Rdistance (version 1.2.2)

ESW: Effective Strip Width for estimated detection functions

Description

Computes effective strip width (ESW) for estimated detection functions.

Usage

ESW(obj)

Arguments

obj

An estimated detection function object. An estimated detection function object has class 'dfunc', and is usually produced by a call to F.dfunc.estim. The estimated detection function may optionally contain a $g(0)$ component. If

Value

• A scalar equal to the area under the detection function from obj$w.lo to obj$w.hi.

Details

The effective strip width (ESW) of a distance function is its integral. That is, ESW is the area under the distance function from its left-truncation limit (obj$w.lo) to its right-truncation limit (obj$w.hi). latex{In mathematical notation, $$ESW = \int_{w.lo}^{w.hi} g(x)dx,$$ where $g(x)$ is the height of the distance function at distance $x$, and $w.lo$ and $w.hi$ are the lower and upper truncation limits used during the survey. } The name effective strip width derives from the fact that under perfect detection, area under the detection function is the half-width of the strip transect. This means that if obj$w.lo = 0 and $g(x)$ = 1, area under the detection function is the half-width of the transect (i.e., obj$w.hi). In this case, the density of objects is estimated as number sighted divided by area surveyed, which is obj$w.hi times total length of transects surveyed. When detection is not perfect, less than the total half-width is effectively covered. Buckland et al. (1993) show that the denominator of the density estimator in this case involves total length of transects surveyed times area under the detection function (i.e., this integral). By analogy with the perfect detection case, this integral can then be viewed as the transect half-width that observers effectively cover. In other words, a survey with imperfect detection and ESW equal to X effectively covers the same area as a study with perfect detection out to a distance of X. The trapazoid rule is used to numerically integrate under the distance function in obj from obj$w.lo to obj$w.hi. Two-hundred trapazoids are used in the approximation to speed calculations. In some rare cases, two hundred trapazoids may not be enough. In these cases, the code for this function can be sink-ed to a file, inspected in a text editor, modified to bump the number of trapazoids, and source-d back in.

References

Buckland, S.T., Anderson, D.R., Burnham, K.P. and Laake, J.L. 1993. Distance Sampling: Estimating Abundance of Biological Populations. Chapman and Hall, London.

See Also

F.dfunc.estim

Examples

# Load the example dataset for sparrow detections from package
data(sparrow.detections)

# Compute perpendicular, off-transect distances from the observer's sight distance and angle
sparrow.detections$dist <- perp.dists(obs.dist=sparrow.detections$sightdist,
                                  obs.angle=sparrow.detections$sightangle)

# Fit detection function object
dfunc <- F.dfunc.estim(sparrow.detections, w.hi=150)

# Compute effective strip width (ESW)
ESW(dfunc)