Evaluate target coverage by solution

Calculate how well feature representation targets are met by a solution to a conservation planning problem. It is useful for understanding if features are adequately represented by a solution. Note that this function can only be used with problems that contain targets.

Usage

eval_target_coverage_summary(
  x,
  solution,
  include_zone = number_of_zones(x) > 1,
  include_sense = number_of_zones(x) > 1
)

# S3 method for class 'ConservationProblem'
eval_target_coverage_summary(
  x,
  solution,
  include_zone = number_of_zones(x) > 1,
  include_sense = number_of_zones(x) > 1
)

# S3 method for class 'MultiConservationProblem'
eval_target_coverage_summary(
  x,
  solution,
  include_zone = number_of_zones(x) > 1,
  include_sense = number_of_zones(x) > 1
)

Arguments

x: problem() or multi_problem() object.
solution: numeric, matrix, data.frame, terra::rast(), or sf::sf() object. Note that solution must have the same format as the planning unit data in x. See the Solution format section for more information.
include_zone: logical value indicating if the returned object should contain a zone column? Defaults to TRUE if x has multiple zones.
include_sense: logical value indicating if the returned object should contain a sense column? Defaults to TRUE if x has multiple zones.

Value

A tibble::tibble() object. Here, each row provides information for a different target. It contains the following columns.

problem: character name of problem. Note that this column is only present if x is a multi_problem() object.
feature: character name of the feature associated with each target.
zone: list of character zone names associated with each target. This column is in a list-column format because a single target can correspond to multiple zones (see add_manual_targets() for details and examples). For an example of converting the list-column format to a standard character column format, please see the Examples section. This column is only included if include_zones = TRUE.
sense: character sense associated with each target. Sense values specify the nature of the target. Typically (e.g., when using the add_absolute_targets() or add_relative_targets() functions), targets are specified using sense values indicating that the total amount of a feature held within a solution (ideally) be greater than or equal to a threshold amount (i.e., a sense value of ">="). Additionally, targets (i.e., using the add_manual_targets() function) can also be specified using sense values indicating that the total amount of a feature held within a solution must be equal to a threshold amount (i.e., a sense value of "=") or smaller than or equal to a threshold amount (i.e., a sense value of "<="). This column is only included if include_sense = TRUE.
met: logical indicating if each target is met by the solution. This column is calculated by checking if the total shortfall associated with each target (i.e., "absolute_shortfall" column) is equal to zero.
total_amount: numeric total amount of the feature available across the entire conservation planning problem for meeting each target (not just planning units selected within the solution). If x has a single zone, then this column is calculated as the sum of all of the values for a given feature (similar to values in the total_amount column produced by the eval_feature_representation_summary() function). Otherwise, if x has multiple zones, then this column is calculated as the sum of the values for the feature associated with target (per the "feature" column), across the zones associated with the target (per the "zone" column).
absolute_target: numeric total threshold amount associated with each target.
absolute_held: numeric total amount held within the solution for the feature and (if relevant) zones associated with each target (per the "feature" and "zone" columns, respectively). This column is calculated as the sum of the feature data, supplied when creating a problem() object (e.g., presence/absence values), weighted by the status of each planning unit in the solution (e.g., selected or not for prioritization).
absolute_shortfall: numeric total amount by which the solution fails to meet each target. This column is calculated as the difference between the total amount held within the solution for the feature and (if relevant) zones associated with the target (i.e., "absolute_held" column) and the target total threshold amount (i.e., "absolute_target" column), with values set to zero depending on the sense specified for the target (e.g., if the target sense is >= then the difference is set to zero if the value in the "absolute_held" is smaller than that in the "absolute_target" column).
relative_target: numeric proportion threshold amount associated with each target. This column is calculated by dividing the total threshold amount associated with each target (i.e., "absolute_target" column) by the total amount associated with each target (i.e., "total_amount" column).
relative_held: numeric proportion held within the solution for the feature and (if relevant) zones associated with each target (per the "feature" and "zone" columns, respectively). This column is calculated by dividing the total amount held for each target (i.e., "absolute_held" column) by the total amount for with each target (i.e., "total_amount" column). Since this metric is only appropriate for describing how well a solution meets targets that have a ">=" sense, targets with a "<=" or "=" sense are assigned missing (NA) values in this column.
relative_shortfall: numeric proportion by which the solution fails to meet each target. This column is calculated by dividing the total shortfall for each target (i.e., "absolute_shortfall" column) by the total threshold amount associated with each target (i.e., "absolute_target" column).
relative_met: numeric proportion of the target that is fulfilled by the solution. This column is calculated by expressing the amount held by the solution (i.e., "absolute_held" column) as a fraction of the target threshold. Since this metric is only appropriate for describing how well a solution meets targets that have a ">=" sense, targets with a "<=" or "=" sense are assigned missing (NA) values in this column.

