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.
abundEstim(dfunc, detectionData, siteData, area = 1, ci = 0.95,
R = 500, plot.bs = FALSE, bySite = FALSE, showProgress = TRUE)An estimated 'dfunc' object produced by dfuncEstim.
A data.frame with each row representing one detection
(see example dataset, sparrowDetectionData) and with at least
the following three columns:
siteID = ID of the transect or point.
groupsize = the number of individuals in the detected group.
dist = the perpendicular, off-transect distance or radial
off-point distance to the detected group.
A data.frame with each row representing one site
(transect or point) (see example dataset,
sparrowSiteData). If the data in detectionData
is from line transects, siteData must have at
least the following two columns:
siteID = ID of the transect or point. This vector
is used during bootstrapping to resample sites.
length = the length of the transect.
If the data in detectionData
is from point transects, siteData must have a
siteID column only. For both data types, siteID
is used during bootstrapping to resample sites.
Total study area size. If area = 1, density is estimated.
Density has units (number of animals) per (squared
units of the distance measurements). For example, if distance values fitted
in dfunc are meters, density is number of individuals per
square meter. If distances are miles, density is number of
individuals per square mile. If area > 1, total abundance on the
study area is estimated and units are (number of animals). This can also
be used to convert units for density. For example, if distance values fitted
in dfunc are meters, and area is set to 10,000, density is number
of individuals per hectare (ha; 1 ha = 10,000 square meters).
square meter.
A scalar 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.
The number of bootstrap iterations to conduct when ci is not
NULL.
A logical scalar indicating whether to plot individual bootstrap iterations.
A logical scalar indicating whether to compute site-level
estimates of abundance. The default (bySite=FALSE) returns only one
overall abundance estimate. This routine does not calculate confidence
intervals for these site-level abundance estimates, so ci is set to
NULL if bySite = TRUE. See estimateN.
A logical indicating whether to show a text-based
progress bar during bootstrapping. Default is TRUE.
It is handy to shut off the
progress bar if running this within another function. Otherwise,
it is handy to see progress of the bootstrap iterations.
If bySite is FALSE, an 'abundance estimate' object, a list of
class c("abund", "dfunc"), containing all the components of a "dfunc"
object (see dfuncEstim), plus the following:
Estimated abundance in the study area (if area >
1) or estimated density in the study area (if area = 1).
The number of detections (not individuals, unless all group sizes = 1) used in the estimate of abundance.
Total area of inference. Study area size
Effective strip width for line-transects, effective
radius for point-transects. Both derived from dfunc.
See ESW
Total number of transects for line-transects, total number of points for point-transects.
Total transect length. NULL for point-transects.
Average group size
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.
A vector or length R containing all bootstrap estimated
population sizes. If a particular iteration 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) ).
The (scalar) confidence level of the
confidence interval for n.hat.
The effective sampling distance at the site. For line- transects, this is ESW at the site. For points, this is EDR.
Average probability of detection at the site. If only site-level covariates appear in the distance function, pDetection is constant within a site. When detection-level covariates are present, pDetection is the average at the site.
The total number of individuals detected at a site.
Estimated abundance at the site. This is the sum of inflated group sizes at the site. i.e., each group size at the site is divided by its pDetection, and then summed.
Estimated density at the site. This is abundance at the site divided by the sampled area at the site. E.g., for line transects, this is abundance divided by \(2*w*length\). For points, this is abundance divided by \(pi*w^2\).
The effective area sampled at the site. This could be used as an offset in a subsequent linear model. For line transects, this is \(2*ESW*length\). For points, this is \(pi*EDR^2\).
The abundance estimate for line transect surveys (if no covariates
are included in the detection function) 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 (lines or points, hereafter "sites") are independent.
The bias corrected bootstrap
method used here resamples the units of replication (sites) 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, after which the bias
corrected confidence intervals are computed using the method given in Manly
(1997, section 3.4).
Setting plot.bs=FALSE and showProgress=FALSE
suppresses all intermediate output. This is good when calling
abundEstim from within other functions or during simulations.
Manly, B.F.J. (1997) Randomization, bootstrap, and monte-carlo methods in biology, London: Chapman and Hall.
Buckland, S.T., D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, and L. Thomas. (2001) Introduction to distance sampling: estimating abundance of biological populations. Oxford University Press, Oxford, UK.
# NOT RUN {
# Load example sparrow data (line transect survey type)
data(sparrowDetectionData)
data(sparrowSiteData)
# Fit half-normal detection function
dfunc <- dfuncEstim(formula=dist~1,
detectionData=sparrowDetectionData,
likelihood="halfnorm", w.hi=100, pointSurvey=FALSE)
# 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 <- abundEstim(dfunc, detectionData=sparrowDetectionData,
siteData=sparrowSiteData, area=10000, R=20, ci=0.95,
plot.bs=TRUE, bySite=FALSE)
# Print results
fit
# }
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