Rdistance (version 1.3.2)

F.abund.estim: Estimate abundance from distance-sampling data.

Description

Estimate abundance (or density) given an estimated detection function and supplemental information on observed group sizes, transect lengths, area surveyed, etc. Also computes confidence intervals of abundance (or density) using the bias corrected bootstrap method.

Usage

F.abund.estim(dfunc, detection.data, transect.data, area=1, ci=0.95, R=500,
by.id=FALSE, plot.bs=FALSE)

Arguments

dfunc

An estimated 'dfunc' object produced by F.dfunc.estim.

detection.data

A data.frame where each row represents one detection (see example dataset, sparrow.detections) and with at least the following three columns with the names siteID, groupsize, and dist:

• siteID = the name of the transect.

• groupsize = the number of individuals in the detected group.

• dist = the perpendicular, off-transect distance.

transect.data

A data.frame where each transect surveyed is represented as one row (see example dataset, sparrow.transects) and with at least the following two columns with the names siteID and length:

• siteID = the name of the transect. This vector is used during bootstrapping to resample transects.

• length = the length of the transect.

area

Total study area size. If area = 1, density is estimated. Density has units (number of animals) per (z), where (z) is the square units of the distance measurements. For example, if distance values fitted in dfunc were in meters, density will be number of individuals per square meter. If distances are miles, density will be number of individuals per square mile. If area > 1, total abundance on the study area is estimated and units are (number of animals).

ci

A scaler indicating the confidence level of confidence intervals. Confidence intervals are computed using the bias corrected bootstrap method. If ci = NULL, confidence intervals are not computed.

R

The number of bootstrap iterations to conduct when ci is not NULL.

by.id

A logical scalar indicating whether to compute transect-level estimates of abundance. The default (by.id=FALSE) returns only one overall abundance estimate).

plot.bs

A logical scalar indicating whether to plot individual bootstrap iterations.

Value

An 'abundance estimate' object, a list of class c("abund", "dfunc"), containing all the components of a "dfunc" object (see F.dfunc.estim), plus,

n.hat

Estimated abundance in the study area (if area > 1) or estimated density in the study area (if area = 1).

ci

The bias corrected bootstrap confidence interval for n.hat. The names of this component give the quantiles of the bootstrap distribution used to compute the bias corrected interval.

B

A vector or length R containing all bootstrap estimated population sizes. If a particular interation did not converge, the corresponding entry in B will be NA. The bootstrap distribution of n.hat can be plotted with hist(x$B), where x is an 'abundance estimate' object. The confidence interval in ci can be reproduced with quantile(x$B[!is.na(x$B)], p=names(x$ci) ).

alpha

The (scalar) confidence level of the confidence interval for n.hat.

n

The number of detections (not individuals, unless all group sizes = 1) used in the estimate of abundance.

area

The study area size used in the estimate of abundance.

tran.len

The total length of transects used in the estimate of abundance.

esw

Effective strip width used in the estimate of abundance. This can be computed with ESW(dfunc).

avg.group.size

The average group size used in the estimate.

nhat.df

A data.frame of transect-level abundance (or density) estimates (if by.id = TRUE).

Details

The abundance estimate is $$N = \frac{n.indiv*area}{2*ESW*tot.trans.len}$$ where n.indiv is either avg.group.size * n or sum(group.sizes), and ESW is the effective strip width computed from the estimated distance function (i.e., ESW(dfunc)).

The confidence interval for abundance assumes that the fundamental units of replication (transects) are independent. The bias corrected bootstrap method used here resamples the units of replication (transects) and recalculates the model's parameter estimates. If a double-observer data frame is included in dfunc, rows of the double-observer data frame are re-sampled each bootstrap iteration. No model selection is performed. By default, R = 500 iterations are performed, afterwhich the bias corrected confidence intervals are computed using the method given in Manly (1997, section 3.4).

References

Manly, B. F. J. (1997) Randomization, bootstrap, and monte carlo methods in biology, London: Chapman and Hall.

See Also

F.dfunc.estim

Examples

# NOT RUN {
# Load the example datasets of sparrow detections and transects from package
data(sparrow.detections)
data(sparrow.transects)

# Fit detection function to perpendicular, off-transect distances
dfunc <- F.dfunc.estim(sparrow.detections, w.hi=150)

# Estimate abundance given a detection function
# Note, area=10000 converts to density per hectare (for distances measured in meters)
# Note, a person should do more than R=20 iterations 
fit <- F.abund.estim(dfunc, detection.data=sparrow.detections, transect.data=sparrow.transects,
                     area=10000, R=20, ci=0.95, plot.bs=TRUE, by.id=FALSE)
# }