Notes

In prior versions (< 8.0.6.7), this function calculated the relative shortfall for a target by dividing the total shortfall for the target (i.e., "absolute_shortfall" column) by the total amount associated with each target (i.e., "total_amount" column). This was subsequently changed to ensure consistency with the minimum shortfall objective (add_min_shortfall_objective()).

Solution format

Broadly speaking, solution must be in the same format as the planning unit data in x. Further details on the correct format are listed separately for each of the different planning unit data formats.

x has numeric planning units: Here 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 x. Additionally, any planning units with missing cost (NA) values should also have missing (NA) values in the solution.
x has matrix planning units: Here 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 x. Additionally, any planning units with missing cost (NA) values for a particular zone should also have a missing (NA) values in solution.
x has terra::rast() planning units: Here solution be a terra::rast() object where different cells 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 x. Additionally, any planning units with missing cost (NA) values for a particular zone should also have missing (NA) values in solution.
x has data.frame planning units: Here 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 with missing cost (NA) values for a particular zone should also have missing (NA) values in solution.
x has sf::sf() planning units: Here 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, solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units with missing cost (NA) values for a particular zone should also have missing (NA) values in solution.

Examples

# 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
#> size        : 10, 10, 1  (nrow, ncol, nlyr)
#> resolution  : 0.1, 0.1  (x, y)
#> extent      : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
#> coord. ref. : WGS 84 / Pseudo-Mercator (EPSG:3857)
#> source(s)   : memory
#> varname     : sim_pu_raster
#> name        : layer
#> min value   :     0
#> max value   :     1

# plot solution
plot(s1, main = "solution", axes = FALSE)


# calculate target coverage by the solution
r1 <- eval_target_coverage_summary(p1, s1)
print(r1, width = Inf) # note: `width = Inf` tells R to print all columns
#> # A tibble: 5 × 10
#>   feature   met   total_amount absolute_target absolute_held absolute_shortfall
#>   <chr>     <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
#> 1 feature_1 TRUE          83.3            8.33          8.91                  0
#> 2 feature_2 TRUE          31.2            3.12          3.13                  0
#> 3 feature_3 TRUE          72.0            7.20          7.34                  0
#> 4 feature_4 TRUE          42.7            4.27          4.35                  0
#> 5 feature_5 TRUE          56.7            5.67          6.01                  0
#>   relative_target relative_held relative_shortfall relative_met
#>             <dbl>         <dbl>              <dbl>        <dbl>
#> 1             0.1         0.107                  0            1
#> 2             0.1         0.100                  0            1
#> 3             0.1         0.102                  0            1
#> 4             0.1         0.102                  0            1
#> 5             0.1         0.106                  0            1

