Compares observed and simulated emergent space use with empirical grid utilization distributions and the 1-Wasserstein distance between those discretized empirical distributions. This is not a kernel density estimate and should not be interpreted as the exact Wasserstein distance between continuous utilization distributions. The observed statistic is the mean Wasserstein distance between the observed grid UD and each simulated grid UD. Simulated reference statistics are leave-one-out mean simulation-to-simulation Wasserstein distances. Computation increases with the number of occupied grid cells and with pairwise comparisons among simulated tracks.
Arguments
- observed
Observed track-like object.
- simulated
A list of simulated track-like objects or a data frame with a simulation identifier column.
- grid_size
Integer scalar or length-two integer vector giving the number of grid cells in the x and y directions.
- bounds
Optional named numeric vector with
xmin,xmax,ymin, andymax. IfNULL, bounds are computed from observed and simulated tracks. If supplied, the bounds must contain all observed and simulated track coordinates. Coordinate units should be meaningful Euclidean distance units.- ...
Passed to
as_gmov_simulations().
Value
A list with observed and simulated empirical grid UDs, Wasserstein distances between those grid UDs, discrepancy statistics, and a Monte Carlo rank test.
References
Nicosia, A. (2026). Beyond the next step: A multi-criteria generative validation framework for step selection functions. Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210x.70313
Examples
observed <- data.frame(x = c(0, 1, 1), y = c(0, 0, 1))
simulated <- list(
data.frame(x = c(0, 1, 2), y = c(0, 0, 0)),
data.frame(x = c(0, 0, 1), y = c(0, 1, 1))
)
validate_ud(observed, simulated, grid_size = 4)
#> gmov utilization distribution diagnostic
#> Method: empirical_grid_wasserstein
#> Simulated tracks: 2
#> Statistic: 0.3586
#> Monte Carlo p-value: 1.000
#> Alternative: greater