CREEM, Univ of St Andrews
April 2025
Survey Design for Distance Sampling
The most up-to-date copies of these vignettes can now be found on the
distance sampling examples page of our website: https://distancesampling.org/resources/vignettes.html
Distance Sampling techniques provide design based estimates of
density and abundance for populations, the accuracy of these estimates
therefore relies on valid survey design. The process of designing a
survey involves deciding on the required survey effort in order to
achieve a desired precision followed by deciding where exactly the
effort (the lines or points) will be located within the survey
region.
Before proceeding to the design stage there are a number of
considerations which first need to be addressed. The first steps in
conducting a survey are to clearly define the study population and the
objectives of the study. In addition, the use of spatial stratification
to improve precision should also be considered, the ‘Multiple Strata in
dssd’ vignette details how to work with multi-strata study regions. We
recommend consulting Buckland et al.
(2001) chapter 7 and Strindberg, Buckland,
and Thomas (2004) before using dssd to design your distance
sampling survey.
Once you have defined your population and study objectives, and
estimated the required effort, dssd (Marshall
2019a) can help ensure you meet the survey design assumptions
associated with distance sampling. Distance sampling assumes that the
survey transects are a representative sample of the study region and are
laid out at random with respect to the population. dssd achieves both
these objectives by randomising the locations of the transects. Designs
may be fully random with each transect being randomly located
independently of other transects or a systematic design with a random
start point should also meet this assumption.
The next assumption is that each point within the study region is
equally likely to be sampled as any other, we call this uniform
coverage. We can assess the coverage across the study region using a
grid of points called a coverage grid. Some designs have more uniform
coverage than others and dssd can help assess how uniform the coverage
is via simulation. If non-uniform coverage is of concern dssd can be
used in conjunction with DSsim (Marshall
2019b) the distance sampling simulations package to better assess
the effects of non-uniform coverage under normal and worst case
scenarios to allow a more informed choice of design.
Setting up the Region
The first step in creating a survey design is to set up your study
region. The easiest way to do this is using a shapefile which has
already been created to define your study region. The dssd package
contains the example shapefile used in this vignette and can be accessed
using the code below. Here we use this shapefile to define the study
region and then plot it.
library(dssd)
shapefile.name <- system.file("extdata", "TrackExample.shp", package = "dssd")
region <- make.region(region.name = "study area",
shape = shapefile.name)
plot(region)
Creating a Coverage Grid
Ideally, a coverage grid is created separately before creating the
design. The same coverage grid can then be used for multiple designs. If
a coverage grid is not passed to the design then this will be detected
when the coverage simulation is run and a grid with 1000 points will
automatically be generated.
cover <- make.coverage(region,
n.grid.points = 1000)
Defining the Design
dssd provides a number of point and line transect designs. The design
refers to a description of how the transect locations are selected and
does not specify the locations of a single set of transects. We will
later refer to a single set of transects generated from the design as a
survey. A survey can then be thought if as a single random realisation
of a design.
Here we will demonstrate a systematic parallel line design. We will
define the desired effort as 1300 km. Note that the line length units
will always be the same as the region coordinate units. Usually edge
effects for line transect surveys are minimal so we will choose to carry
out minus sampling, when only transects within the survey region are
sampled. The design angle for parallel line designs is 0 for vertical
lines and then moves round in a clockwise direction. Here I have left
the design angle as 0 as this maximises the number of transects, the
study region is larger in the x-dimension than the y-dimension. I have
set the truncation distance to be 2 km, this is the maximum distance at
which it is possible to make detections and is used to define the
covered area. The covered area refers to the area of the study region
which is sampled during the survey, this is a set of rectangles around
line transects or a set of circles around point transects which are then
clipped to the strata boundaries. If these rectangles or circles
overlap, then the areas of overlap are counted twice. This means that it
is possible, with a sufficiently large truncation distance, to sample
more than 100% of the survey region.
design <- make.design(region = region,
design = "systematic",
line.length = 1300,
edge.protocol = "minus",
design.angle = 0,
truncation = 2,
coverage.grid = cover)
Generating a Survey
Now we have defined the design we should check that it generated
transects as we would expect by generating a survey. You can then view
statistics about this survey and plot the transects.
transects <- generate.transects(design)
transects
##
## Strata study area:
## ___________________
## Design: systematically spaced parallel transects
## Spacing: 9.258935
## Line length: 1346.139
## Trackline length: 1536.667
## Cyclic trackline length: 1722.431
## Number of samplers: 21
## Design angle: 0
## Edge protocol: minus
## Covered area: 5282.704
## Strata coverage: 43.89%
## Strata area: 12036.62
##
## Study Area Totals:
## _________________
## Line length: 1346.139
## Trackline length: 1536.667
## Cyclic trackline length: 1722.431
## Number of samplers: 21
## Covered area: 5282.704
## Average coverage: 43.89%
We can see that this survey has an on effort line length of 1346 km,
close to the 1300 km we asked for. It was generated based on a spacing
of 9.26 km, a value calculated based on the requested line length, and
resulted in 21 transects. We are also given the trackline length and
cyclic trackline lengths. The trackline length is the sum of the lengths
of the transects plus the off-effort transit time required to complete
the survey from the beginning of the first transect to the end of the
last transect. The off-effort transit distance is calculated as the crow
flies and may be longer in reality if transit is required around lakes,
islands or coastlines etc. The cyclic trackline length is the trackline
length plus the off-effort transit distance required to return from the
end of the last transect to the beginning of the first transect. Please
see the appendix for more details and figures.
