Distance sampling

Distance sampling is a widely used group of closely related methods for estimating the density and/or abundance of populations. The main methods are based on line transects or point transects. In this method of sampling, the data collected are the distances of the objects being surveyed from these randomly placed lines or points, and the objective is to estimate the average density of the objects within a region.

Basic line transect methodology

Basic distance sampling survey approach using line transects. A field observer detects an object and records distance r and angle θ to the transect line. This allows calculation of object distance to the transect (x). All x from the survey are used to model how detectability decreases with distance from the transect, which allows estimation of total population density in the surveyed area.

A common approach to distance sampling is the use of line transects. The observer traverses a straight line (placed randomly or following some planned distribution). Whenever they observe an object of interest (e.g., an animal of the type being surveyed), they record the distance from their current position to the object (r), as well as the angle of the detection to the transect line (θ). The distance of the object to the transect can then be calculated as x = r * sin(θ). These distances x are the detection distances that will be analyzed in further modeling.

Objects are detected out to a pre-determined maximum detection distance w. Not all objects within w will be detected, but a fundamental assumption is that all objects at zero distance (i.e., on the line itself) are detected. Overall detection probability is thus expected to be 1 on the line, and to decrease with increasing distance from the line. The distribution of the observed distances is used to estimate a "detection function" that describes the probability of detecting an object at a given distance. Given that various basic assumptions hold, this function allows the estimation of the average probability P of detecting an object given that is within width w of the line. Object density can then be estimated as D = n / (P*a), where n is the number of objects detected and a is the size of the region covered (total length of the transect (L) multiplied by 2w).

In summary, modeling how detectability drops off with increasing distance from the transect allows estimating how many objects there are in total in the area of interest, based on the number that were actually observed.

Detection function

Half-normal detection function (red line) fitted to PDF of detection data. Data have been collated into distance bands (either collected as such, or combined after collection to improve model fitting). Detection probability decreases with distance from center line (y = 0).

The drop-off of detectability with increasing distance from the transect line is modeled using a detection function g(y) (here y is distance from the line). This function is fitted to the distribution of detection ranges represented as a probability density function (PDF). The PDF is a histogram of collected distances and describes the probability that an object at distance y will be detected by an observer on the center line, with detections on the line itself (y = 0) assumed to be certain (P = 1).

By preference, g(y) is a robust function that can represent data with unclear or weakly defined distribution characteristics, as is frequently the case in field data. Several types of functions are commonly used, depending on the general shape of the detection data's PDF:

Detection function	Form
Uniform	1/w
Half-normal	exp(-y2/2σ2)
Hazard-rate	1-exp(-(y/σ)-b)
Negative exponential	exp(-ay)

Here w is the overall detection truncation distance and a, b and σ are function-specific parameters. The half-normal and hazard-rate functions are generally considered to be most likely to represent field data that was collected under well-controlled conditions. In contrast, both the uniform and negative exponential functions assume that detection probability does not drop off from the center line but remains at the same level (uniform) or increases (negative exponential); these circumstances may be indicative of problems with data collection or survey design.

External links

• Encyclopedia of Environmetrics
• Bibliography of nearly 1000 publications in the scientific literature