the shape of the curve must be assumed to some extent and the validity of the assump-
tion determines the accuracy of the method.
We present only two of the many models available, mainly to give some idea of
their diversity. The first is the Hayne (1949) estimate, which is derived from the assump-
tion that the surveyed animals have a fixed flushing distance and will be detected
only when the observer crosses that threshold. If kis the number of animals detected
and rthe radial distance from a detected animal to the observer:
D=(1/2L)∑k(1/r)where Lis the length of the line. Hence density is the sum of the reciprocals of the
radial sighting distances divided by twice the length of the line.
It is implicit in Hayne’s model that sinθ, the sine of the sighting angle, is
uniformly distributed between 0 and 1, and that the theoretically expected mean
sighting angle is 32.7°. Hence the reality of the model can be tested against the data.
Eberhardt (1978) recommended tabulating the frequency of sinθin 10 intervals of
0.1 (0.0–0.1, 0.1–0.2...0.9–1.0) and testing the uniformity of the frequencies by
chi-square. He gave a worked example for a survey of the side-blotched lizard (Uta
stansburiana). Robinette et al. (1974) and Burnham et al. (1980) suggested that most
mean sighting distances tended to be around 40° or more, the latter authors being
convinced that the Hayne estimate is used far too uncritically in wildlife manage-
ment. Robinette et al. (1974) compared the accuracy of the Hayne estimate with that
of eight other line-transect models, showing that when applied to inanimate objects
or to elephants it tended to overestimate considerably. However, Pelletier and Krebs
(1997) found that both the Hayne estimate and line-transect estimates provided
relatively unbiased results when compared with a known population of ptarmigan
(Lagopus species) in Yukon. Buckland et al. (1993) provide a starting point for read-
ing further about line-transect methods.
Our second example is a non-parametric method developed by Eberhardt (1978)
from work by Cox (1969). First, we choose arbitrarily a distance,∆, perpendicular
from the line. Eberhardt’s estimate of density is:
D=(3k 1 −k 2 )/4L∆where k 1 and k 2 are the number of animals seen on either side of the line transect
at distances that fall within the interval 0 to ∆and ∆to 2∆, respectively. Eberhardt
(1978) considered that the method is most useful as only a cross-check on the results
of other methods because its estimate is likely to be imprecise. Precision is enhanced
by choosing a large value of ∆but accuracy is enhanced by choosing a small ∆(Seber
1982).
Much of the present use of line transects in wildlife management stems from
the belief that they are somehow more “scientific” than strip transects, just as
there was once a belief that quadrats are statistically superior to transects. There
are rare situations in which transect sampling will not work and where line-transect
methodology might (e.g. in very thick cover). The unbounded line-transect
method has advanced considerably with the use of the computer software DISTANCE
(http://www.ruwpa.st-and.ac.uk /distance) developed by Buckland et al. (1993, 2001).
Although the software is not easy to use, it is currently the most powerful tool for