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3 marked and unmarked animals die or leave the area at the same rate;

4 no marks are lost.

Assumption (2) is not needed when marked animals are recaptured on more than

one occasion, but the others are common to all elaborations of the Petersen estimate.

The least realistic is the assumption of equal catchability, which is routinely violated

by almost any population the wildlife manager is called upon to estimate (Eberhardt

1969). For this reason the Petersen estimate and its elaborations (Bailey’s triple catch,

Schnabel’s estimate, the Jolly–Seber estimate, and many others) are of limited utility

in wildlife management.

Frequency-of-capture models

Petersen models work only when all animals in the population are equally catchable.

Frequency-of-capture models are not constrained in that way but will work only if

the population is closed, if there are no losses from or gains to the population over

the interval of the experiment. That is easy enough to approximate by running the

exercise over a short period.

Animals are captured on a number of occasions, usually on successive nights, and

marked individually at the first capture. At the end of the experiment each indi-

vidual caught at least once can be scored according to the number of times it was

captured. The data come in the form:

Number of times caught (i): 1 2345678 ...18

Number of animals (fi): 4316860210 ... 0

which are from Edwards and Eberhardt (1967) who trapped a penned population of

wild cottontail rabbits for 18 days. Of these, 43 were caught once only, 16 twice,

eight three times, and so on. ∑fi=76 gives the number of rabbits caught at least

once and so the population must be at least that large. If we could estimate f 0 , the

number of rabbits never caught, we would have an estimate of population size:

Y=f 0 +^76

Traditionally this has been attempted by fitting a zero-truncated statistical distribu-

tion (Poisson, geometric, negative binomial) to the data and thereby estimating the

unknown zero frequency. Eberhardt (1969) exemplifies this approach. More com-

plex mark–recapture models use sophisticated analytical techniques to cope with

variation in the probability of capture due to time (seasonal trends, changes in weather),

variation among individual animals (site fidelity, sex differences, dominance rela-

tionships), prior trapping history (capture-shyness and capture-proneness), and various

combinations of these (Pollock 1974; Burnham and Overton 1978; Otis et al. 1978).

The fit of each model can be tested against the data and an objective decision made

as to which is the most appropriate model, often using information theory (see Chapter

15). The computations are too lengthy to be attempted by hand but several software

programs are freely available on the web: CAPTURE (White et al. 1982), SURGE

(Lebreton et al. 1992), and MARK(White and Burnham 1999).

Estimation of density

All previously reviewed mark–recapture methods yield a population sizeY that

can be converted to a density Donly when the area Arelating to Yis known. In

238 Chapter 13