Question

What is detectability function? Describe estimation of the population total and density with constant detectability.

Answer 1

Distance sampling provides a rigorous framework for estimating detectability, allowing us to correct counts of detected animals in covered areas for those that were missed. The fundamental concept involved in estimating detectability in the distance sampling context is the detection function, which represents the probability of detecting an object of interest as a function of its distance from the line or point. Thus a key step in any distance sampling analysis is to choose a plausible and parsimonious model for the detection function.

Distance Sampling is a process in which a study area is surveyed in order to estimate the size of the population within it. It can be thought of as an extension to plot sampling. However, while plot sampling assumes that all objects within the plots are detected, distance sampling relaxes this assumption. To do this Distance sampling makes an assumptions about the distribution of objects with respect to the transects and to satisfy these assumptions the transects (the points or lines) must be randomly located within the study region. Note that for the purposes of distance sampling an object can either be an individual or a cluster or individuals.

The next step in distance sampling is then to record the distances from each detected object to the transect it was detected from and fit a detection function. From this function we can estimate how many objects were missed and hence the total number in the covered area. For example, Figure 1 shows histograms of distances that might be collected on a line transect survey, with a fitted detection function. If the lines have been placed at random within the study region then we would expect on average the same number of object to occur at any given distance from the transect. Therefore the drop in number of detection with increasing distance from the line can be attributed to a failure to detect all objects. We can therefore estimate from this detetection function that the probability of seeing an object within the covered region out to a chosen truncation distance is the area under the curve (shaded grey) divided by the area of the rectangle.