Estimate abundance (or density) from an estimated detection function and supplemental information on observed group sizes, transect lengths, area surveyed, etc. Computes confidence intervals on abundance (or density) using a the bias corrected bootstrap method.
abundEstim(
object,
area = NULL,
propUnitSurveyed = 1,
ci = 0.95,
R = 500,
plot.bs = FALSE,
showProgress = TRUE
)An Rdistance 'abundance estimate' object, which is a list of
class c("abund", "dfunc"), containing all the components of a "dfunc"
object (see dfuncEstim), plus the following:
A tibble containing fitted coefficients in the distance function, density in the area(s) surveyed, abundance on the study area, the number of groups seen between w.lo and w.hi, the number of individuals seen between w.lo and w.hi, study area size, surveyed area, average group size, and average effective detection distance.
If confidence intervals were requested, a tibble
containing all bootstrap values of coefficients,
density, abundance, groups seen, individuals seen,
study area size, surveyed area size, average group size,
and average effective detection distance. The number of rows is always
R, the requested number of bootstrap
iterations. If an iteration fails, the
corresponding row in B is NA (hence, use 'na.rm = TRUE'
when computing summaries). Columns 1 through length(coef(dfunc))
contain bootstrap realizations of the distance function's coefficients.
Confidence level of the confidence intervals
An Rdistance model frame or fitted distance function,
normally produced by a call to dfuncEstim.
A scalar containing the total area of inference. Usually, this is
study area size. If area is NULL (the default),
area will be set to 1 square unit of the output units and density estimates
will be produced.
If area is not NULL, it must have measurement units
assigned by the units package.
The units on area must be convertible
to squared output units. Units
on area must be two-dimensional.
For example, if output units are "foo",
units on area must be convertible to "foo^2" by the units
package. Units of "km^2", "cm^2", "ha", "m^2", "acre", "mi^2", and several
others are acceptable.
A scalar or vector of real numbers between 0 and 1.
The proportion of the default sampling unit that
was surveyed. If both sides of line transects were observed,
propUnitSurveyed
= 1. If only a single side of line transects were observed, set
propUnitSurveyed = 0.5. For point transects, this should be set to
the proportion of each circle that was observed. Length must either be
1 or the total number of transects in x.
A scalar indicating the confidence level of confidence intervals.
Confidence intervals are computed using a bias corrected bootstrap
method. If ci = NULL or ci == NA, 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 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.
Rdistance's nested data frames (produced by RdistDf)
contain all information required to estimate bootstrap CIs.
To compute bootstrap CIs, Rdistance resamples, with replacement,
the rows of the $data component contained in Rdistance
fitted models. Rdistance assumes each row of $data
contains one information on on transect.
The $data component also contains
information on which observations go into the
detection functions, which should be counted as detected targets,
and which count toward transect length.
After resampling rows of $data, Rdistance
refits the distance function using non-missing distances,
recomputes the detected number of targets using non-missing
group sizes on transects with non-missing length,
and re-computes total transect length from transects
with non-missing lengths.
By default, R = 500 bootstrap iterations are
performed, after which bias
corrected confidence intervals are computed (Manly, 1997, section 3.4).
The distance function is not re-selected during bootstrap resampling. The model of the input object is re-fitted every iteration.
During bootstrap iterations, the distance function can fail.
An iteration can fail for a two reasons:
(1) no detections on the iteration, and (2) a bad configuration
of distances that push the distance function's parameters to their
limits. When an iteration fails, Rdistance
skips the iteration and effectively ignores the
failed iterations.
If the proportion of failed iterations is small
(less than 20
is probably valid and no warning is issued. If the proportion of
non-convergent iterations
is not small (exceeds 20
The warning can be modified
by re-setting the Rdistance_maxBSFailPropForWarning option.
Setting options(Rdistance_masBSFailPropForWarning = 1.0) will turn
off the warning.
Setting options(Rdistance_masBSFailPropForWarning = 0.0) will
warn if any iteration failed. Results (density and effective
sampling distance)
from all successful iterations are contained in the
non-NA rows of data frame 'B' in the output object.
Transect lengths can be missing in the RdistDf object. Missing length transects are equivalent to 0 [m] transects and do not count toward total surveyed units nor to group sizes on these transects count toward total detected individuals. Use NA-length transects to include their associated distances when estimating the distance function, but not when estimating abundance. For example, this allows estimation of abundance on one study area using off-transect distances from another. This allows sightability to be estimated using two or more similar targets (e.g., two similar species), but abundance to be estimated separate for each target type. Include NA-length transects by including the "extra" distance observations in the detection data frame, with valid site IDs, but set the length of those site IDs to NA in the site data frame.
Point transects do not have a physical measurement for length. The "length" of point transects is the number of points on the transect. Point transects can contain only one point. Rdistance treats transects of points as independent and bootstrap resamples them to estimate variance. The number of points on each point transect must exist in the RdistDf and cannot have physical measurement units (it is a count, not a distance).
The abundance estimate for line-transect surveys (if no covariates
are included in the detection function and both sides of the transect
are observed) is
$$N =\frac{n(A)}{2(ESW)(L)}$$
where n is total number of sighted individuals
(i.e., sum(groupSizes(dfunc))), L is the total length of
surveyed transect (i.e., sum(effort(dfunc))),
and ESW is effective strip width
computed from the estimated distance function (i.e., ESW(dfunc)).
If only one side of transects were observed, the "2" in the denominator
is not present (or, replaced with a "1").
The abundance estimate for point transect surveys (if no covariates are
included) is
$$N =\frac{n(A)}{\pi(ESR^2)(P)}$$
where n is total number of sighted individuals (i.e., sum(groupSizes(dfunc))),
P is the total number of surveyed points (i.e., sum(effort(dfunc))),
and ESR is effective search radius
computed from the estimated distance function (i.e., ESR(dfunc)).
Setting plot.bs=FALSE and showProgress=FALSE
suppresses all intermediate output.
Estimation of site-specific density (e.g., on every transect) is accomplished by
predict(x, type = "density"), which returns a
tibble containing density and abundance on the area surveyed by every
transect.
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.
dfuncEstim, autoDistSamp,
predict.dfunc with 'type = "density"'.
# Load example sparrow data (line transect survey type)
# sparrowDf <- RdistDf(sparrowSiteData, sparrowDetectionData)
data(sparrowDf)
# Fit half-normal detection function
dfunc <- sparrowDf |>
dfuncEstim(formula=dist ~ groupsize(groupsize)
, likelihood="halfnorm"
, w.hi=units::set_units(150, "m")
)
# Estimate abundance - Convenient for programming
abundDf <- estimateN(dfunc
, area = units::set_units(4105, "km^2")
)
# Same - Nicer output
# Set ci=0.95 (or another value) to estimate bootstrap CI's on ESW, density, and abundance.
fit <- abundEstim(dfunc
, area = units::set_units(4105, "km^2")
, ci = NULL
)
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