Mark, release, and recapture methods

There are four different ways to determine the number of animals within a habitat or population: counting the total number of animals present, sampling part of the area (a quadrat) and extrapolating to find a total, sampling along a line-transect and measuring the distance and angle to where the animal being counted was first seen, and using the mark-recapture approach. Different types of animals require different techniques for population estimation. The mark-recapture approach is often used for groups of animals whose populations are too large or too secretive for other methods. These are usually vertebrates, although mark-recapture procedures have also been used for invertebrates, such as grasshoppers.

All mark-recapture calculations are based on how many individual animals are marked (denoted M) in the population being studied, how many animals are captured during sampling (n), and how many of the captured animals have been previously marked (m). The estimated population is commonly indicated n̂. The basic mathematical relationship of these data is n̂/M = n/m, when n̂ = Mn/m. An estimate of population density can be obtained by dividing the area being sampled by the estimate of N.

Marking

Animals may be either temporarily or permanently marked. Temporary marking may be daubing paint on an animal’s body, clipping some hair off a mouse’s back, or pulling off a few scales from a snake’s belly. Other techniques include tagging an animal with a global positioning system in their ear, back, or on a harness they wear around their torso. Small tattoos on an area with little or no hair are also common. The choice depends on the animal being studied. In fish, tags are sometimes used, but clipping a notch into a fin is more common, as it is cost-effective and practical. If each animal is given a unique mark, such as a number or symbol, it is possible to determine how long the particular animal lives, its home range, and patterns of movement, such as immigration and emigration rates. Some mark-recapture calculations require knowing how many times an individual animal is captured; the “recaptured” animals must be separated individually for these calculations.

There are pitfalls in this census method that should not be overlooked. Several conditions must be met to ensure that mark-recapture population estimates are valid. The marked animals must neither lose nor gain marks. Care must be taken if natural marks, such as missing toes on a mouse, are used; additional mice losing toes would lead to an error in population estimation. Marked animals must be as subject to sampling as unmarked ones. Because of the excitement of being captured, many animals will not return to a live trap a second time, leading to an overestimation of animal abundance. If an animal becomes easily caught and frequently returns to the trap, like kangaroo rats often do in the desert, then this trap-happy animal produces an underestimate of population size. The marked animals must also suffer the same natural mortality as unmarked ones, and the stress of being captured and marked may cause a higher mortality rate in the animals that are marked. If this occurs, the population estimate will be too high.

The marked animals must become randomly mixed with the unmarked ones in the population, or the distribution of sampling effort must be proportional to the number of animals in different parts of the habitat being studied. If the animals are “clumped,” population estimates will be either too high or too low, depending on whether the clumps of marked animals are included in the sample. Marked animals must be recognized and reported on recovery. Technicians working with the animals must be able to recognize marked animals or read the individual numbers per animal correctly. If marked animals are not recognized, population estimates are too high. There can only be a negligible amount of recruitment or loss to the population being sampled during the sampling period; emigration, if occurring, should be balanced by immigration. A short time between marking the animals and collecting the additional samples for the population estimate is necessary, or the ratio of N to M changes from that existing when n:m was established.

Even under the ideal conditions above, it is apparent, according to the laws of chance, that the ratio of marked-to-unmarked animals in the sample will not always be the same as that of marked-to-unmarked animals in the population; in fact, the two ratios may seldom be the same. Possibilities for sampling error can be decreased by enlarging the size of the sample. As the sample size approaches the population in size, chances for error become smaller. When the point is reached where the sample includes the entire population, there can be no error in estimation. In general, at least 50 percent of the population should be marked, and the number of marked animals in the sample should be 1.5 times the number of unmarked animals in the sample. In actual practice, it is difficult (if not impossible) to meet all these requirements. Consequently, it is often best that mark-recapture population estimates be used as measures of trends in major population fluctuations from year to year, and that scientists understand that these population estimates may have significant error margins, making their application limited.

Applications of the Method

There are many formulas for utilizing the mark-recapture data to produce estimates of population size for any animals that can be marked and recaptured or observed later. The first use of the ratio of marked-to-unmarked animals for population estimation was for fish and ducks; the technique is usually called the Lincoln-Petersen method or index. Its formula is N = Mn/m, where N is the total estimated population, n is the number of animals sampled or captured, M represents the number of animals marked in the population before sample size n is drawn, and m equals the number of previously marked animals recovered in sample size n.

An example of how the calculations for the Lincoln-Petersen index would be made is shown by the following information. If 375 quail were banded and later, in a sample of 545, there were 85 previously banded birds recovered, therefore N = Mn/m, or 375 × 545/85 = 2,404 quail estimated to be present in the population being sampled.

When, as is the case with ring-necked pheasants, there is a variation in the capture of the sexes, caused perhaps by capturing technique, the formula can be applied to both sexes or even to age classes, to arrive at a better estimate of the total population. For example, if 500 males and 750 females were banded before hunting season and then 360 males and 150 females were recovered after the harvest, with 150 banded males found in the 360 males checked and 50 banded females recovered in the 150 females checked, a population estimate can be made. The estimate would be 500 × 360/150, equaling 1,200 males in the population. The female population estimate would be 750 × 150/50, equaling 2,250 females in the population. The total population of pheasants would be estimated to be 1,200 males and 2,250 females, equaling a total of 3,450 pheasants.