# 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)

# 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
#> Projected CRS: WGS 84 / Pseudo-Mercator
#> # A tibble: 6 × 5
#>    cost locked_in locked_out solution_1                                 geometry
#>   <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 1…
#> 3  207. FALSE     FALSE               0 ((0.2 1, 0.3 1, 0.3 0.9, 0.2 0.9, 0.2 1…
#> 4  209. FALSE     TRUE                0 ((0.3 1, 0.4 1, 0.4 0.9, 0.3 0.9, 0.3 1…
#> 5  214. FALSE     FALSE               0 ((0.4 1, 0.5 1, 0.5 0.9, 0.4 0.9, 0.4 1…
#> 6  214. FALSE     FALSE               0 ((0.5 1, 0.6 1, 0.6 0.9, 0.5 0.9, 0.5 1…

# plot solution
plot(s2[, "solution_1"])


# calculate target coverage by the solution
r2 <- eval_target_coverage_summary(p2, s2[, "solution_1"])
print(r2, width = Inf)
#> # A tibble: 5 × 10
#>   feature   met   total_amount absolute_target absolute_held absolute_shortfall
#>   <chr>     <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
#> 1 feature_1 TRUE          74.5            7.45          8.05                  0
#> 2 feature_2 TRUE          28.1            2.81          2.83                  0
#> 3 feature_3 TRUE          64.9            6.49          6.65                  0
#> 4 feature_4 TRUE          38.2            3.82          3.87                  0
#> 5 feature_5 TRUE          50.7            5.07          5.41                  0
#>   relative_target relative_held relative_shortfall relative_met
#>             <dbl>         <dbl>              <dbl>        <dbl>
#> 1             0.1         0.108                  0            1
#> 2             0.1         0.101                  0            1
#> 3             0.1         0.103                  0            1
#> 4             0.1         0.101                  0            1
#> 5             0.1         0.107                  0            1

# 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: WGS 84 / Pseudo-Mercator
#> # 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                    0
#> 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>,
#> #   geometry <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 target coverage by the solution
r3 <- eval_target_coverage_summary(
  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
print(r3, width = Inf)
#> # A tibble: 15 × 12
#>    feature   zone      sense met   total_amount absolute_target absolute_held
#>    <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
#>  1 feature_1 <chr [1]> >=    TRUE          75.1           13.8          15.2 
#>  2 feature_2 <chr [1]> >=    TRUE          28.0            4.82          5.14
#>  3 feature_3 <chr [1]> >=    TRUE          65.0           12.8          13.6 
#>  4 feature_4 <chr [1]> >=    TRUE          38.0            5.58          5.94
#>  5 feature_5 <chr [1]> >=    TRUE          51.2            9.27          9.90
#>  6 feature_1 <chr [1]> >=    TRUE          75.1            9.06         14.3 
#>  7 feature_2 <chr [1]> >=    TRUE          28.0            4.23          5.46
#>  8 feature_3 <chr [1]> >=    TRUE          65.0           12.5          13.1 
#>  9 feature_4 <chr [1]> >=    TRUE          38.0            6.96          7.31
#> 10 feature_5 <chr [1]> >=    TRUE          51.2            8.76          9.19
#> 11 feature_1 <chr [1]> >=    TRUE          75.1            9.63         14.0 
#> 12 feature_2 <chr [1]> >=    TRUE          28.0            5.29          5.63
#> 13 feature_3 <chr [1]> >=    TRUE          65.0           11.5          12.1 
#> 14 feature_4 <chr [1]> >=    TRUE          38.0            4.43          7.23
#> 15 feature_5 <chr [1]> >=    TRUE          51.2            8.86          9.50
#>    absolute_shortfall relative_target relative_held relative_shortfall
#>                 <dbl>           <dbl>         <dbl>              <dbl>
#>  1                  0           0.183         0.202                  0
#>  2                  0           0.173         0.184                  0
#>  3                  0           0.198         0.210                  0
#>  4                  0           0.147         0.156                  0
#>  5                  0           0.181         0.193                  0
#>  6                  0           0.121         0.191                  0
#>  7                  0           0.151         0.195                  0
#>  8                  0           0.193         0.202                  0
#>  9                  0           0.183         0.192                  0
#> 10                  0           0.171         0.180                  0
#> 11                  0           0.128         0.186                  0
#> 12                  0           0.189         0.201                  0
#> 13                  0           0.176         0.186                  0
#> 14                  0           0.116         0.190                  0
#> 15                  0           0.173         0.186                  0
#>    relative_met
#>           <dbl>
#>  1            1
#>  2            1
#>  3            1
#>  4            1
#>  5            1
#>  6            1
#>  7            1
#>  8            1
#>  9            1
#> 10            1
#> 11            1
#> 12            1
#> 13            1
#> 14            1
#> 15            1

