Rdistance (version 2.1.3)

ESW: Effective Strip Width for line transect data

Description

Computes effective strip width (ESW) for estimated detection functions from line transect data

Usage

ESW(obj, newdata)

Arguments

obj

An estimated detection function object. An estimated detection function object has class 'dfunc', and is usually produced by a call to dfuncEstim. The estimated detection function may optionally contain a \(g(0)\) component. If no \(g(0)\) component is found, \(g(0)\) = 1 is assumed.

newdata

A data frame containing new values of the covariates at which ESW's are sought. If NULL or missing and obj contains covariates, the covariates stored in obj are used. See Value section.

Value

If newdata is not missing and not NULL and covariates are present in obj, returned value is a vector with length equal to the number of rows in newdata. If newdata is missing or NULL and covariates are present in obj, returned value is a vector with length equal to the number of detections in obj$dist. In either of the above cases, elements in the returned vector are the effective strip widths for the corresponding set of covariates.

If obj does not contain covariates, newdata is ignored and a scalar equal to the (constant) effective strip width for all detections is returned.

Details

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).

Under perfect detection, area under the detection function is the entire half-width of the strip transect (from obj$w.lo to obj$w.hi). Under perfect detection, density is the number sighted targets divided by area surveyed, where area surveyed is obj$w.hi-obj$w.lo times total length of transects.

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 surveyed transects times area under the detection function (i.e., this integral). By analogy with the perfect detection case, this integral can 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 trapezoid rule is used to numerically integrate under the distance function in obj from obj$w.lo to obj$w.hi. Two-hundred trapezoids are used in the approximation to speed calculations. In some rare cases, two hundred trapezoids 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 trapezoids, 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

dfuncEstim, EDR

Examples

# NOT RUN {
# Load example sparrow data (line transect survey type)
data(sparrowDetectionData)

# Fit half-normal detection function
dfunc <- dfuncEstim(formula=dist~1,
                    detectionData=sparrowDetectionData,
                    likelihood="halfnorm", w.hi=100, pointSurvey=FALSE)

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

# ESW only applies to line transect surveys
# EDR is the point transect equivalent
# The effectiveDistance function tests whether the dfunc was
# fit to line or point data, and returns either ESW or EDR accordingly
effectiveDistance(dfunc)
# }