Introduction
The most up-to-date copies of these vignettes can now be found on the
distance sampling examples page of our website: https://examples.distancesampling.org
This vignette assumes the reader is familiar with the topics covered
in the getting started vignette. It expands on that content,
demonstrating how to use the distance sampling survey design package,
dssd (Marshall 2019) when your study
region is made up of multiple strata. This vignette will detail how you
can select different designs (within the same design category, either
lines or points) for each stratum and provide stratum specific design
parameters. Please note that the examples provided in this vignette are
designed to make the reader aware of what is possible inside the dssd
package and the designs are not necessarily something that we would
recommended for these example survey regions.
Stratified Designs - why stratify?
There are a number of reasons that we may wish to create a stratified
design. Firstly, it may be for efficiency reasons. For example, we may
wish to divide our region into a number of more convex shapes when using
an equal spaced zigzag design to reduce off-effort transit time at the
survey region boundary. Figure 1 presents an example of a Minke whale
survey, in the left panel when the zigzag design is generated in the
study region as a whole we can see that it is fairly inefficient with
large distances between the ends of transects (note that only the
lengths of transect inside the shaded study area will be surveyed). In
the right panel we have reduced the off effort transit time by dividing
the study area into a number of strata. As the purpose of this
stratification is simply to improve efficiency we would still want to
try to achieve equal coverage across all strata.
Figure 1: Example survey design for a Minke
whale survey. The shaded polygons represent the study area and the
dotted lines represent convex hulls stretched around the study region
polygons. While the full length of the zigzag transects is shown only
the parts inside the shaded area will be surveyed. Left panel shows an
equal spaced zigzag design generated inside a convex hull applied to the
study region as a whole. The right panel shows an equal spaced zigzag
design generated inside a number of strata selected so that the study
region was divided into a number of almost convex shapes.
Another reason some people consider stratifying their survey region
is to improve precision. More precise estimates of density / abundance
can sometimes be achieved by allocating more effort to areas of high
density and less effort to areas of low density. This allows
inter-stratum differences to be estimated rather than have them
contribute to the variance of the estimates. Certainly, if there are
large areas where you expect to see very little it might be unwise to
spend a lot of expensive resources in these areas. However, there are
dangers of unequal effort allocation (otherwise called non-uniform
coverage). There may be differences in encounter rate, detection
function or mean cluster size across the different strata. If any of
these are estimated by pooling across strata when in fact they differ
between strata then within stratum estimates will be biased and the
global estimates may also be biased. The only way to be sure if
inter-stratum differences exist is to ensure that you have sufficient
data in each strata to estimate the encounter rate, detection function
and mean cluster size by stratum. Otherwise you will need to rely on
making biological assumptions.
A third scenario in which you may want to stratify is that you wish
to make inference about a particular sub-region of your study area. In
addition, if you plan on fitting a spatial model to your distance
sampling data you may have regions of particular interest in which you
would like to detect changes in density at smaller scales than in other
regions.
Finally you may wish to stratify as you plan to survey from two
different platforms, for example marine surveys when some strata will be
surveyed from a ship while others are surveyed from the air. Ship-board
surveys often use zigzag designs for efficiency to maximise on-effort
survey time. Ships have sufficient space for multiple sets of observers
so ship board surveys can achieve continuous observation while
travelling along the transects. In contrast, aerial surveys often use
systematic parallel line designs. Firstly the tight turns at the end of
zigzags can be hard to achieve in an airplane (and unpleasant for the
crew) and secondly the time taken to transit between parallel transects
can be useful periods of rest for a single set of observers. The Small
Cetaceans in the European Atlantic and North Sea II (SCANS II) strata
were designed to implement this mixed platform approach.
Defining the Study Area
First we need to load the dssd library.
The study area can be defined in the same way as for a single stratum
study region by providing a shapefile. This shapefile however will
contain multiple polygon features. The first example study region used
in this vignette is one of the Danish coastal strata from the SCANS II
survey, Figure 2. The coastline is the study region border along the
east of the study area. The study area had been divided into two strata
for the purposes of maximising samplers and keeping the samplers roughly
perpendicular to the coastline. For the design examples in this vignette
we will treat this strata as the entire study region and the parts as
separate strata. Note that the units for this shapefile are in metres so
all design arguments relating to distances must also be provided in
metres.
shapefile.name <- system.file("extdata", "Strata.shp", package = "dssd")
region <- make.region(region.name = "study.area",
strata.name = c("North", "South"),
shape = shapefile.name)
plot(region)
Additional information on how to manually create multi-strata study
regions inside R can be found in the ‘manual creation of study areas’
appendix.
