The estimation of animal abundance is an important problem in both the theoretical and applied biological sciences. Serious work to develop estimation methods began during the 1950s, with a few attempts before that time. The literature on estimation methods has increased tremendously during the past 25 years (Cormack 1968, Seber 1973).

However, in large part, the problem remains unsolved. Past efforts toward comprehensive and systematic estimation of density (D) or population size (N) have been inadequate, in general. While more than 200 papers have been published on the subject, one is generally left without a unified approach to the estimation of abundance of an animal population

This situation is unfortunate because a number of pressing research problems require such information. In addition, a wide array of environmental assessment studies and biological inventory programs require the estimation of animal abundance. These needs have been further emphasized by the requirement for the preparation of Environmental Impact Statements imposed by the National Environmental Protection Act in 1970.

This publication treats inference procedures for certain types of capture data on closed animal populations. This includes multiple capture-recapture studies (variously called capture-mark-recapture, mark-recapture, or tag-recapture studies) involving livetrapping techniques and removal studies involving kill traps or at least temporary removal of captured individuals during the study. Animals do not necessarily need to be physically trapped; visual sightings of marked animals and electrofishing studies also produce data suitable for the methods described in this monograph.

To provide a frame of reference for what follows, we give an exampled of a capture-recapture experiment to estimate population size of small animals using live traps. The general field experiment is similar for all capture-recapture studies (a removal study is, of course, slightly different). A typical field experiment is the following: a number of traps are positioned in the area to be studied, say 144 traps in a 12 X 12 grid, 7 m apart. At the beginning of the study (j=1) a sample size of n₁ is taken from the population, the animals are tagged and marked for future identification, and then returned to the population, usually at the same point where they were trapped. After allowing time of the marked and unmarked animals to mix, a second sample (j=2, often the following day) or n₂ animals is then taken.the second sample normally contains both marked and unmarked animals. The unmarked animals are marked and all captured animals are released back into the population. This procedure continues for t periods where t ≥ 2. The animals should be marked in such a way that the capture-recapture history of each animal caught during the study is known. In practice, toes are often clipped to uniquely identify individual animals (Taber and Cowan 1969) or serially numbered tags are sometimes used on larger animals.

Such capture studies are classified by 2 schemes that are directly related to what class of models are appropriate and what parameters can be estimated. The first classification addresses the subject of closure. Closure usually means the size of the population is constant over the priod of investigation, i.e., no recruitment (birth or immigration) or losses (death or emigration). This is a strong assumption and, of course, never completely true in a natural biological population. For greater generality, we define closure to mean there are no unknown changes to the initial population. In practice, this means known losses (trap death), or deliberate removals) do not violate our definition of closure. If the study is properly designed, closure can be met at least approximately. Open or nonclosed populations explicitly allow for one or more types of recruitment or losses to operate during the course of the experiment (Jolly 1965, Seber 1965, Robson 1969, Pollock 1975). Only closed populations will be considered in this monograph.

The second classification depends on the type of data collected with 2 possibilities occurring (Pollock 1974, unpublished doctoral dissertation, Cornell University, Ithaca, New York):

(1) only information on the recovery of marked animals is available for each sampling occasion, j, j=1, 2, ... t.

(2) information on both marked and unmarked animals is available for each sampling occasion, j, j=1, 2, ... t.

In case (1), population size (N) is not identifiable, however, other parameters can be estimated (Brownie et al. 1978). In case (2), N can be estimated using a wide variety of approaches depending upon what we wish to assume. Only case (2) will be dealt with here.