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Distance sampling is a commonly implemented method used to provide reliable estimates of abundance and density (Buckland et al., 2001). In distance sam- pling the observer measures the distance from a line or point to each detected individual animal, group of animals, or cue (e.g., nests or dung, see Section 2.7). The distribution of observed distances is used to estimate a ‘detection function’ (i.e., the probability of detecting an individual as a function of distance from a line or point). Given not all individuals are detected in the area surveyed, the detection function is used to estimate the proportion of individuals detected

( ˆPa). Density is then estimated as:

ˆ

D= n

a.Pˆa

(2.1) wherenis the number of individuals detected andais the area surveyed (Buck- land et al., 2001). The development of the free software Distance

(http://www.ruwpa.st-and.ac.uk/distance/) and two comprehensive books writ- ten by Buckland et al. (2001, 2004) have greatly increased the ease with which distance sampling studies can be planned, conducted and analysed.

2.2.1 Line transect sampling

In line transect sampling, the observer records the perpendicular distance from the line to each animal detected (Buckland et al., 2001). In the standard ap- proach (‘conventional distance sampling’), all animals on or near the line should be detected, but a proportion of animals within distance w of the line may be missed. The perpendicular distance, xi (where i indicates the ith animal,

i = 1, ..., n), from the line may be measured directly, or calculated from the radial distanceri and sighting angleθi, i.e., xi =risin(θi).

Line transects have many advantages. Firstly, the method does not require all animals to be detected within the covered strips, a common feature of survey data. Secondly, efficiency is increased as a wider strip can be searched when it is not necessary to detect all animals in the strip. Thirdly, distance sampling methods also have an additional property of pooling robustness not possessed by capture-recapture methods (see section 2.3). Models of detectability are pooling robust if the data can be pooled over many factors that affect detection probabil- ity (e.g., vegetation cover) and still yield a reliable estimate of density (Buckland et al., 2004). This is a very useful feature of the method because not all factors

affecting detection probability (e.g., environmental variables) are known and can be measured. In distance sampling, because of pooling robustness, this need not cause a significant bias in the estimate of abundance.

Conventional line transect methods require some important assumptions (all of which can be relaxed in more advanced variants of the methods, Buckland et al. 2004):

1. Transect lines are located randomly with respect to the distribution of an- imals. Given random line placement, one can safely assume that animals are uniformly distributed with respect to perpendicular distance from the line (or distributed according to a triangular distribution with distance from a point in point transect sampling). In addition, random line place- ment ensures lines are representative of habitat conditions throughout the survey region, such that results can be extrapolated to the whole study area, and not just the area surveyed;

2. All animals on the transect line are detected with certainty. Any violation of this assumption translates directly into a negative bias in the density estimate. For example, if detection probability on the transect line is 0.9, the density estimate will show a 10% negative bias. Design of surveys must fully consider ways to ensure that this assumption is met, or to allow g(0) to be estimated;

3. Animals are detected at their initial location, i.e., a ‘snap shot’ is taken at time of survey. Movement in response to the observer, either an attraction toward or away from the line, should not occur. Generally, animal move- ment independent of the observer is problematic, unless the mean speed of movement of the animal is slow relative to the speed of the observer; and 4. Distance measurements are exact. When distances and/or angles have

been rounded (especially to zero), grouping data into intervals can help, assuming that on average, the estimates are accurate (i.e., errors are un- biased and not too large). A histogram of data can reveal heaping and outliers.

Two other less critical assumptions are that animals are identified correctly and observations are independent (i.e., detecting one individual does not influ- ence whether another will be detected).

2.2.2 Point transect sampling

Instead of walking a line transect, an observer may remain stationary at a point for a fixed period of time, and measure the sighting (radial) distance from the point to each of the animals detected. This may be useful when, for example, there is rough terrain that makes it difficult for the observer to walk along the transect safely while also concentrating on detecting animals.

Such a procedure can be advantageous over line transect sampling, as the observer has time to observe animals close to the point, and different species can be studied simultaneously (Seber, 1986). However, measurement errors generate substantially more bias in density estimates than do errors of similar magnitude in line transect sampling (Buckland et al., 2004). In addition, any movement of animals during the count period can also generate substantial bias in density estimates, even if the movement is independent of the observer (Buckland, 2006). The success of applying line or point transect sampling to small mammals has been variable. Hounsome et al. (2005) walked line transects and spotlighted for badgers (Meles meles) in south east England and found similar results to capture-recapture estimates, with less survey effort. Healy and Welsh (1992) also successfully used line transects to estimate density of the grey squirrel (Sciurus

carolinensis) in Massachusetts.

However, when detectability of animals is low, the assumption that de- tectability on the line or point is perfect is often violated. In addition, with low detectability, a large amount of survey effort is required to obtain enough detections to reliably model the detection function. In these instances, distance sampling tends to perform badly. For example, Morrison and Kennedy (1989) walked line transects to estimate density of chipmunks (Tamias sp.) in New Mexico concluding that g(0)<1 and that by walking the transects, individuals were being flushed away from the transect line. Also, Gitzen et al. (2001) drove line transects at night and used spotlights to detect jackrabbits (Lepus califor- nicus) in Washington State. However, the detectability of jackrabbits using this approach was so low, too few individuals were detected to estimate density us- ing distance sampling theory. In theses instances, detectability of individuals typically relies on trapping and data are analysed within a capture-recapture framework.