Creating a Coverage Grid
The coverage grid can be created in the same way as for a single
stratum study region. The creation of the coverage grid involves
creating a single grid of points over the entire study area and so is
unaffected by the region being subdivided into multiple strata, Figure
3.
cover <- make.coverage(region,
n.grid.points = 1000)
plot(region, cover, cex = 0.7)
Defining the Design
This section will demonstrate a number of example designs to show how
design, design angle, effort, edge sampling and other design parameters
can be varied across strata.
Default Design (with specified design angles)
Similar to single stratum regions, the default design for
multi-strata regions is 20 systematic parallel lines with a design angle
of 0 (i.e. the lines run perpendicular to the x-axis) and using a minus
sampling edge protocol. The spacing is selected at the global level to
achieve a total of approximately 20 lines across all strata. In this
first example, we will leave the default effort but specify design
angles which will mean that our parallel lines run roughly perpendicular
to the coastline. Our survey should therefore have around 20 lines which
have the same spacing in both the North and South strata. The default
design has a truncation distance of 1 which will rarely be applicable so
we have specified it here as 2000 m. A single survey generated from this
design is plotted in Figure 4.
default.design <- make.design(region = region,
transect.type = "line",
design = "systematic",
samplers = 20,
design.angle = c(155, 90),
edge.protocol = "minus",
truncation = 2000,
coverage.grid = cover)
transects <- generate.transects(default.design)
plot(region, transects, lwd = 0.8, col = "blue")
We can also view a summary of the survey shown in Figure 4. The
output shown below tells us that dssd selected a spacing of around 17.9
km (17946.09 m) between the systematic parallel lines. As both strata
used the same systematic design the spacing values were calculated
globally and are identical for both strata. It also tells us that the
percentage of the study region covered was around 22% in both strata and
that for this particular survey we have achieved exactly 20 transects,
11 in the northern strata and 9 in the southern strata.
##
## Strata North:
## ______________
## Design: systematically spaced parallel transects
## Spacing: 17946.09
## Line length: 525341
## Trackline length: 724166.8
## Cyclic trackline length: 904116.6
## Number of samplers: 11
## Design angle: 155
## Edge protocol: minus
## Covered area: 2083756793
## Strata coverage: 22.45%
## Strata area: 9280648398
##
## Strata South:
## ______________
## Design: systematically spaced parallel transects
## Spacing: 17946.09
## Line length: 643553.8
## Trackline length: 814796.6
## Cyclic trackline length: 958365.9
## Number of samplers: 9
## Design angle: 90
## Edge protocol: minus
## Covered area: 2563013876
## Strata coverage: 21.88%
## Strata area: 11716012130
##
## Study Area Totals:
## _________________
## Line length: 1168895
## Trackline length: 1538963
## Cyclic trackline length: 1862483
## Number of samplers: 20
## Covered area: 4646770669
## Average coverage: 22.13%
Vary design by stratum
Within the categories of line and point transect designs, different
types of design may be selected for each stratum. Here we will use an
equally spaced zigzag design in the northern stratum and a systematic
parallel line in the southern stratum. Note the design angle has a
different definition for zigzag designs than parallel line designs so
the first value has been modified to 65 degrees (at right angles to the
parallel line design above). To maximise the efficiency of the zigzag
design we will specify the bounding shape for this stratum as a convex
hull. Note that no bounding shape is used in the systematic parallel
line design so the second value for bounding shape argument is NA. This
design also explicitly declares the edge protocol as minus sampling,
which will be applied to both strata. The effort for this design is
supplied as a single line length and as we have not defined effort
allocation the total line length of 1200 km (1200000 m) will be shared
among the strata based on their areas. An example survey generated from
this design is shown in Figure 5.
design <- make.design(region = region,
transect.type = "line",
design = c("eszigzag", "systematic"),
line.length = 1200000,
design.angle = c(65, 90),
bounding.shape = c("convex.hull", NA),
edge.protocol = "minus",
truncation = 2000,
coverage.grid = cover)
transects <- generate.transects(design)
plot(region, transects, lwd = 0.8, col = "blue")
Let us now run a coverage check on this design to see if the coverage
is roughly the same in both strata. Looking at Figure 6 the coverage
probabilities look to be roughly the same on average for the two strata.
