Provides the maximum values of benefits to achieve for each feature given a set of data inputs.
getPotentialBenefit(x)data-class object.
For a given feature \(s\), let \(I_s\) be the set of planning units associated with \(s\), let \(r_{is}\) is the amount of feature \(s\) in planning unit \(i\), let \(K_{s}\) be the set of threats associated with \(s\), and let \(K_{i}\) be the set of threats associated with \(i\). The local benefit associated with \(s\) in a unit \(i\) is given by:
$$ b_{is} = p_{is} r_{is} \\ b_{is} = \frac{ \sum_{k \in K_i \cap K_s}{x_{ik}}}{|K_i \cap K_s|} r_{is} $$
Where \(x_{ik}\) is a decision variable such that \(x_{ik} = 1\) if an action againts threat \(k\) is applied in unit \(i\), and \(x_{ik} = 0\), otherwise. This expression for the probability of persistence of the feature (\(p_{is}\)) is defined only for the cases where we work with values of binary intensities (presence or absence of threats). See the sensitivities vignette to know the work with continuous intensities.
While the total benefit is calculated as the sum of the local benefits per feature:
$$ b_{s} = \sum_{i \in I_{s}}\frac{ \sum_{k \in K_i \cap K_s}{x_{ik}}}{|K_i \cap K_s|} r_{is} $$
Since the potential benefit is being calculated, all variables \(x_{ik}\) are assumed to be equal
to 1; that is, all possible actions are carried out, and only those that have a lock-out
status are kept out of the planning (see inputData() function for more information).
# set seed for reproducibility
set.seed(14)
## Load data
data(sim_pu_data, sim_features_data, sim_dist_features_data,
sim_threats_data, sim_dist_threats_data, sim_sensitivity_data,
sim_boundary_data)
## Create data instance
problem_data <- inputData(
pu = sim_pu_data, features = sim_features_data, dist_features = sim_dist_features_data,
threats = sim_threats_data, dist_threats = sim_dist_threats_data,
sensitivity = sim_sensitivity_data, boundary = sim_boundary_data
)
## Get maximum benefits to obtain
getPotentialBenefit(problem_data)
#> feature dist dist_threatened maximum.conservation.benefit
#> 1 1 47 47 0
#> 2 2 30 28 2
#> 3 3 66 56 10
#> 4 4 33 33 0
#> maximum.recovery.benefit maximum.benefit
#> 1 47 47
#> 2 28 30
#> 3 56 66
#> 4 33 33