Calculate the total cost of a solution to a conservation planning problem. For example, if the planning unit cost data describe land acquisition costs (USD), then the total cost would be net cost (USD) needed to acquire all planning units selected within the solution.
Arguments
- x
problem()object.- solution
numeric,matrix,data.frame,terra::rast(), orsf::sf()object. The argument should be in the same format as the planning unit cost data in the argument tox. See the Solution format section for more information.
Value
A tibble::tibble() object containing the solution cost.
It contains the following columns:
- summary
characterdescription 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).- cost
numericcost value. Greater values correspond to solutions that are more costly to implement. Thus conservation planning exercises typically prefer solutions with smaller values, because they are cheaper to implement (assuming all other relevant factors, such as feature representation, are equal).
Details
This metric is equivalent to the Cost metric reported by the
Marxan software (Ball et al. 2009).
Specifically, the cost of a solution is defined as the sum of the cost
values, supplied when creating a problem() object
(e.g., using the cost_column argument),
weighted by the status of each planning unit in the solution.
Solution format
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:
xhasnumericplanning unitsThe argument to
solutionmust be anumericvector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument tox. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument tosolution.xhasmatrixplanning unitsThe argument to
solutionmust be amatrixvector 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 tox. Additionally, any planning units missing cost (NA) values for a particular zone should also have a missing (NA) values in the argument tosolution.xhasterra::rast()planning unitsThe argument to
solutionbe aterra::rast()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 tox. Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument tosolution.xhasdata.frameplanning unitsThe argument to
solutionmust be adata.framewith 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 adata.frameobject containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example withsf::sf()data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument tosolution.xhassf::sf()planning unitsThe argument to
solutionmust be asf::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 thesf::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 tosolutionmust 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 tosolution.
References
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.
See also
See summaries for an overview of all functions for summarizing solutions.
Other summaries:
eval_asym_connectivity_summary(),
eval_boundary_summary(),
eval_connectivity_summary(),
eval_feature_representation_summary(),
eval_n_summary(),
eval_target_coverage_summary()
Examples
# \dontrun{
# set seed for reproducibility
set.seed(500)
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_pu_polygons <- get_sim_pu_polygons()
sim_features <- get_sim_features()
sim_zones_pu_polygons <- get_sim_zones_pu_polygons()
sim_zones_features <- get_sim_zones_features()
# 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 : SpatRaster
#> dimensions : 10, 10, 1 (nrow, ncol, nlyr)
#> resolution : 0.1, 0.1 (x, y)
#> extent : 0, 1, 0, 1 (xmin, xmax, ymin, ymax)
#> coord. ref. : Undefined Cartesian SRS
#> source(s) : memory
#> varname : sim_pu_raster
#> name : layer
#> min value : 0
#> max value : 1
# plot solution
plot(s1, main = "solution", axes = FALSE)
# calculate cost of the solution
r1 <- eval_cost_summary(p1, s1)
print(r1)
#> # A tibble: 1 × 2
#> summary cost
#> <chr> <dbl>
#> 1 overall 1994.
# build minimal conservation problem with polygon data
p2 <-
problem(sim_pu_polygons, 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)
# plot solution
plot(s2[, "solution_1"])
# print solution
print(s2)
#> Simple feature collection with 90 features and 4 fields
#> Geometry type: POLYGON
#> Dimension: XY
#> Bounding box: xmin: 0 ymin: 0 xmax: 1 ymax: 1
#> Projected CRS: Undefined Cartesian SRS
#> # A tibble: 90 × 5
#> cost locked_in locked_out solution_1 geom
#> <dbl> <lgl> <lgl> <dbl> <POLYGON [m]>
#> 1 216. FALSE FALSE 0 ((0 1, 0.1 1, 0.1 0.9, 0 0.9, 0 1))
#> 2 213. FALSE FALSE 0 ((0.1 1, 0.2 1, 0.2 0.9, 0.1 0.9, 0.1 …
#> 3 207. FALSE FALSE 0 ((0.2 1, 0.3 1, 0.3 0.9, 0.2 0.9, 0.2 …
#> 4 209. FALSE TRUE 0 ((0.3 1, 0.4 1, 0.4 0.9, 0.3 0.9, 0.3 …
#> 5 214. FALSE FALSE 0 ((0.4 1, 0.5 1, 0.5 0.9, 0.4 0.9, 0.4 …
#> 6 214. FALSE FALSE 0 ((0.5 1, 0.6 1, 0.6 0.9, 0.5 0.9, 0.5 …
#> 7 210. FALSE FALSE 0 ((0.6 1, 0.7 1, 0.7 0.9, 0.6 0.9, 0.6 …
#> 8 211. FALSE TRUE 0 ((0.7 1, 0.8 1, 0.8 0.9, 0.7 0.9, 0.7 …
#> 9 210. FALSE FALSE 0 ((0.8 1, 0.9 1, 0.9 0.9, 0.8 0.9, 0.8 …
#> 10 204. FALSE FALSE 1 ((0.9 1, 1 1, 1 0.9, 0.9 0.9, 0.9 1))
#> # ℹ 80 more rows
# calculate cost of the solution
r2 <- eval_cost_summary(p2, s2[, "solution_1"])
print(r2)
#> # A tibble: 1 × 2
#> summary cost
#> <chr> <dbl>
#> 1 overall 1811.
# manually calculate cost of the solution
r2_manual <- sum(s2$solution_1 * sim_pu_polygons$cost, na.rm = TRUE)
print(r2_manual)
#> [1] 1810.705
# build multi-zone conservation problem with polygon data
p3 <-
problem(
sim_zones_pu_polygons, sim_zones_features,
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 solution
print(s3)
#> Simple feature collection with 90 features and 9 fields
#> Geometry type: POLYGON
#> Dimension: XY
#> Bounding box: xmin: 0 ymin: 0 xmax: 1 ymax: 1
#> Projected CRS: Undefined Cartesian SRS
#> # A tibble: 90 × 10
#> cost_1 cost_2 cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
#> <dbl> <dbl> <dbl> <lgl> <lgl> <lgl> <dbl>
#> 1 216. 183. 205. FALSE FALSE FALSE 0
#> 2 213. 189. 210. FALSE FALSE FALSE 0
#> 3 207. 194. 215. TRUE FALSE FALSE 0
#> 4 209. 198. 219. FALSE FALSE FALSE 0
#> 5 214. 200. 221. FALSE FALSE FALSE 0
#> 6 214. 203. 225. FALSE FALSE FALSE 0
#> 7 211. 209. 223. FALSE FALSE FALSE 0
#> 8 210. 212. 222. TRUE FALSE FALSE 0
#> 9 204. 218. 214. FALSE FALSE FALSE 1
#> 10 213. 183. 206. FALSE FALSE FALSE 0
#> # ℹ 80 more rows
#> # ℹ 3 more variables: solution_1_zone_2 <dbl>, solution_1_zone_3 <dbl>,
#> # geom <POLYGON [m]>
# 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 cost of the solution
r3 <- eval_cost_summary(
p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
print(r3)
#> # A tibble: 4 × 2
#> summary cost
#> <chr> <dbl>
#> 1 overall 10137.
#> 2 zone_1 3595.
#> 3 zone_2 3151.
#> 4 zone_3 3390.
# }