The Lincoln-Petersen index differs from other mark-recapture calculations in that only two periods, the initial period when animals are marked and the second period when the sample (n) is collected, are used. If several capture periods are used, sequential formulas, such as the Schnabel method, must be utilized. In each sample taken, all unmarked animals are marked and returned to the population; marking and recapture are done concurrently. The sequential approach makes allowances for the increasing number of marked animals in the population (M). M usually increases with time, but it may decrease with known mortality or removal of marked animals from the population. All the assumptions for the Lincoln-Petersen index should also be met for the Schnabel method to produce accurate population estimates.

The Schnabel method formula for multiple sampling periods is N = Σ(CTMT)/RT. Each line of the Schnabel method calculation corresponds to a line in the Lincoln-Petersen index calculation. C represents the number captured during sampling time one, M is the total marked, and R is the number of recaptures. The subscript T is the sample time.

An example of the Schnabel calculation can be demonstrated using the following data. For four days of trapping, the following data were obtained: on day one, five animals were captured, with no recaptures; on day two, ten animals were captured, five previously marked animals in the population at the start of the second day of trapping, three previously marked animals in the day two sample; day three, fifteen animals captured, fifteen previously marked animals in the population at the start of day three of trapping, three previously marked animals in day three of trapping; day four, ten animals captured, twenty previously marked animals in the population at the start of day four, and four previously marked animals among the animals captured on day four. For the four days of trapping, then, ten animals were recaptured. From these data, the Schnabel method estimate of population density would be N = (5 × 0) + (10 × 5) + (15 × 15) + (10 × 20)/(0 + 3 + 3 + 4) with N = 50.5.

Another approach to the estimation of animal numbers has been developed that differs from the usual approach to mark-recapture population estimation calculations. The Eberhardt method is based not on the ratio of marked-to-unmarked animals but on the number of times an individual is recaptured during the recovery operations; the assumption is that this recapture frequency is related to the total population size. The relationship is believed to be a hypergeometric one. Eberhardt’s formula is N = n/1 - (n/t), where n = the number of individuals handled in recovery operations and t = the total number of captures of individuals. In this tally, t will always be greater than n unless all animals are captured only once. To use these modified mark-recapture data, individual animals must be recognizable. This calculation has been used for a number of mice studies. For example, if twenty different kangaroo rats in the Mojave Desert were captured thirty-five times, the estimated population would be N = 20/1 - (20/35); N = 46.67 animals.

These represent only a few of the mark-recapture formulas available for the estimation of population size and animal density. Many other, more complicated, formulas for the calculation of population estimates based on mark-recapture ratios (such as the Schumacher-Eschymeyer, DeLury, and Jolly procedures) exist, but the simplest formulas often provide the best, most usable estimates of animal numbers.

Uses of the Method

The use of mark-recapture procedures allows the biologist to determine numbers of animals present in a given area. Without these numbers, the future of these animals cannot be predicted. This knowledge allows appropriate management strategies to be developed, either protecting them or providing needed control activities, such as spraying insecticides on agricultural crops before severe economic damage to the crops results. Information about animal populations is essential for determining the effects of environmental changes or human activities, such as construction, on animal communities.

The populations of different areas may be compared; population numbers between seasons or years may also be studied. The fact that certain areas have high numbers of individuals implies that these areas have good conditions for them. Wildlife managers need to know why these areas have higher numbers so that they can improve the relevant conditions in other areas. Learning this would not be possible without knowing population sizes on these respective sites. The success of management work can be judged by changes in population size.

Mark and recapture techniques are applicable to more population situations than are the other options for population estimation. The wide variety of methods available for marking animals often allows previously marked animals to be identified without actually being handled. This minimizes the stress on the marked animal by reducing human contact. This is particularly important for endangered species. Obtaining a relatively accurate population estimates without disturbing a vulnerable population of wildlife ensures conservationists can track their progress and adjust their tactics accordingly.

If information on how long an animal lives in the wild is needed, individual marking from population work can also serve this purpose. From their recapture points, the area used by individuals on a daily, seasonal, and yearly basis, known as the home range, can be determined. The degree of movement of individuals within the population can also be estimated. These data are economical to obtain because the marking and capture of the animals for the population estimate also funds the cost of obtaining home range, movement, and longevity data. The rate of exploitation of the population and the rate of recruitment of new members can also be calculated from the ratio of marked-to-unmarked animals collected during the population studies. The biology of organisms in the wild cannot be adequately studied without accurate estimates of their population levels and fluctuations being known. Mark and recapture procedures are among the important scientific tools for the collection of this information.

Principal Terms

Density: The number of animals present per unit of area being sampled

Emigration: The movement of animals out of an area; one-way movement from a habitat type

Habitat: The physical environment, usually that of soil and vegetation as well as space, in which an animal lives

Home Range: The space or area that an animal uses in its life activities

Immigration: The movement of animals into an area; a one-way movement into a habitat type

Marked: An individual animal that is identifiable by marks that may be either human-made, such as metal bands or tags, or natural, such as the pattern of a giraffe

N: A standard abbreviation for the size of an actual population; if capped with a ^ (n̂) it is an estimated value

Population: A group of animals of the same species occupying the same physical space at the same time

Recaptured: A previously marked animal that is either seen, trapped, or collected again after its initial marking

Sampling: The process of collecting data, usually in such a manner that a statistically valid set of data can be acquired

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