Calculates spatial availability, an accessibility measured proposed by Soukhov et al. (2023) that takes into account competition effects. The accessibility levels that result from using this measure are proportional both to the demand in each origin and to the travel cost it takes to reach the destinations.

This function is generic over any kind of numeric travel cost, such as distance, time and money.

  alpha = 1,
  group_by = character(0),
  fill_missing_ids = TRUE,
  detailed_results = FALSE



A data frame. The travel matrix describing the costs (i.e. travel time, distance, monetary cost, etc.) between the origins and destinations in the study area. Must contain the columns from_id, to_id and any others specified in travel_cost.


A data frame. The distribution of opportunities within the study area cells. Must contain the columns id and any others specified in opportunity.


A string. The name of the column in land_use_data with the number of opportunities/resources/services to be considered when calculating accessibility levels.


A string. The name of the column in travel_matrix with the travel cost between origins and destinations.


A string. The name of the column in land_use_data with the number of people in each origin that will be considered potential competitors.


A fuction that converts travel cost into an impedance factor used to weight opportunities. This function should take a numeric vector and also return a numeric vector as output, with the same length as the input. For convenience, the package currently includes the following functions: decay_binary(), decay_exponential(), decay_power() and decay_stepped(). See the documentation of each decay function for more details.


A numeric. A parameter used to modulate the effect of demand by population. When less than 1, opportunities are allocated more rapidly to smaller centers relative to larger ones; values higher than 1 achieve the opposite effect.


A character vector. When not character(0) (the default), indicates the travel_matrix columns that should be used to group the accessibility estimates by. For example, if travel_matrix includes a departure time column, that specifies the departure time of each entry in the data frame, passing "departure_time" to this parameter results in accessibility estimates grouped by origin and by departure time.


A logical. When calculating grouped accessibility estimates (i.e. when by_col is not NULL), some combinations of groups and origins may be missing. For example, if a single trip can depart from origin A at 7:15am and reach destination B within 55 minutes, but no trips departing from A at 7:30am can be completed at all, this second combination will not be included in the output. When TRUE (the default), the function identifies which combinations would be left out and fills their respective accessibility values with 0, which incurs in a performance penalty.


A logical. Whether to return spatial availability results aggregated by origin-destination pair (TRUE) or by origin (FALSE, the default). When TRUE, the output also includes the demand, impedance and combined balancing factors used to calculate spatial availability. Please note that the argument fill_missing_ids does not affect the output when detailed_results is TRUE.


A data frame containing the accessibility estimates for each origin/destination (depending if active is TRUE or FALSE) in the travel matrix.


Soukhov A, Páez A, Higgins CD, Mohamed M (2023). “Introducing Spatial Availability, a Singly-Constrained Measure of Competitive Accessibility.” PLOS ONE, 18(1), e0278468. ISSN 1932-6203, doi:10.1371/journal.pone.0278468 .


# the example below is based on Soukhov et al. (2023) paper

travel_matrix <- data.table::data.table(
  from_id = rep(c("A", "B", "C"), each = 3),
  to_id = as.character(rep(1:3, 3)),
  travel_time = c(15, 30, 100, 30, 15, 100, 100, 100, 15)
land_use_data <- data.table::data.table(
  id = c("A", "B", "C", "1", "2", "3"),
  population = c(50000, 150000, 10000, 0, 0, 0),
  jobs = c(0, 0, 0, 100000, 100000, 10000)

df <- spatial_availability(
  opportunity = "jobs",
  travel_cost = "travel_time",
  demand = "population",
  decay_function = decay_exponential(decay_value = 0.1)
#>        id       jobs
#>    <char>      <num>
#> 1:      A  66833.466
#> 2:      B 133203.363
#> 3:      C   9963.171

detailed_df <- spatial_availability(
  opportunity = "jobs",
  travel_cost = "travel_time",
  demand = "population",
  decay_function = decay_exponential(decay_value = 0.1),
  detailed_results = TRUE
#>    from_id  to_id demand_bal_fac impedance_bal_fac combined_bal_fac
#>     <char> <char>          <num>             <num>            <num>
#> 1:       A      1     0.23809524      0.8174384949     5.990064e-01
#> 2:       A      2     0.23809524      0.1823951823     6.922691e-02
#> 3:       A      3     0.23809524      0.0002033856     1.013219e-03
#> 4:       B      1     0.71428571      0.1823951823     4.009692e-01
#> 5:       B      2     0.71428571      0.8174384949     9.307605e-01
#> 6:       B      3     0.71428571      0.0002033856     3.039656e-03
#> 7:       C      1     0.04761905      0.0001663229     2.437577e-05
#> 8:       C      2     0.04761905      0.0001663229     1.262535e-05
#> 9:       C      3     0.04761905      0.9995932288     9.959471e-01
#>            jobs
#>           <num>
#> 1: 59900.642536
#> 2:  6922.691048
#> 3:    10.132187
#> 4: 40096.919886
#> 5: 93076.046417
#> 6:    30.396561
#> 7:     2.437577
#> 8:     1.262535
#> 9:  9959.471253