ct_fit_ds: Fit detection functions and estimate density/abundance

In ct: Camera Trap Data Management and Multi-Method Ecological Analysis

Fit detection functions and estimate density/abundance

Description

ct_fit_ds fits detection functions to camera trap distance sampling data and estimates animal density or abundance using bootstrap variance estimation. Supports both single model fitting and automated model selection procedures.

Usage

ct_fit_ds(
  data,
  estimate = c("density", "abundance"),
  cutpoints = NULL,
  truncation = set_truncation(data = data, cutpoints = cutpoints),
  formula = ~1,
  key = c("hn", "hr", "unif"),
  adjustment = c("cos", "herm", "poly"),
  nadj = NULL,
  order = NULL,
  select_model = FALSE,
  model_params = list(key = list("hn", "hr", "unif"), adjustment = list("cos", "herm",
    "poly"), nadj = list(0, 1, 2), order = NULL),
  availability,
  n_bootstrap = 100,
  n_cores = 1,
  fast_bootstrap = TRUE,
  seed = NULL,
  ...
)

Arguments

data	A data frame containing distance sampling observations. Must include following columns: distance: the midpoint (m) of the assigned distance interval between animal and camera object: a unique identifier for each observation Sample.Label: identifier for the sample (transect id) Effort: number of a given second (e.g 0.25, 2, or 3) time steps the camera operated (i.e. temporal effort) Region.Label: label for a given stratum Area: area of the strata in km^2 fraction: fraction of a full circle covered (field of view/360) Other columns could be used as covariate. Note that in the simplest case (one area surveyed only once) there is only one Region.Label and a single corresponding Area duplicated for each observation.
estimate	Character string specifying the parameter to estimate. Either "density" (animals per km^2) or "abundance" (total number of animals). Default is "density".
cutpoints	if the data are binned, this vector gives the cutpoints of the bins. Supplying a distance column in your data and specifying cutpoints is the recommended approach for all standard binned analyses. Ensure that the first element is 0 (or the left truncation distance) and the last is the distance to the end of the furthest bin. (Default NULL, no binning.) Provide distbegin and distend columns in your data only when your cutpoints are not constant across all your data, e.g. planes flying at differing altitudes then do not specify the cutpoints argument.
truncation	either truncation distance (numeric, e.g. 5) or percentage (as a string, e.g. "15%","15"). Can be supplied as a list with elements left and right if left truncation is required (e.g. list(left=1,right=20) or list(left="1%",right="15%") or even list(left="1",right="15%")). By default for exact distances the maximum observed distance is used as the right truncation. When the data is binned, the right truncation is the largest bin end point. Default left truncation is set to zero.
formula	formula for the scale parameter. For a CDS analysis leave this as its default ~1.
key	key function to use; "hn" gives half-normal (default), "hr" gives hazard-rate and "unif" gives uniform. Note that if uniform key is used, covariates cannot be included in the model.
adjustment	adjustment terms to use; "cos" gives cosine (default), "herm" gives Hermite polynomial and "poly" gives simple polynomial. A value of NULL indicates that no adjustments are to be fitted.
nadj	the number of adjustment terms to fit. In the absence of covariates in the formula, the default value (NULL) will select via AIC (using a sequential forward selection algorithm) up to max.adjustment adjustments (unless order is specified). When covariates are present in the model formula, the default value of NULL results in no adjustment terms being fitted in the model. A non-negative integer value will cause the specified number of adjustments to be fitted. Supplying an integer value will allow the use of adjustment terms in addition to specifying covariates in the model. The order of adjustment terms used will depend on the keyand adjustment. For key="unif", adjustments of order 1, 2, 3, ... are fitted when adjustment = "cos" and order 2, 4, 6, ... otherwise. For key="hn" or "hr" adjustments of order 2, 3, 4, ... are fitted when adjustment = "cos" and order 4, 6, 8, ... otherwise. See Buckland et al. (2001) p. 47 for details.
order	order of adjustment terms to fit. The default value (NULL) results in ds choosing the orders to use - see nadj. Otherwise a scalar positive integer value can be used to fit a single adjustment term of the specified order, and a vector of positive integers to fit multiple adjustment terms of the specified orders. For simple and Hermite polynomial adjustments, only even orders are allowed. The number of adjustment terms specified here must match nadj (or nadj can be the default NULL value).
