Calculate the exposed boundary length (perimeter) associated with a
solution to a conservation planning problem()
.
This summary statistic is useful for evaluating the spatial fragmentation of
planning units selected within a solution.
eval_boundary_summary(x, ...)
# S3 method for default
eval_boundary_summary(x, ...)
# S3 method for ConservationProblem
eval_boundary_summary(
x,
solution,
edge_factor = rep(0.5, number_of_zones(x)),
zones = diag(number_of_zones(x)),
data = NULL,
...
)
x 


...  not used. 
solution 

edge_factor 

zones 

data 

tibble::tibble()
object containing the boundary length of the
solution.
It contains the following columns:
character
description of the summary statistic.
The statistic associated with the "overall"
value
in this column is calculated using the entire solution
(including all management zones if there are multiple zones).
If multiple management zones are present, then summary statistics
are also provided for each zone separately
(indicated using zone names).
numeric
exposed boundary length value.
Greater values correspond to solutions with greater
boundary length and, in turn, greater spatial fragmentation.
Thus conservation planning exercises typically prefer solutions
with smaller values.
This summary statistic is equivalent to the Connectivity_Edge
metric
reported by the Marxan software
(Ball et al. 2009).
It is calculated using the same equations used to penalize solutions
according to their total exposed boundary (i.e. add_boundary_penalties()
).
See the Examples section for examples on how differences zone
arguments
can be used to calculate boundaries for different combinations of zones.
The argument to data
can be specified using the following formats.
Note that boundary data must always describe symmetric relationships
between planning units.
NULL
boundary data are automatically calculated
using the boundary_matrix()
function. This argument is the
default. Note that the boundary data must be supplied
using one of the other formats below if the planning unit data
in the argument to x
do not explicitly contain spatial information
(e.g. planning unit data are a data.frame
or numeric
class).
matrix
, Matrix
where rows and columns represent different planning units and the value of each cell represents the amount of shared boundary length between two different planning units. Cells that occur along the matrix diagonal represent the amount of exposed boundary associated with each planning unit that has no neighbor (e.g. these value might pertain to boundaries along a coastline).
data.frame
with the columns "id1"
,
"id2"
, and "boundary"
. The "id1"
and "id2"
columns contain
identifiers (indices) for a pair of planning units, and the "boundary"
column contains the amount of shared boundary length between these
two planning units.
This format follows the the standard Marxan format for boundary
data (i.e. per the "bound.dat" file).
Broadly speaking, the argument to solution
must be in the same format as
the planning unit data in the argument to x
.
Further details on the correct format are listed separately
for each of the different planning unit data formats:
x
has numeric
planning unitsThe argument to solution
must be a
numeric
vector with each element corresponding to a different planning
unit. It should have the same number of planning units as those
in the argument to x
. Additionally, any planning units missing
cost (NA
) values should also have missing (NA
) values in the
argument to solution
.
x
has matrix
planning unitsThe argument to solution
must be a
matrix
vector with each row corresponding to a different planning
unit, and each column correspond to a different management zone.
It should have the same number of planning units and zones
as those in the argument to x
. Additionally, any planning units
missing cost (NA
) values for a particular zone should also have a
missing (NA
) values in the argument to solution
.
x
has Raster
planning unitsThe argument to solution
be a Raster
object where different grid cells (pixels) correspond
to different planning units and layers correspond to
a different management zones. It should have the same dimensionality
(rows, columns, layers), resolution, extent, and coordinate reference
system as the planning units in the argument to x
. Additionally,
any planning units missing cost (NA
) values for a particular zone
should also have missing (NA
) values in the argument to solution
.
x
has data.frame
planning unitsThe argument to solution
must
be a data.frame
with each column corresponding to a different zone,
each row corresponding to a different planning unit, and cell values
corresponding to the solution value. This means that if a data.frame
object containing the solution also contains additional columns, then
these columns will need to be subsetted prior to using this function
(see below for example with sf::sf()
data).
Additionally, any planning units missing cost
(NA
) values for a particular zone should also have missing (NA
)
values in the argument to solution
.
x
has Spatial
planning unitsThe argument to solution
must be a Spatial
object with each column corresponding to a
different zone, each row corresponding to a different planning unit, and
cell values corresponding to the solution value. This means that if the
Spatial
object containing the solution also contains additional
columns, then these columns will need to be subsetted prior to using this
function (see below for example with sf::sf()
data).
Additionally, the argument to solution
must also have the same
coordinate reference system as the planning unit data.
Furthermore, any planning units missing cost
(NA
) values for a particular zone should also have missing (NA
)
values in the argument to solution
.
x
has sf::sf()
