Distance Sampling: its relevance to wildlife management
By R. M. Fewster and S.T. Buckland
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Notes
'Distance Sampling: its relevance to wildlife management'
is a response to the following paper:
Barry, S. C. and Welsh, A. H. (2001) Distance Sampling
Methodology.
Journal of the Royal Statistical Society, Series
B, 63, 31-53.
In their paper, Barry and Welsh raise concerns that the density and
variance estimators used in Distance Sampling are severely biased.
They investigate the properties of the estimators mathematically and by
simulation studies. They present several tables in which the performance
of the estimators can be seen to be extremely poor.
In our response, we explain that the poor results of Barry and Welsh
are due to systematic biases in their sampling schemes. A summary
of the main points is as follows.
Non-representative sampling design
-
To investigate design-based properties of the estimators, Barry and Welsh
use a non-representative design: that is, they do not ensure that
every point in the survey area has equal probability of being sampled.
In particular, points at the edges of the region are undersampled compared
with points in the centre. The results in their Tables 1, 2, and
3 are all severely distorted by this problem. The effect is
exacerbated by the extreme spatial clustering that they use in their simulations.
Object positions generated from Beta distributions with parameters (5,
1), (5, 0.5), and (5, 0.25) place most of the objects at the far edges
of the survey area. Because the edges are undersampled in their design,
density appears to be negatively biased.
Inattention to area sampled
-
Barry and Welsh perform simulations using wide search strips that extend
outside the area of interest. This means that the object density
in the sampled area is lower than the object density in the area of interest,
because the sampled area includes extraneous regions that contain no objects.
They do not adjust for this before reporting their results. Again,
this produces density estimates that appear to be negatively biased for
the area of interest.
This effect can be seen in Table 1 for large w (strip width).
For example, when w=1, the sampled region is twice the width of
the region of interest, and object density in the sampled region is half
the object density in the region of interest. This explains values
of close to 0.5 when the detection parameter (theta) is high.
Inadequate number of sampling units
- In line transect sampling, as in other forms of sampling, a reasonable
number of samplers should be selected to allow reliable inference. This means that a
design should consist of at least 10 or 12 lines, and preferably at least 20.
Barry and Welsh mostly use designs with just a single transect, and the remaining
results are based on designs with just 5 transects.
Problems with model-based analyses
In Tables 4, 5, and 6 of their paper, Barry and Welsh present a model-based
analysis in which the positions of the transects are fixed, and the object
positions are allowed to vary according to selected probability distributions.
These analyses suffer from the following problems:
-
The transects are fixed in an unrepresentative subset of the area of interest,
but the transect-specific density estimates are extrapolated to the whole
of the area of interest. It is not possible to obtain unbiased density
estimates unless the sampled area is representative of the whole area.
-
The gradients in object density are extreme and unrealistic. See
Figure 1, page 25 of our response, for some of the scenarios investigated
by Barry and Welsh. (Note that the original paper contains no figures
to display their scenarios.)
-
Transects are placed at right angles to the density gradient, instead of
parallel as recommended by Buckland et al (1993).
It is true that distance sampling estimators require the within-strip object
distribution to satisfy certain conditions. In particular, if there
is responsive movement due to the observer, an advanced sampling scheme
may be needed (for example, a double platform scheme). In our
response, we investigate conditions on the within-strip object distribution
that are necessary for successful density estimation. We believe
that these conditions are realistic in a wide range of circumstances, but
recommend further literature for situations where they cannot be met.
For a full set of guidelines as to survey design and practice, readers
should consult the books by Buckland et al:
1993 book (available free of charge for download)
or
2001 book.
Rachel Fewster 17th May 2002