untitled

Or we might count all ducks on a sample of ponds, the shoreline of the pond pro-

viding a strict boundary to the sampling unit.

The alternative to fixed boundaries is unbounded sampling units (Buckland et al.

1993, 2001). Instead of restricting the counting to those animals within 100 m of

a line of march, those outside the transect being ignored, we might count all the

animals that we see. Since the observed density will fall away with distance from the

observer, the raw counts are no longer an estimate of true density. They must there-

fore be corrected.

Of these two options (sampling units with boundaries and sampling units with-

out boundaries) the first has immense advantages of simplicity and realism. If the

transect width is appropriately chosen, what the observer sees is what the observer

gets. The mathematics of such sampling are simple, elegant, and absolutely solid. In

contrast, the accuracy of corrected density estimated from unbounded transects

depends heavily upon which model is chosen for the analysis. There are many to

choose from and they give markedly different answers for the same data. The advan-

tage of unbounded transects is in all the sightings being used, none being discarded.

Since the precision of an estimate is related tightly to the number of animals actu-

ally counted, any sampling scheme increasing the number of sightings also tends to

increase the precision of the estimate. That is an advantage if the increased precision

is obtained without the sacrifice of too much accuracy.

The choice of one or other system is often determined by density. If the species is

rare then one might be tempted to use all the data one can get. If it is common one

might be content to use the more dependable sampling units with fixed boundaries,

knowing that fewer things can go wrong.

The appropriate analysis depends on whether the sampling units are of equal or unequal

size, and how they are selected. Formulae were originally developed by Jolly 1969

(see also Norton-Griffiths 1978) based on Cochran (1977).

Notation

y=the number of animals on a given sampled unit

a=the area of a given sampled unit

A=the total area of the region being surveyed

n=the number of units sampled

D(or d) =the estimate of mean density

SE(D)=the standard error of estimated mean density

Y=the estimate of total numbers in the region of size A

SE(Y)=the standard error of the estimate of total numbers

The simple estimate (for equal-sized sampling units)

The simple estimate is used when sampling units are of constant size, as when the

region being surveyed is a rectangle which can be subdivided into quadrats or tran-

sects. It will provide an unbiased, although imprecise, estimate, even when sampling

units differ in size, but more appropriate designs are available for that case. We will

explore this design at some length because most of the principles are shared with

the other designs.

The region to be surveyed, of area A, is divided on a map or in one’s head into an

exhaustive set of non-overlapping sampling units, each of constant area a. Let us assume,

COUNTING ANIMALS 227

13.5.1Fixed
boundaries to
sampling units