select_model	Logical. If TRUE, performs automated model selection using the procedure in Howe et al. (2019). If FALSE (default), fits a single model with specified parameters. When TRUE, model_param defines the candidate model set.
model_params	Named list defining candidate models for selection when select_model = TRUE. Elements can include: key - List of key functions to test adjustment - List of adjustment types nadj - List of adjustment term numbers order - List vector of adjustment orders (must match nadj)
availability	A list containing availability rate corrections (output from ct_availability()). Must include elements availability rate (0-1) and/or standard error of availability rate
n_bootstrap	Integer. Number of bootstrap replicates for variance estimation of density/abundance. Default is 100. Larger values provide more precise confidence intervals but increase computation time.
n_cores	Integer. Number of CPU cores to use for parallel bootstrap computation. Default is 1. Used only when the bootstrap is run by Distance::bootdht().
fast_bootstrap	Logical. If TRUE (default), and the selected detection function is intercept-only (half-normal, hazard-rate or uniform key, with optional cosine or simple polynomial adjustments) fitted to binned distances in a single stratum, each replicate is refitted from its distance-bin counts instead of the full data set. This gives the same likelihood, detection probability and density as Distance::bootdht() (resampling camera stations) and is several hundred times faster. Each refit starts from the full-data estimates and from the key function fitted alone, and keeps the higher likelihood. Other models, or fast_bootstrap = FALSE, use Distance::bootdht().
seed	Optional integer. If supplied, the random-number generator is seeded with this value immediately before bootstrapping, making the resampling reproducible. If NULL (default), the current RNG state is used and results vary between runs. Note that a single fixed seed can occasionally land on a resample that is slow to fit; leave it NULL unless you specifically need reproducible bootstrap draws.
...	Arguments passed on to Distance::ds scale the scale by which the distances in the adjustment terms are divided. Defaults to "width", scaling by the truncation distance. If the key is uniform only "width" will be used. The other option is "scale": the scale parameter of the detection dht_group should density abundance estimates consider all groups to be size 1 (abundance of groups) dht_group=TRUE or should the abundance of individuals (group size is taken into account), dht_group=FALSE. Default is FALSE (abundance of individuals is calculated). monotonicity should the detection function be constrained for monotonicity weakly ("weak"), strictly ("strict") or not at all ("none" or FALSE). See Monotonicity, below. (Default "strict"). By default it is on for models without covariates in the detection function, off when covariates are present. method optimization method to use (any method usable by optim or optimx). Defaults to "nlminb". mono_method optimization method to use when monotonicity is enforced. Can be either slsqp or solnp. Defaults to slsqp. initial_values a list of named starting values, see mrds_opt. Only allowed when AIC term selection is not used. max_adjustments maximum number of adjustments to try (default 5) only used when order=NULL. er_method encounter rate variance calculation: default = 2 gives the method of Innes et al. (2002), using expected counts in the encounter rate. Setting to 1 gives observed counts (which matches Distance for Windows) and 0 uses negative binomial variance (only useful in the rare situation where study area = surveyed area). See dht.se for more details, noting this er_method argument corresponds to the varflag element of the options argument in dht.se. dht_se should uncertainty be calculated when using dht? Safe to leave as TRUE, used in bootdht. optimizer By default this is set to 'both'. In this case the R optimizer will be used and if present the MCDS optimizer will also be used. The result with the best likelihood value will be selected. To run only a specified optimizer set this value to either 'R' or 'MCDS'. See mcds_dot_exe for setup instructions. winebin If you are trying to use our MCDS.exe optimizer on a non-windows system then you may need to specify the winebin. Please see mcds_dot_exe for more details.

Value

A named list containing: A list containing:

• QAIC: (only if select_model = TRUE) QAIC comparison table.

• Chi2: (only if select_model = TRUE) Chi-squared goodness-of-fit comparison.

• best_model: The best fitted detection function model selected.

• rho: Estimated effective detection radius (in meters).

