spec_interp_area_targets: Specify targets based on interpolating area-based thresholds

In prioritizr: Systematic Conservation Prioritization in R

Specify targets based on interpolating area-based thresholds

Description

Specify targets by interpolating them between area-based thresholds. Briefly, this method involves (i) setting target thresholds for rare features to a particular percentage threshold, (ii) setting target thresholds for common features to a particular percentage threshold, and (iii) interpolating target thresholds for features with spatial distributions that range between the those for the rare and common features. Additionally, features can (optionally) have their targets capped at a particular threshold. This method is especially useful for setting targets based on interpolation procedures when features have data expressed as an area-based unit of measurement (e.g., km²). Note that this function is designed to be used with add_auto_targets() and add_group_targets().

Usage

spec_interp_area_targets(
  rare_area_threshold,
  rare_relative_target,
  rare_area_target,
  rare_method,
  common_area_threshold,
  common_relative_target,
  common_area_target,
  common_method,
  cap_area_target,
  interp_method,
  area_units
)

Arguments

rare_area_threshold	numeric value indicating the threshold area for identifying rare features. This value must be expressed in the same units as the feature data. In particular, features with a total spatial extent smaller than this value will be considered rare during the target setting calculations.
rare_relative_target	numeric value indicating the relative target for rare features. Note that this value must be a proportion between 0 and 1. For example, a value of 0.1 corresponds to 10%.
rare_area_target	numeric value denoting the area-based target for rare features. This value must be expressed in the same units as area_units. To avoid setting an area-based target for rare features, a missing (NA) value can be specified.
rare_method	character value indicating how the target for rare features should be calculated. Available options include "min" and "max". For example, a value of "max" means that the target for a rare features is calculated as the maximum based on rare_relative_target and rare_area_threshold. Note that rare_method will have no effect on the target calculations if rare_area_target is a missing (NA) value.
common_area_threshold	numeric value indicating the threshold area for identifying common features. This value must be expressed in the same units as area_units. In particular, features with a total spatial extent greater than this value will be considered common during the target setting calculations.
common_relative_target	numeric value denoting the relative target for common features. Note that this value must be a proportion between 0 and 1. For example, a value of 0.1 corresponds to 10%.
common_area_target	numeric value denoting the area-based target for common features. This value must be expressed in the same units as area_units. To avoid setting an area-based target for common features, a missing (NA) value can be specified.
common_method	character value indicating how the target for common features should be calculated. Available options include "min" and "max". For example, a value of "max" means that the target for a common feature is calculated as the maximum based on common_relative_target and common_area_threshold. Note that common_method will have no effect on the target calculations if common_area_target is a missing (NA) value.
cap_area_target	numeric value denoting the area-based target cap. This value must be expressed in the same units as area_units. In particular, all targets are clamped to this value during target setting calculations. To avoid setting a target cap, a missing (NA) value can be specified.
interp_method	character value denoting the interpolation method. Available options include "linear" for linear interpolation and "log10" for log-linear interpolation.
area_units	character value denoting the unit of measurement for the area-based arguments (e.g., ⁠"km^2", ⁠"ha"⁠, ⁠"acres"').

Details

This method has been applied to set target thresholds at global and national scales (e.g., Butchart et al. 2015; Rodrigues et al. 2004; Polak et al. 2015). It is based on the rationale that species with a smaller geographic distribution are at a greater risk of extinction, and so require a larger percentage of their geographic distribution to be represented by a prioritization (Rodrigues et al. 2004). When using this method in a planning exercise, it is important to ensure that the threshold parameters reflect the stakeholder objectives. Additionally, the threshold parameters may need to set according to the spatial extent of the planning region.

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().

Mathematical formulation

This method provides a flexible approach for setting target thresholds based on an interpolation procedure and the spatial extent of the features. To express this mathematically, we will define the following terminology. Let f denote the total spatial extent of a feature (e.g., geographic range size), a the threshold for identifying rare features (per rare_area_threshold and area_units), b the relative targets for rare features (per rare_relative_target), c the area-based targets for rare features (per rare_area_target and area_units), d() the function for calculating targets for rare features as a maximum or minimum value (per rare_method), e the threshold for identifying common features (per common_area_threshold and area_units), g the relative targets for common features (per common_relative_target), h the area-based targets for common features (per common_area_target and area_units), i() the method for calculating targets for common features as a maximum or minimum value (per common_method), and j the target cap (per cap_area_target and area_units), and k() the interpolation method for features with a spatial distribution that is larger than a rare features and smaller than a common feature (per interp_method). In particular, k() is either a linear or log-linear interpolation procedure based on the thresholds for identifying rare and common features as well as the relative targets for rare and common features. Given this terminology, the target threshold (t) for the feature is calculated as follows.

• If f < a, then t = min(d(c, b \times f), j).

• If f > e, then t = min(i(h, g \times f), j).

• If a \leq f \leq e, then t = min(k(f, a, b, e, g), j).

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.

Polak T, Watson JEM, Fuller RA, Joseph LN, Martin TG, Possingham HP, Venter O, Carwardine J (2015) Efficient expansion of global protected areas requires simultaneous planning for species and ecosystems. Royal Society Open Science, 2: 150107.

Rodrigues ASL, Akçakaya HR, Andelman SJ, Bakarr MI, Boitani L, Brooks TM, Chanson JS, Fishpool LDC, Da Fonseca GAB, Gaston KJ, Hoffmann M, Marquet PA, Pilgrim JD, Pressey RL, Schipper J, Sechrest W, Stuart SN, Underhill LG, Waller RW, Watts MEJ, Yan X (2004) Global gap analysis: priority regions for expanding the global protected-area network. BioScience, 54: 1092–1100.

See Also

Other target setting methods: spec_absolute_targets(), spec_area_targets(), spec_duran_targets(), spec_interp_absolute_targets(), spec_jung_targets(), spec_max_targets(), spec_min_targets(), spec_polak_targets(), spec_pop_size_targets(), spec_relative_targets(), spec_rl_ecosystem_targets(), spec_rl_species_targets(), spec_rodrigues_targets(), spec_rule_targets(), spec_ward_targets(), spec_watson_targets(), spec_wilson_targets()

Examples

## Not run: 
# 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()

# create problem with interpolated targets.
# here, targets will be set as 100% for features smaller than 1000 km^2
# in size, 10% for features greater than 250,000 km^2 in size,
# log-linearly interpolated for features with an intermediate range size,
# and capped at 1,000,000 km^2
p1 <-
  problem(sim_complex_pu_raster, sim_complex_features) %>%
  add_min_set_objective() %>%
  add_auto_targets(
    method = spec_interp_area_targets(
     rare_area_threshold = 1000,
     rare_relative_target = 1,
     rare_area_target = NA,            # not used
     rare_method = "max",              # not used
     common_area_threshold = 250000,
     common_relative_target = 0.1,
     common_area_target = NA,          # not used
     common_method = "max",            # not used
     cap_area_target = 1000000,
     interp_method = "log10",
     area_units = "km^2"
    )
  ) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problem
s1 <- solve(p1)

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

## End(Not run)

prioritizr documentation built on Nov. 10, 2025, 5:07 p.m.