We do however see the sharp corners of the northern stratum displaying a
higher coverage due to the zigzag design being generated in a convex
hull.
design <- run.coverage(design, reps = 1000)
plot(design)
## 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()
We can also look at the design statistics from the 1000 surveys
generated, displayed below. We can see in this multiple strata example
we are now given stratum-specific statistics as well as values for the
study region as a whole in the Total columns. We can see from the strata
areas information that the southern strata is slightly bigger than the
northern strata and also looking at the covered area table we see that
the covered area is larger in the southern strata. If we look at the %
of region covered statistics we see that the coverage is approximately
the same in both strata, having a percentage covered of 22.09% in the
northern stratum and 22.67% in the southern stratum.
##
## Strata North:
## ______________
## Design: equal spaced zigzag
## Spacing: NA
## Number of samplers: NA
## Line length: 1200000 (shared across strata)
## Design angle: 65
## Edge protocol: minus
##
## Strata South:
## ______________
## Design: systematically spaced transects
## Spacing: NA
## Number of samplers: NA
## Line length: 1200000 (shared across strata)
## Design angle: 90
## Edge protocol: minus
##
## Strata areas: 9280648398, 11716012130
## Region and effort units: m
## Coverage Simulation repetitions: 1000
##
## Number of samplers:
##
## North South Total
## Minimum 9.0 9.0 18.0
## Mean 10.7 9.5 20.2
## Median 11.0 10.0 20.0
## Maximum 12.0 10.0 22.0
## sd 0.6 0.5 0.8
##
## Covered area:
##
## North South Total
## Minimum 1955116049 2513421503 4481285619
## Mean 2049652296 2656340209 4705992505
## Median 2070366837 2670394472 4713693428
## Maximum 2091766860 2782781204 4870589559
## sd 36486449 82822551 91678794
##
## % of region covered:
##
## North South Total
## Minimum 21.07 21.45 21.34
## Mean 22.09 22.67 22.41
## Median 22.31 22.79 22.45
## Maximum 22.54 23.75 23.20
## sd 0.39 0.71 0.44
##
## Line length:
##
## North South Total
## Minimum 497407.9 631156.05 1128751.83
## Mean 521716.3 669307.22 1191023.50
## Median 525731.8 670981.00 1192041.07
## Maximum 535469.7 706157.31 1239785.11
## sd 9013.4 23011.45 24965.31
##
## Trackline length:
##
## North South Total
## Minimum 512691.24 798122.48 1311004.79
## Mean 538759.40 846771.69 1385531.09
## Median 541724.36 856097.28 1392394.59
## Maximum 550794.04 891391.01 1440740.61
## sd 8958.67 31339.93 32758.02
##
## Cyclic trackline length:
##
## North South Total
## Minimum 683046.12 938100.75 1621340.14
## Mean 722453.73 1005787.30 1728241.03
## Median 727656.40 1031911.48 1741506.91
## Maximum 737260.78 1066109.12 1801958.77
## sd 13922.31 47925.48 50049.89
##
## Coverage Score Summary:
##
## 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()
## 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()
## 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()
## old-style crs object detected; please recreate object with a recent sf::st_crs()
## North South Total
## Minimum 0.0870000 0.12000000 0.08700000
## Mean 0.2201493 0.22586538 0.22337377
## Median 0.2190000 0.22300000 0.22200000
## Maximum 0.3910000 0.27000000 0.39100000
## sd 0.0309947 0.02553877 0.02817631
Segmented Line Design
This example uses a segmented grid design to further demonstrate how
design parameters can be varied across strata. In this example the
spacing, segment length and segment threshold values have been specified
explicitly for each strata. In the northern stratum we have segments of
5km in length separated by 10km. The segment threshold of 50 means that
any segments less than 50% of the segment length (i.e. 2.5km) will be
discarded. In the southern stratum we have segments of 12km separated by
20km and where we retain all segments no matter how short they are
(segment threshold of 0). An example survey from this design is shown in
Figure 7.