We are also told that this survey covers 43.9% of the study area. If
we wish to view the covered area for this particular set of transects we
can plot it using the code below. The covered area is the rectangles
delineated by the black lines.
plot(region, transects, covered.area = TRUE)
Assessing Coverage Uniformity and Design Statistics
Once we have checked that our design appears to be correctly
specified we can assess how uniform the coverage is and also how values
such as total line length, trackline length and cyclic trackline length
vary across many surveys generated from our design. While we were given
single values for these statistics from our one survey above it is
important to check that all potential surveys from our design can be
completed in the effort available, i.e. the maximum trackline/cyclic
trackline length from the simulation should be achievable within the
limits of the study. It is not permissible to generate more than one set
of transects for the final survey and select the set with shorter/longer
trackline length as then the selection of transect locations will no
longer be purely random.
Parallel line designs should give uniform coverage across the
majority of the survey region. The only exception to this is around the
edge of the study region when we are using minus sampling, as we are
using here. We will assess the effects of this now via a simulation
which will generate 999 sets of transects from our design.
design <- run.coverage(design, reps = 999)
We can now view the coverage scores by plotting our design
object.
plot(design, subtitle = "Systematic Parallel, line.length = 1300km")
## old-style crs object detected; please recreate object with a recent sf::st_crs()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
The plot above indicates that coverage is fairly uniform over the
majority of the study region. There are a few points around the edge of
the survey region which have lower coverage than the others due to the
minus sampling protocol, however for this example we would expect the
effects of non-uniform coverage on the study estimates to be very small.
The coverage grid points with lower coverage are very few in number and
represent a very small proportion of the study region area.
We can also look at the design statistics, these are shown below.
##
## Strata study area:
## ___________________
## Design: systematically spaced transects
## Spacing: NA
## Number of samplers: NA
## Line length: 1300 (shared across strata)
## Design angle: 0
## Edge protocol: minus
##
## Strata areas: 12037
## Region and effort units: km
## Coverage Simulation repetitions: 999
##
## Number of samplers:
##
## study area Total
## Minimum 20.0 20.0
## Mean 20.5 20.5
## Median 20.0 20.0
## Maximum 21.0 21.0
## sd 0.5 0.5
##
## Covered area:
##
## study area Total
## Minimum 5050.77 5050.77
## Mean 5147.14 5147.14
## Median 5101.63 5101.63
## Maximum 5310.94 5310.94
## sd 90.43 90.43
##
## % of region covered:
##
## study area Total
## Minimum 41.96 41.96
## Mean 42.76 42.76
## Median 42.38 42.38
## Maximum 44.12 44.12
## sd 0.75 0.75
##
## Line length:
##
## study area Total
## Minimum 1268.02 1268.02
## Mean 1299.52 1299.52
## Median 1282.34 1282.34
## Maximum 1348.13 1348.13
## sd 31.17 31.17
##
## Trackline length:
##
## study area Total
## Minimum 1450.50 1450.50
## Mean 1485.09 1485.09
## Median 1463.06 1463.06
## Maximum 1538.98 1538.98
## sd 35.32 35.32
##
## Cyclic trackline length:
##
## study area Total
## Minimum 1637.21 1637.21
## Mean 1672.06 1672.06
## Median 1649.37 1649.37
## Maximum 1724.80 1724.80
## sd 35.20 35.20
##
## Coverage Score Summary:
##
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## old-style crs object detected; please recreate object with a recent sf::st_crs()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
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## study area Total
## Minimum 0.19619620 0.19619620
## Mean 0.42611584 0.42611584
## Median 0.43243243 0.43243243
## Maximum 0.45845846 0.45845846
## sd 0.03585962 0.03585962
First you are given a summary of the design, systematically spaced
transects where the spacing was to be selected to achieve around 1300 km
of effort. The lines were to be placed on a design angle of 0 and a
minus sampling protocol was to be used.
We are then told the area of the study region, the units of the
region coordinates and how many times the coverage simulation was
repeated.
We now move on to the summary statistics from the 999 sets of
transects generated during the simulation. We are told that each survey
has between 20 and 21 samplers and that the minimum and maximum covered
areas are 5051 and 5311 km^2 which equate to 42.0% and 44.1% of the
study area, respectively. The minimum on-effort line length is 1268 km
and the maximum on-effort line length is 1348 km, with a mean value of
very close to the 1300km requested. We are then given the minimum, mean,
median, maximum and standard deviation values for the trackline and
cyclic trackline lengths. The maximum values for these statistics should
be used to ensure that any set of transects randomly generated from the
design is achievable in the total effort available given any time and
financial constraints of the survey.
