Specify targets following a set of rules

Specify targets based on a set of rules for ecological and ecosystem criteria. This is a customizable version of the approach in Harris and Holness (2023). To help prevent widespread features from obscuring priorities, targets are capped following Butchart et al. (2015). This method was designed to help set targets for a broad range of features (e.g., species, ecosystems, ecosystem services, ecological processes) at local and national scales. Note that this function is designed to be used with add_auto_targets() and add_group_targets().

Usage

spec_rule_targets(
  baseline_relative_target,
  rules_relative_target,
  data,
  cap_area_target = 1e+06,
  area_units = "km^2"
)

Arguments

baseline_relative_target: numeric value indicating the baseline target values as a proportion (ranging between 0 and 1). Depending on context of the prioritization exercise, a value of 0.3 (i.e., 30%) may be appropriate (Harris et al. 2023).
rules_relative_target: named numeric vector with name-value key pairs denoting the values that should be added together when calculating the relative target for a given feature. Note that values must range between -1 and 1, and the names must correspond to column names of data.
data: data.frame indicating if each feature meets the criteria for applying each rule (or not) during the target calculations. Here, each row must correspond to a different feature, and each column contains information about the feature (per feature_names(x)). In particular, data must have a "feature" column that contains character values with the feature names. Additionally, data must also contain columns with logical (TRUE/FALSE) values that indicate if the feature meets a particular criterion for calculating targets. For example, data could contain columns that indicate if each feature corresponds to a threatened species, ecosystem service, or culturally important site. Note that if different rules should be applied to species based on their particular threat status (e.g., Critically Endangered and Vulnerable species should receive different target thresholds), then data should contain a column for each threat status (separately).
cap_area_target: numeric value denoting the area-based target cap. To avoid setting a target cap, a missing (NA) value can be specified. Defaults to 1000000 (i.e., 1,000,000 km²).
area_units: character value denoting the unit of measurement for the area-based arguments. Defaults to "km^2" (i.e., km²).

Value

An object (TargetMethod) for specifying targets that can be used with add_auto_targets() and add_group_targets() to add targets to a problem().

Details

This method has been applied to set target thresholds at national scales (e.g., Harris et al. 2023). It may also be especially useful for local scales. It is based on the rationale that it is appropriate to set the target for a feature based on a linear combination of values. When using this method in a planning exercise, it is important to ensure that the criteria and values used to parameterize the rules reflect the stakeholder objectives. Additionally, the baseline relative target (per baseline_relative_target) and cap threshold (per cap_area_target and area_units) may need to set based on the features and spatial extent of the planning region. Please note that this function is provided as convenient method to set targets for problems with a single management zone, and cannot be used for those with multiple management zones.

Mathematical formulation

This method provides a flexible approach for setting target thresholds based on a set of rules. To express this mathematically, we will define the following terminology. Let $f$ denote the total abundance of a feature (e.g., geographic range), $b$ denote the baseline relative target threshold (per baseline_relative_target), and let $c$ denote the cap threshold (per cap_area_target and area_units). To describe the rules, let $U$ denote the set of rules (indexed by $u$), $d_u$ indicate if the target for the feature should be calculated based on each rule $u \in U$ (using binary values, per data), and $a_u$ denote the value that should be added to the target given each rule $u \in U$ (per rules_relative_target). Given this terminology, the target threshold ($t$) for the feature is calculated as follows. $$ t = min(f \times max(min(b + \sum_{u \in U} d_u \times a_u, 1), 0), c) $$

Data calculations

This function involves calculating targets based on the spatial extent of the features in x. Although it can be readily applied to problem() objects that have the feature data provided as a terra::rast() object, you will need to specify the spatial units for the features when initializing the problem() objects if the feature data are provided in a different format. In particular, if the feature data are provided as a data.frame or character vector, then you will need to specify an argument to feature_units when using the problem() function. See the Examples section of the documentation for add_auto_targets() for a demonstration of specifying the spatial units for features.

References

Butchart SHM, Clarke M, Smith RJ, Sykes RE, Scharlemann JPW, Harfoot M, Buchanan GM, Angulo A, Balmford A, Bertzky B, Brooks TM, Carpenter KE, Comeros‐Raynal MT, Cornell J, Ficetola GF, Fishpool LDC, Fuller RA, Geldmann J, Harwell H, Hilton‐Taylor C, Hoffmann M, Joolia A, Joppa L, Kingston N, May I, Milam A, Polidoro B, Ralph G, Richman N, Rondinini C, Segan DB, Skolnik B, Spalding MD, Stuart SN, Symes A, Taylor J, Visconti P, Watson JEM, Wood L, Burgess ND (2015) Shortfalls and solutions for meeting national and global conservation area targets. Conservation Letters, 8: 329–337.

