Fit detection functions and calculate abundance from line or point transect data

Description

This function fits detection functions to line or point transect data and then (provided that survey information is supplied) calculates abundance and density estimates. The examples below illustrate some basic types of analysis using ds().

Usage

ds(data, truncation = ifelse(is.null(cutpoints), ifelse(is.null(data$distend),
  max(data$distance), max(data$distend)), max(cutpoints)),
  transect = c("line", "point"), formula = ~1, key = c("hn", "hr",
  "unif"), adjustment = c("cos", "herm", "poly"), order = NULL,
  scale = c("width", "scale"), cutpoints = NULL, dht.group = FALSE,
  monotonicity = ifelse(formula == ~1, "strict", "none"),
  region.table = NULL, sample.table = NULL, obs.table = NULL,
  convert.units = 1, method = "nlminb", quiet = FALSE, debug.level = 0,
  initial.values = NULL)

Arguments

Value

a list with elements:

Details

If abundance estimates are required then the data.frames region.table and sample.table must be supplied. If data does not contain the columns Region.Label and Sample.Label thenthe data.frame obs.table must also be supplied. Note that stratification only applies to abundance estimates and not at the detection function level.

Clusters/groups

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

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.

Binning

Note that binning is performed such that bin 1 is all distances greater or equal to cutpoint 1 (>=0 or left truncation distance) and less than cutpoint 2. Bin 2 is then distances greater or equal to cutpoint 2 and less than cutpoint 3 and so on.

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 in mrds.

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

Units

In extrapolating to the entire survey region it is important that the unit measurements be consistent or converted for consistency. A conversion factor can be specified with the convert.units variable. The values of Area in region.table, must be made consistent with the units for Effort in sample.table and the units of distance in the data.frame that was analyzed. It is easiest if the units of Area are the square of the units of Effort and then it is only necessary to convert the units of distance to the units of Effort. For example, if Effort was entered in kilometers and Area in square kilometers and distance in meters then using convert.units=0.001 would convert meters to kilometers, density would be expressed in square kilometers which would then be consistent with units for Area. However, they can all be in different units as long as the appropriate composite value for convert.units is chosen. Abundance for a survey region can be expressed as: A*N/a where A is Area for the survey region, N is the abundance in the covered (sampled) region, and a is the area of the sampled region and is in units of Effort * distance. The sampled region a is multiplied by convert.units, so it should be chosen such that the result is in the same units as Area. For example, if Effort was entered in kilometers, Area in hectares (100m x 100m) and distance in meters, then using convert.units=10 will convert a to units of hectares (100 to convert meters to 100 meters for distance and .1 to convert km to 100m units).

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.

Author(s)

David L. Miller

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.

Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., and Thomas, L. (2004). Advanced Distance Sampling. Oxford University Press. Oxford, UK.

See Also

flatfile

Examples

# An example from mrds, the golf tee data.
library(Distance)
data(book.tee.data)
tee.data<-book.tee.data$book.tee.dataframe[book.tee.data$book.tee.dataframe$observer==1,]
ds.model <- ds(tee.data,4)
summary(ds.model)
plot(ds.model)

## Not run: 
# same model, but calculating abundance
# need to supply the region, sample and observation tables
region <- book.tee.data$book.tee.region
samples <- book.tee.data$book.tee.samples
obs <- book.tee.data$book.tee.obs

ds.dht.model <- ds(tee.data,4,region.table=region,
             sample.table=samples,obs.table=obs)
summary(ds.dht.model)

# specify order 2 cosine adjustments
ds.model.cos2 <- ds(tee.data,4,adjustment="cos",order=2)
summary(ds.model.cos2)

# specify order 2 and 3 cosine adjustments, turning monotonicity
# constraints off
ds.model.cos23 <- ds(tee.data,4,adjustment="cos",order=c(2,3),
                   monotonicity=FALSE)
# check for non-monotonicity -- actually no problems
check.mono(ds.model.cos23$ddf,plot=TRUE,n.pts=100)

# include both a covariate and adjustment terms in the model
ds.model.cos2.sex <- ds(tee.data,4,adjustment="cos",order=2,
                        monotonicity=FALSE, formula=~as.factor(sex))
# check for non-monotonicity -- actually no problems
check.mono(ds.model.cos2.sex$ddf,plot=TRUE,n.pts=100)

# truncate the largest 10% of the data and fit only a hazard-rate
# detection function
ds.model.hr.trunc <- ds(tee.data,truncation="10%",key="hr",adjustment=NULL)
summary(ds.model.hr.trunc)

## End(Not run)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Distance)
Loading required package: mrds
This is mrds 2.1.14
Built: R 3.3.1; ; 2016-07-02 00:29:24 UTC; unix
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Distance/ds.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ds
> ### Title: Fit detection functions and calculate abundance from line or
> ###   point transect data
> ### Aliases: ds
> 
> ### ** Examples
> 
> # An example from mrds, the golf tee data.
> library(Distance)
> data(book.tee.data)
> tee.data<-book.tee.data$book.tee.dataframe[book.tee.data$book.tee.dataframe$observer==1,]
> ds.model <- ds(tee.data,4)
Starting AIC adjustment term selection.
Fitting half-normal key function
Key only models do not require monotonicity contraints. Not constraining model for monotonicity.
AIC= 311.138
Fitting half-normal key function with cosine(2) adjustments
AIC= 313.124


half-normal key function selected!
No survey area information supplied, only estimating detection function.

> summary(ds.model)

Summary for distance analysis 
Number of observations :  124 
Distance range         :  0  -  4 

Model : Half-normal key function 
AIC   : 311.1385 

Detection function parameters
Scale Coefficients:  
             estimate         se
(Intercept) 0.6632435 0.09981249

                       Estimate          SE         CV
Average p             0.5842744  0.04637627 0.07937413
N in covered region 212.2290462 20.85130509 0.09824906
> plot(ds.model)
> 
> ## Not run: 
> ##D # same model, but calculating abundance
> ##D # need to supply the region, sample and observation tables
> ##D region <- book.tee.data$book.tee.region
> ##D samples <- book.tee.data$book.tee.samples
> ##D obs <- book.tee.data$book.tee.obs
> ##D 
> ##D ds.dht.model <- ds(tee.data,4,region.table=region,
> ##D              sample.table=samples,obs.table=obs)
> ##D summary(ds.dht.model)
> ##D 
> ##D # specify order 2 cosine adjustments
> ##D ds.model.cos2 <- ds(tee.data,4,adjustment="cos",order=2)
> ##D summary(ds.model.cos2)
> ##D 
> ##D # specify order 2 and 3 cosine adjustments, turning monotonicity
> ##D # constraints off
> ##D ds.model.cos23 <- ds(tee.data,4,adjustment="cos",order=c(2,3),
> ##D                    monotonicity=FALSE)
> ##D # check for non-monotonicity -- actually no problems
> ##D check.mono(ds.model.cos23$ddf,plot=TRUE,n.pts=100)
> ##D 
> ##D # include both a covariate and adjustment terms in the model
> ##D ds.model.cos2.sex <- ds(tee.data,4,adjustment="cos",order=2,
> ##D                         monotonicity=FALSE, formula=~as.factor(sex))
> ##D # check for non-monotonicity -- actually no problems
> ##D check.mono(ds.model.cos2.sex$ddf,plot=TRUE,n.pts=100)
> ##D 
> ##D # truncate the largest 10% of the data and fit only a hazard-rate
> ##D # detection function
> ##D ds.model.hr.trunc <- ds(tee.data,truncation="10%",key="hr",adjustment=NULL)
> ##D summary(ds.model.hr.trunc)
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>