planning unitsThe argument to solution
must be
a sf::sf()
object with each column corresponding to a different
zone, each row corresponding to a different planning unit, and cell values
corresponding to the solution value. This means that if the
sf::sf()
object containing the solution also contains additional
columns, then these columns will need to be subsetted prior to using this
function (see below for example).
Additionally, the argument to solution
must also have the same
coordinate reference system as the planning unit data.
Furthermore, any planning units missing cost
(NA
) values for a particular zone should also have missing (NA
)
values in the argument to solution
.
Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen A, Wilson KA, and Possingham HP. Oxford University Press, Oxford, UK.
# \dontrun{
# set seed for reproducibility
set.seed(500)
# load data
data(sim_pu_raster, sim_pu_sf, sim_features,
sim_pu_zones_sf, sim_features_zones)
# build minimal conservation problem with raster data
p1 < problem(sim_pu_raster, sim_features) %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_binary_decisions() %>%
add_default_solver(verbose = FALSE)
# solve the problem
s1 < solve(p1)
# print solution
print(s1)
#> class : RasterLayer
#> dimensions : 10, 10, 100 (nrow, ncol, ncell)
#> resolution : 0.1, 0.1 (x, y)
#> extent : 0, 1, 0, 1 (xmin, xmax, ymin, ymax)
#> crs : NA
#> source : memory
#> names : layer
#> values : 0, 1 (min, max)
#>
# plot solution
plot(s1, main = "solution", axes = FALSE, box = FALSE)
# calculate boundary associated with the solution
r1 < eval_boundary_summary(p1, s1)
print(r1)
#> # A tibble: 1 x 2
#> summary boundary
#> <chr> <dbl>
#> 1 overall 2.25
# build minimal conservation problem with polygon (sf) data
p2 < problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_binary_decisions() %>%
add_default_solver(verbose = FALSE)
# solve the problem
s2 < solve(p2)
# print first six rows of the attribute table
print(head(s2))
#> Simple feature collection with 6 features and 4 fields
#> Geometry type: POLYGON
#> Dimension: XY
#> Bounding box: xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
#> CRS: NA
#> cost locked_in locked_out solution_1 geometry
#> 1 215.8638 FALSE FALSE 0 POLYGON ((0 1, 0.1 1, 0.1 0...
#> 2 212.7823 FALSE FALSE 0 POLYGON ((0.1 1, 0.2 1, 0.2...
#> 3 207.4962 FALSE FALSE 0 POLYGON ((0.2 1, 0.3 1, 0.3...
#> 4 208.9322 FALSE TRUE 0 POLYGON ((0.3 1, 0.4 1, 0.4...
#> 5 214.0419 FALSE FALSE 0 POLYGON ((0.4 1, 0.5 1, 0.5...
#> 6 213.7636 FALSE FALSE 0 POLYGON ((0.5 1, 0.6 1, 0.6...
# plot solution
plot(s2[, "solution_1"])
# calculate boundary associated with the solution
r2 < eval_boundary_summary(p2, s2[, "solution_1"])
print(r2)
#> # A tibble: 1 x 2
#> summary boundary
#> <chr> <dbl>
#> 1 overall 2.05
# build multizone conservation problem with polygon (sf) data
p3 < problem(sim_pu_zones_sf, sim_features_zones,
cost_column = c("cost_1", "cost_2", "cost_3")) %>%
add_min_set_objective() %>%
add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
ncol = 3)) %>%
add_binary_decisions() %>%
add_default_solver(verbose = FALSE)
# solve the problem
s3 < solve(p3)
# print first six rows of the attribute table
print(head(s3))
#> Simple feature collection with 6 features and 9 fields
#> Geometry type: POLYGON
#> Dimension: XY
#> Bounding box: xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
#> CRS: NA
#> cost_1 cost_2 cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
#> 1 215.8638 183.3344 205.4113 FALSE FALSE FALSE 0
#> 2 212.7823 189.4978 209.6404 FALSE FALSE FALSE 0
#> 3 207.4962 193.6007 215.4212 TRUE FALSE FALSE 0
#> 4 208.9322 197.5897 218.5241 FALSE FALSE FALSE 0
#> 5 214.0419 199.8033 220.7100 FALSE FALSE FALSE 0
#> 6 213.7636 203.1867 224.6809 FALSE FALSE FALSE 0
#> solution_1_zone_2 solution_1_zone_3 geometry
#> 1 0 1 POLYGON ((0 1, 0.1 1, 0.1 0...
#> 2 0 0 POLYGON ((0.1 1, 0.2 1, 0.2...
#> 3 0 0 POLYGON ((0.2 1, 0.3 1, 0.3...
#> 4 0 0 POLYGON ((0.3 1, 0.4 1, 0.4...
#> 5 0 0 POLYGON ((0.4 1, 0.5 1, 0.5...
#> 6 1 0 POLYGON ((0.5 1, 0.6 1, 0.6...
# create new column representing the zone id that each planning unit
# was allocated to in the solution
s3$solution < category_vector(
s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
s3$solution < factor(s3$solution)
# plot solution
plot(s3[, "solution"])
# calculate boundary associated with the solution
# here we will use the default argument for zones which treats each
# zone as completely separate, meaning that the "overall"
# boundary is just the sum of the boundaries for each zone
r3 < eval_boundary_summary(
p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
print(r3)
#> # A tibble: 4 x 2
#> summary boundary
#> <chr> <dbl>
#> 1 overall 12.5
#> 2 zone_1 3.90
#> 3 zone_2 4.05
#> 4 zone_3 4.6
# let's calculate the overall exposed boundary across the entire
# solution, assuming that the shared boundaries between planning
# units allocated to different zones "count" just as much
# as those for planning units allocated to the same zone
# in other words, let's calculate the overall exposed boundary
# across the entire solution by "combining" all selected planning units
# together (regardless of which zone they are allocated to in the solution)
r3_combined < eval_boundary_summary(
p3, zones = matrix(1, ncol = 3, nrow = 3),
s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
print(r3_combined)
#> # A tibble: 4 x 2
#> summary boundary
#> <chr> <dbl>
#> 1 overall 6.95
#> 2 zone_1 3.90
#> 3 zone_2 4.05
#> 4 zone_3 4.6
# we can see that the "overall" boundary is now less than the
# sum of the individual zone boundaries, because it does not
# consider the shared boundary between two planning units allocated to
# different zones as "exposed" when performing the calculations
# }