untitled

Two counts

Caughley (1974) showed that if the counts of two observers of equivalent efficiency

were divided into those animals (or groups of animals) seen by only one observer

and those seen by both, the size of the population could be estimated. Henny et al.

(1977) and Magnusson et al. (1978) extended the method to allow for the two observers

being of disparate efficiency.

Essentially the method is a Petersen estimate, although animals are neither marked

nor captured. Suppose that the entities being surveyed are stationary and that their

individual positions can be mapped. Magnusson et al. (1978) surveyed crocodile nests

and Henny et al. (1977) the nests of ospreys. If the area is surveyed independently

twice, perhaps once from the ground and once from the air, the entities can be divided

into four categories:

S 1 =the number seen on the first survey but missed on the second

S 2 =the number seen on the second survey but missed on the first

B=the number tallied by both surveys

M=the number missed on both

This is equivalent to a mark–recapture exercise. The first survey maps (marks) a

set of entities, each of which may or may not be seen (recaptured) on the second

survey. But unlike a true mark–recapture exercise the model is symmetrical and the

first and second surveys are interchangeable.

If P 1 is the probability of an entity being seen on the first survey andP 2 the prob-

ability of its being seen on the second survey:

P 1 =B/(B+S 2 )

P 2 =B/(B+S 1 )

M=S 1 S 2 /B

Y=[(B+S 1 )(B+S 2 )]/B

where Yis an estimate of the size of the population. The last equation may be

corrected for statistical bias (Chapman 1951) to:

Y=[((B+S 1 +1)(B+S 2 +1))/(B+1)] −^1

which has a variance given by Seber (1982) of:

Var(Y) =[S 1 S 2 (B+S 1 +1)(B+S 2 +1)]/[(B+1)^2 (B+2)]

Magnusson et al. (1978) reported that, although the method is based on the assump-

tions that the two surveys are uncolluded and that there is a constant probability of

seeing an entity on a given survey (equal catchability), the second assumption is not

critical. The population estimate is close enough even when the probability of being

seen varies greatly between individuals.

Caughley and Grice (1982) extended the method to moving targets, dropping the

requirement that the position of stationary entities must be mapped so that they could

be identified as seen or not seen at the two surveys. Groups of emus (Dromaius novae-

hollandiae) were tallied simultaneously but independently by two observers seated

240 Chapter 13