Distance sampling

Distance sampling is a widely used group of closely related methods for estimating the density and/or abundance of populations.

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.

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.

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.

Detection probability appearing to increase or remain constant with distance from the transect line may indicate problems with data collection or survey design.

[2] A frequently used method to improve the fit of the detection function to the data is the use of series expansions.

[2][4] Since distance sampling is a comparatively complex survey method, the reliability of model results depends on meeting a number of basic assumptions.

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.
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).
An indication of avoidance behaviour in the data - detections initially increase rather than decrease with added distance to the transect line
An indication of angle rounding to zero in the data - there are more detections than expected in the very first data interval