Rdistance (version 1.1)

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

Description

Estimate abundance given an estimated distance function, group sizes, and total length of transect.

Usage

F.abund.estim(dfunc, avg.group.size = 1, group.sizes, area = 1, 
    tot.trans.len = 1, n = length(dfunc$dist), ci=0.95, R=500, plot.bs=FALSE, 
    transects=NULL)

Arguments

dfunc

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

avg.group.size

Average group size for all sighted objects, estimated from some other source. Either avg.group.size or group.sizes must be specified. Specifying the vector of group.sizes takes precedent over a

group.sizes

Vector of group sizes associated with each sighted object. Takes precedence over avg.group.size

area

Total study area size. If area = 1, density is estimated. Density has units (# of animals) per (z), where (z) is the square units of the distance measurements. For example, if distance values fitted in dfunc w

tot.trans.len

Total length of transects surveyed. Units must be same as those of raw distance measures, and the square root of units of area.

n

Number of groups seen. Normally, this is length(dist), but this is left as a parameter so that a previously estimated distance function can be applied to another set of surveys. For example, if dfunc is estimated and assume

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.

plot.bs

A logical scalar indicating whether to plot individual bootstrap iterations

transects

A vector containing the transect ID's of the targets sighted. This vector is used during bootstrapping to resample transects in order to estimate variance in estimated size. Length must be either 0 (NULL) or length(dfunc$dist). Th

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 targets used in the estimate of abundance. Usually this is length(dist), but when supplied as an argument, it can be different.
• 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.

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 or individual sightings) are independent. The bias corrected bootstrap method used here resamples the units of replication 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

#   Fake offtransect distances (x), transect id's (tran.id), and group sizes (grp.size)
set.seed(234092)
x <- rnorm(1000) * 100
tran.id <- rep(1:100, each=10)
grp.size <- rpois(1000, 2.5)
tran.id <- tran.id[ 0 < x & x < 100 ]
grp.size <- grp.size[ 0 < x & x < 100 ]
x <- x[ 0 < x & x < 100 ]

#   Fit a distance function
hn.dfunc <- F.dfunc.estim( x, likelihood="halfnorm", w.hi = 100)

#   Assume surveyed 10000 m in study area of size 1000 hectares.
#   Original offtransect distances must be in meters, and area must be square meters. 
#   Without group sizes, this estimates number of groups in the area. 
F.abund.estim( hn.dfunc, tot.trans.len=10000, area=1000*10000, ci=NULL)

#   Include group sizes to estimate number of individuals. 
F.abund.estim( hn.dfunc, group.sizes = grp.size, tot.trans.len=10000, area=1000*10000, ci=NULL)

#   Or,
F.abund.estim( hn.dfunc, avg.group.size=2.5, tot.trans.len=10000, area=1000*10000, ci=NULL)

#   Bootstrap resample the transects to compute CI for N (A person should do more than R=100 iterations)
F.abund.estim( hn.dfunc, group.sizes=grp.size, tot.trans.len=10000, area=1000*10000, ci=.95, transects=tran.id, R=100, plot.bs=TRUE)