Harris LR, Holness SD (2023) A practical approach to setting heuristic marine biodiversity targets for systematic conservation planning. Biological Conservation, 285: 110218.

Examples

# \dontrun{
# set seed for reproducibility
set.seed(500)

# load data
sim_complex_pu_raster <- get_sim_complex_pu_raster()
sim_complex_features <- get_sim_complex_features()

# calculate total distribution size for features in km^2
feature_size <- as.numeric(units::set_units(
  units::set_units(
    terra::global(sim_complex_features, "sum", na.rm = TRUE)[[1]] *
      prod(terra::res(sim_complex_features)),
    "m^2"
  ),
  "km^2"
))

# simulate data that provide additional information for each feature
rule_data <- tibble::tibble(feature = names(sim_complex_features))

# add a column indicating if each feature has a small distribution,
rule_data$small_distribution <- feature_size <= 1000

# add a column indicating if each feature has a large distribution,
rule_data$large_distribution <- feature_size >= 5000

# add a column indicating if each feature has low quality data
# associated with it, based on random simulated values
rule_data$low_quality <- sample(
  c(TRUE, FALSE), terra::nlyr(sim_complex_features),
  replace = TRUE, prob = c(0.2, 0.8)
)

# next, we will add simulate dat for columns indicating the threat status of
# the features. since all columns must contain logical (TRUE/FALSE) values,
# we will add a column for each threat status separately. note that these
# values will be simulated such that a feature will only have a value of
# TRUE for, at most, a single threat status

# add a column indicating if each feature has a Vulnerable threat status
rule_data$vulnerable <- sample(
  c(TRUE, FALSE), terra::nlyr(sim_complex_features),
  replace = TRUE, prob = c(0.3, 0.7)
)

# add a column indicating if each feature has an Endangered threat status,
# based on random simulated values
rule_data$endangered <- sample(
  c(TRUE, FALSE), terra::nlyr(sim_complex_features),
  replace = TRUE, prob = c(0.3, 0.7)
) & !rule_data$vulnerable

# add a column indicating if each feature has a Critically Endangered threat
# status, based on random simulated values
rule_data$critically_endangered <- sample(
  c(TRUE, FALSE), terra::nlyr(sim_complex_features),
  replace = TRUE, prob = c(0.3, 0.7)
) & !rule_data$endangered & !rule_data$vulnerable

# preview rule data
print(rule_data)
#> # A tibble: 100 × 7
#>    feature    small_distribution large_distribution low_quality vulnerable
#>    <chr>      <lgl>              <lgl>              <lgl>       <lgl>     
#>  1 feature_1  FALSE              TRUE               TRUE        TRUE      
#>  2 feature_2  FALSE              TRUE               FALSE       FALSE     
#>  3 feature_3  FALSE              TRUE               TRUE        TRUE      
#>  4 feature_4  FALSE              TRUE               FALSE       FALSE     
#>  5 feature_5  FALSE              TRUE               TRUE        TRUE      
#>  6 feature_6  FALSE              TRUE               FALSE       TRUE      
#>  7 feature_7  FALSE              TRUE               FALSE       FALSE     
#>  8 feature_8  FALSE              TRUE               TRUE        FALSE     
#>  9 feature_9  FALSE              TRUE               TRUE        TRUE      
#> 10 feature_10 FALSE              TRUE               FALSE       FALSE     
#> # ℹ 90 more rows
#> # ℹ 2 more variables: endangered <lgl>, critically_endangered <lgl>

# create problem with rule based targets, wherein targets are calculated
# with a baseline of 30%, features with a small distribution are assigned
# targets of an additional 10%, features with a large distribution are
# assigned targets reduced by 10%, features with low quality data are
# assigned targets reduced by 10%, features with a Vulnerable threat status
# are assigned targets of an additional 5%, features with an Endangered
# threat status are assigned targets of an additional 10%, and features with
# a Critically Endangered threat status are assigned targets of an
# additional 20%
p1 <-
  problem(sim_complex_pu_raster, sim_complex_features) %>%
  add_min_set_objective() %>%
  add_auto_targets(
    method = spec_rule_targets(
      baseline_relative_target = 0.3,
      rules_relative_target = c(
        "small_distribution" = 0.1,
        "large_distribution" = -0.1,
        "low_quality" = -0.1,
        "vulnerable" = 0.05,
        "endangered" = 0.1,
        "critically_endangered" = 0.2
      ),
      data = rule_data
    )
  ) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problem
s1 <- solve(p1)

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

# }