design <- make.design(region = region,
transect.type = "line",
design = "segmentedgrid",
spacing = c(10000,20000),
seg.length = c(5000,12000),
design.angle = c(150, 90),
seg.threshold = c(50,0),
edge.protocol = "minus",
truncation = 3000,
coverage.grid = cover)
transects <- generate.transects(design)
plot(region, transects, lwd = 0.8, col = "blue")
We can then have a look at the coverage scores to examine coverage in
the two strata. We observe on average the coverage is higher in the
northern stratum than the southern stratum because spacing was half as
large in the northern stratum, Figure 8.
design <- run.coverage(design, reps = 1000)
plot(design)
## 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()
When there are differences in average coverage between strata it is
sometimes difficult to visualise non-uniform coverage within strata. The
survey design package also provides the functionality to view the
coverage score plot for individual strata, Figures 9 and 10. While the
minor edge effects in the northern stratum were apparent when the study
area was plotted as a whole, Figure 8, the edge effects in the southern
stratum were not detectable in this plot. However, we can see from
Figure 10 that the edge effects in the southern stratum are also very
small in comparison to the stratum area.
plot(design, strata.id = 1, subtitle = "Coverage Northern Strata")
## 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()
## 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()
plot(design, strata.id = 2, subtitle = "Coverage Southern Strata")
## 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()
## 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()
Point transect design
For this point transect example we will use a different study region.
This is an area of forest in Scotland between Dundee and St Andrews made
up of two strata, Figure 11. As this region is not projected we will
first need to project the study area onto a flat plane.
#Load the unprojected shapefile
library(sf)
## Linking to GEOS 3.11.1, GDAL 3.6.2, PROJ 9.1.1; sf_use_s2() is TRUE
shapefile.name <- system.file("extdata", "TentsmuirUnproj.shp", package = "dssd")
sf.shape <- read_sf(shapefile.name)
# Define a European Albers Equal Area projection
proj4string <- "+proj=aea +lat_1=56 +lat_2=62 +lat_0=50 +lon_0=-3 +x_0=0
+y_0=0 +ellps=intl +units=m"
# Project the study area on to a flat plane
projected.shape <- st_transform(sf.shape, crs = proj4string)
# Create the survey region in dssd
region.tm <- make.region(region.name = "Tentsmuir",
strata.name = c("Main Area", "Morton Lochs"),
shape = projected.shape)
# Plot the survey region
plot(region.tm, legend.params = list(inset = c(-0.3,0)))
#Create a coverage grid
cover.tm <- make.coverage(region.tm, n.grid.points = 500)
Point transect designs and point transect design parameters can be
varied across strata in the same way as line transect designs. Here we
use a systematic grid of point in both the main and Morton Lochs strata.
We specify that there should be approximately 80 samplers across both
strata and that we would like 25% of the effort allocated to the Morton
Lochs strata and 75% to the main strata. As the Morton Lochs strata is
such a small area it could be prone to edge effects so we will use a
plus sampling strategy. Figure 12 shows one possible realisation of this
design.
design.tm <- make.design(region = region.tm,
transect.type = "point",
design = "systematic",
samplers = 80,
effort.allocation = c(0.75,0.25),
edge.protocol = c("minus","plus"),
truncation = 100,
coverage.grid = cover.tm)
transects.tm <- generate.transects(design.tm)
plot(region.tm, transects.tm, lwd = 0.8, col = "blue")
We can also have a look at the statistics for this particular survey.
The output below shows that although we set the effort to be 80 samplers
in total we have 92. While we see the expected number in the main
stratum 75% of 80 is 60 samplers, we see more than expected in the
Morton Lochs stratum, 32 rather than 20. This is down to the fact that
we are using a plus sampling edge protocol in this stratum and if we
check in Figure 12 above we will see that approximately 20 points
actually fall inside the Morton Lochs stratum. This additional effort
that is required for the plus sampling strategy is something to be aware
of when costing for your survey.
##
## Strata Main Area:
## __________________
## Design: systematically spaced transects
## Spacing: 484.9165
## Number of samplers: 60
## Design angle: 0
## Edge protocol: minus
## Covered area: 1842894
## Strata coverage: 13.06%
## Strata area: 14108643
##
## Strata Morton Lochs:
## _____________________
## Design: systematically spaced transects
## Spacing: 189.1117
## Number of samplers: 32
## Design angle: 0
## Edge protocol: plus
## Covered area: 630454.5
## Strata coverage: 88.14%
## Strata area: 715264.9
##
## Study Area Totals:
## _________________
## Number of samplers: 92
## Effort allocation: 75%, 25%
## Covered area: 2473348
## Average coverage: 16.68%
