FORTLS (version 1.0.6)

distance.sampling: Distance Sampling Methods for Correcting Occlusions Effects

Description

Calculation of the probability of detection of every tree by using distance sampling methodologies (more specifically point transects methods), by means of fitting detection functions to the histogram of tree distribution according to their distance to TLS. Use both half normal and hazard rate functions, without and with dbh as covariate. These probabilities are used for correcting estimation bias caused by lack of detection of trees due to occlusion.

Usage

distance.sampling(tree.list.tls,
                  id.plots = NULL,
                  strata.attributes = NULL)

Arguments

tree.list.tls

Data frame with a list of trees detected and their dbh and horizontal distances from TLS with the same structure and format as tree.detection and tree.detection.multiple ‘Value’.

id.plots

Optional vector with plot identification encoded as character string or numeric for the plots considered. In this case, tree.list.tls argument must include a common column named ‘id’. If this argument is not specified by the user, it will be set to NULL by default, and as a consequence, all plots will be considered.

strata.attributes

Optional data frame inluding plot radius considered at strata level. It must contain a column named ‘stratum’ (numeric) with encoding coinciding with that used in previous functions (normalize, tree.detection and tree.detection.multiple) for identifying strata. Therefore, strata must heve been included previously in ‘tree.list.tls’. Another column named ‘plot.radius’ (numeric) will be required to set maximum horizontal distance (m) considered for fitting detection probability functions. If this argument is not specified by the user, it will be set to NULL by default, and as a consequence, all trees will be included.

Value

List containing the following elements:

tree

Data frame with detection probabilities for every tree and method.

stratum: stratum identification (coincident with strata of tree.list.tls). If there are not strata, it will be set as a single stratum encoded as 1 (numeric).

id: plot identification (coincident with id of tree.list.tls).

tree: tree numbering (coincident with tree of tree.list.tls).

P.hn: tree detection probability according to half normal function.

P.hn.cov: tree detection probability according to half normal function with dbh as covariate.

P.hr: tree detection probability according to half rate function.

P.hr.cov: tree detection probability according to half rate function with dbh as covariate.

parameters

Data frame with parameters estimated for detection functions (see references for understanding their meaning).

P.hn.scale: scale parameter for half normal function (sigma).

P.hn.cov.scale.intercept: alpha.0 parameter of scale parameter for half normal function with dbh as covariate.

P.hn.cov.dbh: alpha.1 parameter of scale parameter for half normal function with dbh as covariate.

P.hr.scale: scale parameter for half rate function (sigma).

P.hr.shape: shape parameter for half rate function (b).

P.hr.cov.scale.intercept: alpha.0 parameter of scale parameter for half normal function with dbh as covariate.

P.hr.cov.dbh: alpha.1 parameter of scale parameter for half normal function with dbh as covariate.

P.hr.cov.shape: shape parameter for half rate function with dbh as covariate (b).

AIC

Data frame with Akaike information criterions (AIC) of every detection function fit.

P.hn: AIC of half normal function fit.

P.hn.cov: AIC of half normal function with dbh as covariate fit.

P.hr: AIC of half rate function fit.

P.hr.cov: AIC of half rate function with dbh as covariate fit.

Details

All internal functions related to distance sampling methodologies are fitted with the ds function included in the Distance package.

Detection functions are left-truncated at 1 m, according to Astrup et al., (2014).

Same warning messages as ds function are provided when fits do not converge or another warnings occur.

For further details on these point transects methods and similar sampling methodologies, as well as their application with R, see Buckland et al., (2001); Marques & Buckland, (2003); Miller & Thomas, (2015) and Clark (2016). Examples of distance sampling analyses, as well as lectures, are available at http://examples.distancesampling.org/ and http://workshops.distancesampling.org/.

References

Astrup, R., Ducey, M. J., Granhus, A., Ritter, T., & von L<U+00FC>pke, N. (2014). Approaches for estimating stand-level volume using terrestrial laser scanning in a single-scan mode. Canadian Journal of Forest Research, 44(6), 666-676. https://doi.org/10.1139/cjfr-2013-0535.

Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., & Thomas, L. (2001). Introduction to distance sampling: estimating abundance of biological populations, Oxford, United Kindown, Oxford University Press.

Clark, R. G. (2016). Statistical efficiency in distance sampling. PloS one, 11(3), e0149298. https://doi.org/10.1371/journal.pone.0149298.

Marques, F. F., & Buckland, S. T. (2003). Incorporating covariates into standard line transect analyses. Biometrics, 59(4), 924-935. https://doi.org/10.1111/j.0006-341X.2003.00107.x.

Miller, D. L., & Thomas, L. (2015). Mixture models for distance sampling detection functions. PloS one, 10(3), e0118726. https://doi.org/10.1371/journal.pone.0118726.

See Also

tree.detection, tree.detection.multiple, metrics.variables, simulations.

ds in Distance package.

Examples

# NOT RUN {
# }
# NOT RUN {
# Loading example data

data(Rioja.data)

tree.list.tls <- Rioja.data$tree.list.tls

# Whithout considering maximum distance

ds <- distance.sampling(tree.list.tls)


# Considering only some plots (first 8 plots)

ds <- distance.sampling(tree.list.tls, id.plots = 1:8)


# Considering strata
# Loading dataset with strata

plot.attributes <- Rioja.data$plot.attributes

# Merging the plot.attributes data set with strata information

tree.list.tls <- merge(tree.list.tls, plot.attributes, by = "id")


# Considering maximum distances of 10 and 15 m for stratum 1 and 2 respectively

strata.attributes = data.frame(stratum = c(1, 2),
                               plot.radius = c(15, 20))

ds <- distance.sampling(tree.list.tls, strata.attributes = strata.attributes)


# }