The Problem

Detection Declines with Distance

In the real world, the probability of detecting a target usually declines as distance from observers increases. Targets close to the transects are easier to see and include than targets farther from transects. Analysts who do not recognize a decline in detection probabilities, and hence believe that target detectors sighted targets equally out to distance w, misstakenly believe they have sampled more area than they actually have. When targets far from the detectors are missed, the sampled area is actually something less than $2wL$.

When naive analysts compute density estimates as the number of observed targets divided by area sampled (i.e., Equation 1 or n/2wL), density is too low because 2wL is too large (Figure 1). Naive, uncorrected density estimates are “biased low”.

The central analysis task of distance-sampling is to correct for this declination in detection probabilities. In other words, analysts correct for the fact that, proportionally, more far-away targets are missed than nearby targets.

Figure 1: Illustration of line-transects when detection declines with distance. Targets far from the transects go undetected. Here, naive density is targets seen, i.e., 2, not 3, divided by putative area sampled. Naive density is too low because putative area sampled is too large.

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But, distance-sampling has a solution.