• density or abundance: A tibble with density or abundance estimates containing: median, mean, se: standard error, lcl: lower confidence limit, ucl: upper confidence limit

Truncation

The right truncation point is by default set to be largest observed distance or bin end point. This is a default will not be appropriate for all data and can often be the cause of model convergence failures. It is recommended that one plots a histogram of the observed distances prior to model fitting so as to get a feel for an appropriate truncation distance. (Similar arguments go for left truncation, if appropriate). Buckland et al. (2001) provide guidelines on truncation.

When specified as a percentage, the largest right and smallest left percent distances are discarded. Percentages cannot be supplied when using binned data.

For left truncation, there are two options: (1) fit a detection function to the truncated data as is (this is what happens when you set left). This does not assume that g(x)=1 at the truncation point. (2) manually remove data with distances less than the left truncation distance – effectively move the centre line out to be the truncation distance (this needs to be done before calling ds). This then assumes that detection is certain at the left truncation distance. The former strategy has a weaker assumption, but will give higher variance as the detection function close to the line has no data to tell it where to fit – it will be relying on the data from after the left truncation point and the assumed shape of the detection function. The latter is most appropriate in the case of aerial surveys, where some area under the plane is not visible to the observers, but their probability of detection is certain at the smallest distance.

Monotonicity

When adjustment terms are used, it is possible for the detection function to not always decrease with increasing distance. This is unrealistic and can lead to bias. To avoid this, the detection function can be constrained for monotonicity (and is by default for detection functions without covariates).

Monotonicity constraints are supported in a similar way to that described in Buckland et al. (2001). 20 equally spaced points over the range of the detection function (left to right truncation) are evaluated at each round of the optimisation and the function is constrained to be either always less than it's value at zero ("weak") or such that each value is less than or equal to the previous point (monotonically decreasing; "strict"). See also check.mono.

Even with no monotonicity constraints, checks are still made that the detection function is monotonic, see check.mono.

Data format

One can supply data only to simply fit a detection function. However, if abundance/density estimates are necessary further information is required. Either the region_table, sample_table and obs_table data.frames can be supplied or all data can be supplied as a "flat file" in the data argument. In this format each row in data has additional information that would ordinarily be in the other tables. This usually means that there are additional columns named: Sample.Label, Region.Label, Effort and Area for each observation. See flatfile for an example.

Clusters/groups

Note that if the data contains a column named size, cluster size will be estimated and density/abundance will be based on a clustered analysis of the data. Setting this column to be NULL will perform a non-clustered analysis (for example if "size" means something else in your dataset).

References

Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., and Thomas, L. (2001). Distance Sampling. Oxford University Press. Oxford, UK.

Howe, E. J., Buckland, S. T., Després-Einspenner, M., & Kühl, H. S. (2017). Distance sampling with camera traps. Methods in Ecology and Evolution, 8(11), 1558-1565. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.12790")}

Howe, E. J., Buckland, S. T., Després-Einspenner, M., & Kühl, H. S. (2019). Model selection with overdispersed distance sampling data. Methods in Ecology and Evolution, 10(1), 38-47. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.13082")}

Rowcliffe, J. M., Kays, R., Kranstauber, B., Carbone, C., & Jansen, P. A. (2014). Quantifying levels of animal activity using camera trap data. Methods in Ecology and Evolution, 5(11), 1170-1179. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.12278")}

See Also

ct_availability(), ct_select_model(), ct_QAIC(), ct_chi2_select()

Examples

## Not run: 
data("duikers")

# Calculates animal availability adjustment factor
trigger_events <- duikers$VideoStartTimesFullDays
avail <- ct_availability(times = trigger_events$time,
                         format = "%H:%M", n_bootstrap = 100)

# Estimate density, building multiple models
flat_data <- duikers$DaytimeDistances %>%
  dplyr::rename(fraction = multiplier) %>%
  dplyr::slice_sample(prop = .2) # sample 20% of rows

duiker_density <- ct_fit_ds(data = flat_data,
                            estimate = "density",
                            select_model = TRUE,
                            model_params = list(key = list("hn", "hr"),
                                                adjustment = list("cos"),
                                                nadj = list(2, 3),
                                                order = NULL),
                            availability = avail,
                            truncation = list(left = 2, right = 15),
                            n_bootstrap = 2,
                            cutpoints = c(seq(2, 8, 1), 10, 12, 15)
)

# View density
duiker_density$density

## End(Not run)

ct documentation built on Oct. 22, 2026, 1:07 a.m.