what is usually termed mark-recapture, although we will first consider cohort studies, since these include estimation of long range migration and survival.
In cohort studies the main interest is in the behaviour and survival of the marked individuals. Observations on unmarked individuals are only really of interest to the extent that they interact with marked animals. The proportion of marked individuals in the total population is of no interest.
Examples include ringing swallow nestlings to determine migration routes, tagging leopards to assess their home ranges and hunting grounds, and tagging seedlings to monitor their subsequent survival.
The key assumption is that marked individuals behave in the same way as the rest of their population. It is immaterial whether marked individuals mix freely with their population, or are equally available to resampling. As a result, much work has been invested in
- making the marking process (including the initial capture, and release) as non-traumatic as possible for the animal and for any social group it may belong to;
- minimizing the effect of the mark, tag, or tracking device upon the animal's subsequent behaviour.
In the past, valid recaptures were in the form of (for example) returns by hunters, mist netting of birds, and spotting marked individuals with binoculars. Nowadays, lightweight radio transmitter collars (with integral GPS, motion detectors, and even cameras) have become the method of choice for any animal large enough to be fitted with them.
Population parameter estimation
A closed population is one in which there is neither immigration nor emigration, nor any births or deaths - at least between marking and recapture occasions. Let us say that, of a population of (N) individuals, you have marked (or can individually recognise) a number (a) of them. Expressed as a proportion, this means you can identify a/N of the population. If you then took a representative (recapture) sample (n) of that population, you would expect the same proportion to be marked. In other words, if r individuals of that sample are marked, you would expect:a / N = r / n
This can be rearranged to give the classic formulation for estimating population size:
Algebraically speaking -
|N|| = || a n
- N is the total population size
- n is the total number in the second sample
- a is the total number of individuals marked
- r is the number of marked individuals in the second sample
In practice, for reasons we explore in Unit 2, what we obtain is an estimate of N. By convention this is written as (pronounced 'N hat'), and is known as the simple Lincoln index or Petersen estimate.
By far the biggest problem with this attractively simple formula is it that is only valid if some (frequently unrealistic) assumptions are met.
- The individuals selected for marking should be representative sample of the population. This is essential because marked individuals should behave and survive the same way as their unmarked fellows. This inherently assumes that the population is homogenous as regards catchability.
- The marking process should not then affect those individuals in any way, either in terms of their survival or their behaviour. Nor should marked individuals loose their marks over time.
- The recapture sample(s) should also be representative of the population, in addition now with respect to individuals' mark status. For this you have to assume that the marked individuals have mixed thoroughly with unmarked individuals in the population.
- For the simple Petersen index (and some other methods), you must also assume that you are dealing with a closed population. In other words there is no natality, mortality, immigration or emigration during the period of the study.
The first three of these assumptions generally have to be met for all mark-release-recapture techniques, although some of the more recent methodologies can deal with lack of homogeneity within the population. The fourth assumption is (usually) limited to single mark - single recapture approaches such as the Petersen estimate.
When it comes to an open population, a single mark - single recapture approach is no longer viable, and multiple recapture occasions are required. For most approaches multiple marking occasions are also required. Loss and gain rates are usually estimated along with population size. Note that one cannot usually separate births from immigration nor deaths from emigration - at least not without further supplementary studies. A marked individual that has died is equally unavailable for recapture as one that has emigrated.
Gains and losses to a population have two, quite different effects:
- Gains reduce the proportion of marked individuals in the population, and in samples thereof - in the same way that adding water to a solution dilutes it.
- Losses reduce the number of marked individuals in the population, and in samples thereof - in the same way that pouring some of the solution away affects the amount remaining.
By looking at changes in the numbers and proportion of marked individuals over time, it is possible to estimate either the gain rate or the loss rate or both. There are a number of different methods available, each of which carries different assumptions on whether or not these rates can vary over time:
Mark once, recapture at intervals
This approach (termed either Jackson's positive method or Parker's method) is usually taken where multiple marking occasions are logistically impractical, but multiple recaptures over time are feasible. It has been used extensively in commercial fisheries, as well as in medical entomology to estimate the population size and survival of disease vectors.
Analysis comprises plotting the recapture rate (number marked (mi) / number in sample (ni)) against time. Providing there is a reasonably smooth trend in this relationship (the ratio is usually log transformed), the line can be extrapolated back to time 0 to estimate the ratio of number of individuals marked (r) to total population size at time zero (N0). (N0) can then be readily determined.
The graph below shows how the recapture rate on the day of marking was estimated for a species of tsetse fly by regressing the proportion of recaptures against time since marking - giving an estimated population of 144,739 females.
Repeatedly mark and recapture.
In other words, you take repeated samples, and record the number of marked individuals in each successive sample and the number of newly marked individuals released. These methods work by building up a subpopulation of marked individuals 'at risk' of recapture. There are many methods which have been used in the past including:
- The Fisher-Ford trellis method: this is a relatively robust method which can be used for fairly small samples - providing the survival rate is more or less constant.
- Bailey triple catch method: this is relatively simple to compute, and requires only three samples. Assumptions are few but it works best with large samples.
- Jolly-Seber stochastic method: this is technically the most efficient and informative method, and enables estimates of (changing) parameters over a period of time. But it is dependent on a reasonably large number of recaptures. It forms the basis of several software programmes for analyzing mark-recapture data.
- Manly and Parr method: this requires a large number of multiple recaptures, but frees one from the assumption of age-independent survival (inherent in all other methods).
Mark-recapture is one area which has developed enormously in the last twenty years, and there is a considerable literature. We have given a few key references in the References section for this More Information page. Perhaps the most useful up-to-date review is given by Seber & Schwarz (2002).