Fig 1.
When the animals avoid the transect or the observer, there can be a peak in sightings at intermediate distances (panel a: theoretical principles; panel b: empirical observation). This pattern causes a lack of fit of the standard, 1D distance sampling detection function (panel c; the grey histogram is the density of sightings), because that function wrongly assumes a detection rate of 1 on the transect and a monotonous decline in the frequency of sightings with the distance to the transect.
Table 1.
A non-exhaustive review of studies evidencing a behavioural response to the transects in forest- or woodland-dwelling mammals.
We only compiled positive reports of behavioural responses. “Distance histogram” means that the distribution of recorded distances followed a shape like in Fig 1, sometimes with additional evidence from further modelling. “GPS tracking” means that geo-tracked individuals avoided the vicinity of the transects more than expected by chance. “Camera trapping” means that the frequency of pictures decreased near transects. “Counts” means that population abundance was larger in a block without transect than in a block with transect.
Fig 2.
Principles of the 2D distance sampling framework [33].
The observer is denoted by a filled circle that progresses along a transect, taking position li at time ti. The animal is denoted by a crossed circle, surrounded by the “detection kernel” in grey. The distance to the observer is recorded in two dimensions, with yi the forward distance and xi the perpendicular distance. In the standard, 1D framework, only xi is recorded. If the observer moves at a constant speed v along the transect (e.g., survey from a vehicle or boat), then yi can be inferred from the geographical coordinates (Xi,Yi) and the time at the detection ti. The transect half-width w is the cut-off perpendicular distance beyond which animals are ignored, typically defined a posteriori based on the maximum recorded distance. The effective forward distance ystart is roughly the maximum forward distance at which an animal that is on the transect can be recorded.
Fig 3.
Estimated detection probability p(x), behavioural response π(x), and expected density of sightings f(x), as a function of the perpendicular distance x, for blue duikers in the Lomako study area, with three ways to simulate the forward distance y.
The binned detection data are provided for comparison (histogram).
Table 2.
Quantifying the bias and Root Mean Squared Error (RMSE) of the abundance estimated using 1D (where only the perpendicular distance to transect is recorded) and 2D (where both the perpendicular and forward distances are recorded) distance sampling, in four scenarios of detectability and intensity of the behavioural response to the transect.
Low detectability means that the detection probability declines quickly with distance to the transect. Strong behavioural response means that the increase in animal abundance with distance from the transect is slow, meaning that they rarely occur near the transect. Results are given in %. A bias of -50% means that the abundance was under-estimated by 50% on average over 150 replicates.