Finally, we are given a summary of the coverage score values. If we
have even coverage then we should see little variation in the coverage
scores. The minimum coverage score is 0.20 and the maximum is 0.46
indicating that some small areas around the edge of the study region (as
shown in Figure 4) are half as likely to be sampled as those within the
main part of the study region. We are given an indication of the
variability of the coverage scores in the standard deviation provided
but it may also be useful to plot a histogram of the coverage scores,
Figure 5. Again this looks fairly reassuring that the parts of the study
with lower coverage do not represent a significant proportion of the
study area. However, if we wanted to be really thorough we could run a
simulation study using DSsim and test a worse case scenario, where
density in these areas of lower coverage varied from the rest of the
study region. If we were worried that this non-uniform coverage could
cause significant bias we could switch to a plus sampling strategy.
hist(get.coverage(design), xlab = "Coverage Scores", main = "Histogram of Coverage Scores")
Exporting transects
When you are confident that your design meets your survey objectives,
you are ready to generate a final set of transects to use during your
survey. To ensure that uniform coverage probability is maintained you
must use the first randomly generated transect set. Regenerating
transects due to an inconvenient transect property (e.g. intersection of
an island or other feature / too few or too many samplers) will result
in non-uniform coverage so must be avoided.
Once you have your final set of survey transects these can be
exported in a number of formats. Below we demonstrate exporting the
coordinates to shapefile and to csv file. See the write.transects help
file for additional examples of exporting to .txt and .gpx. In the
example below these files are written to a temporary directory, you will
want to replace this with your own file path and name.
# File destination - .txt file
file.path <- paste0(tempdir(), "/", "transects.txt")
# Write to .txt file
write.transects(transects, dsn = file.path)
# File destination - .shp file
file.path <- paste0(tempdir(), "/", "transects.shp")
# Write to shapefile
write.transects(transects, dsn = file.path)
## writing: substituting ENGCRS["Undefined Cartesian SRS with unknown unit"] for missing CRS
## Writing layer `transects' to data source
## `C:\Users\lhm\AppData\Local\Temp\RtmpUHPDhy/transects.shp' using driver `ESRI Shapefile'
## Writing 21 features with 2 fields and geometry type Line String.
You can now navigate to your saved files and view their contents.
Appendix: Trackline and Cyclic Trackline Lengths
The following four figures (6 - 10) demonstrate how the trackline
lengths and cyclic trackline lengths are calculated. The red arrows
indicate the trackline path, moving from the start of the first transect
along its length then across off effort to the next transect and so on
until the end of the last transect is reached. The cyclic trackline
length is then the trackline length represented by the red arrows plus
the off effort transit time required to travel from the end of the last
transect back to the beginning of the first as indicated by the light
blue arrow. These values are provided to help you assess the efficiency
of the design by comparing on-effort line length to total trackline
length and also to help you ensure that the entire survey can be
completed within time and budget constraints. Note that the trackline
and cyclic trackline lengths for segmented designs are calculated in a
very similar way to parallel line transect designs. The observer will
start at the beginning of one segment and move up the line of segments
before crossing to the next line of segments and so on.
Figure 6: Illustrates the trackline and cyclic
trackline lengths for random parallel line designs. The sum of the
lengths of the red arrows represent the trackline length. The sum of the
lengths of the red arrows and the light blue arrow represent the cyclic
trackline length.
Figure 7: Illustrates the trackline and cyclic
trackline lengths for systematic parallel line designs. The sum of the
lengths of the red arrows represent the trackline length. The sum of the
lengths of the red arrows and the light blue arrow represent the cyclic
trackline length.
Figure 8: Illustrates the trackline and cyclic
trackline lengths for zigzag designs. The sum of the lengths of the red
arrows represent the trackline length. The sum of the lengths of the red
arrows and the light blue arrow represent the cyclic trackline
length.
Figure 9: Illustrates the trackline and cyclic
trackline lengths for complementary zigzag designs. The sum of the
lengths of the red arrows represent the trackline length. The sum of the
lengths of the red arrows and the light blue arrow represent the cyclic
trackline length.
Bibliography
Buckland, S. T., D. R. Anderson, K. P. Burnham, D. L. Borchers, and L.
Thomas. 2001. Introduction to Distance
Sampling. Estimating Abundance of Biological Populations.
Oxford University Press, Oxford, UK.
Marshall, L. 2019a.
Dssd: Distance Sampling Survey Design.
https://CRAN.R-project.org/package=dssd.
———. 2019b.
DSsim: Distance Sampling Simulations.
https://CRAN.R-project.org/package=DSsim.
Strindberg, S., S. T. Buckland, and L. Thomas. 2004. “Design of
Distance Sampling Surveys and Geographic Information Systems.” In
Advanced Distance Sampling, 190–228. Oxford University Press.