# create a new column with character values containing the zone names,
# by extracting these data out of the zone column
# (which is in list-column format)
r3$zone2 <- vapply(r3$zone, FUN.VALUE = character(1), paste, sep = " & ")

# print r3 again to show the new column
print(r3, width = Inf)
#> # A tibble: 15 × 13
#>    feature   zone      sense met   total_amount absolute_target absolute_held
#>    <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
#>  1 feature_1 <chr [1]> >=    TRUE          75.1           13.8          15.2 
#>  2 feature_2 <chr [1]> >=    TRUE          28.0            4.82          5.14
#>  3 feature_3 <chr [1]> >=    TRUE          65.0           12.8          13.6 
#>  4 feature_4 <chr [1]> >=    TRUE          38.0            5.58          5.94
#>  5 feature_5 <chr [1]> >=    TRUE          51.2            9.27          9.90
#>  6 feature_1 <chr [1]> >=    TRUE          75.1            9.06         14.3 
#>  7 feature_2 <chr [1]> >=    TRUE          28.0            4.23          5.46
#>  8 feature_3 <chr [1]> >=    TRUE          65.0           12.5          13.1 
#>  9 feature_4 <chr [1]> >=    TRUE          38.0            6.96          7.31
#> 10 feature_5 <chr [1]> >=    TRUE          51.2            8.76          9.19
#> 11 feature_1 <chr [1]> >=    TRUE          75.1            9.63         14.0 
#> 12 feature_2 <chr [1]> >=    TRUE          28.0            5.29          5.63
#> 13 feature_3 <chr [1]> >=    TRUE          65.0           11.5          12.1 
#> 14 feature_4 <chr [1]> >=    TRUE          38.0            4.43          7.23
#> 15 feature_5 <chr [1]> >=    TRUE          51.2            8.86          9.50
#>    absolute_shortfall relative_target relative_held relative_shortfall
#>                 <dbl>           <dbl>         <dbl>              <dbl>
#>  1                  0           0.183         0.202                  0
#>  2                  0           0.173         0.184                  0
#>  3                  0           0.198         0.210                  0
#>  4                  0           0.147         0.156                  0
#>  5                  0           0.181         0.193                  0
#>  6                  0           0.121         0.191                  0
#>  7                  0           0.151         0.195                  0
#>  8                  0           0.193         0.202                  0
#>  9                  0           0.183         0.192                  0
#> 10                  0           0.171         0.180                  0
#> 11                  0           0.128         0.186                  0
#> 12                  0           0.189         0.201                  0
#> 13                  0           0.176         0.186                  0
#> 14                  0           0.116         0.190                  0
#> 15                  0           0.173         0.186                  0
#>    relative_met zone2 
#>           <dbl> <chr> 
#>  1            1 zone_1
#>  2            1 zone_1
#>  3            1 zone_1
#>  4            1 zone_1
#>  5            1 zone_1
#>  6            1 zone_2
#>  7            1 zone_2
#>  8            1 zone_2
#>  9            1 zone_2
#> 10            1 zone_2
#> 11            1 zone_3
#> 12            1 zone_3
#> 13            1 zone_3
#> 14            1 zone_3
#> 15            1 zone_3