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Generative validation of SSF / iSSF models

Source: vignettes/generative-validation-ssf.Rmd
generative-validation-ssf.Rmd

Motivation

Step-selection functions (SSFs) and integrated step-selection analyses (iSSAs) are usually fitted to local, one-step movement decisions. A model can therefore look satisfactory at the scale at which it was fitted while still generating unrealistic trajectories when it is iterated forward. Generative validation asks a direct question: if we simulate full trajectories from the fitted model, do the simulated tracks reproduce important trajectory-level patterns in the observed track?

Nicosia (2026) proposes a multi-criteria framework with four complementary pillars:

  1. Emergent space use, comparing observed and simulated utilization distributions.
  2. Diffusion behavior, comparing mean squared displacement (MSD) curves.
  3. Path structure, comparing path straightness or sinuosity.
  4. Barrier interactions, comparing intersections with a known linear barrier.

gmov implements these diagnostics for observed and simulated tracks. It is designed to sit after a modelling workflow such as amt: users fit an SSF or iSSF, simulate replicate tracks, and then pass those tracks to gmov.

Red deer empirical example

The empirical application in Nicosia (2026) uses the red deer trajectory and forest raster distributed with amt (Signer, Fieberg, and Avgar, 2019). The article fits a standard iSSA to a GPS-tracked red deer from northern Germany, using a 6-hour sampling interval, a binary forest covariate, and a 1:25 used-to-available step design. The fitted model includes forest selection and movement-kernel terms:

case_ ~ forest + sl_ + log_sl + cos_ta + strata(step_id_)

Because the empirical example does not specify a known barrier geometry, the article evaluates the first three pillars: emergent space use, MSD, and sinuosity.

This vignette ships a compact, precomputed version of that red deer validation example so that the vignette renders with visible results on installation and on GitHub. The object contains the observed red deer track, 99 simulated tracks from the empirical iSSA workflow used in the article, and the scorecard reported by that workflow. The full amt fitting code is shown later for context.

Load the validation ensemble 

data("red_deer_gmov", package = "gmov")

observed_track <- red_deer_gmov$observed_track
simulated_tracks <- red_deer_gmov$simulated_tracks

data.frame(
  observed_locations = nrow(observed_track),
  observed_steps = nrow(observed_track) - 1,
  simulated_tracks = length(simulated_tracks),
  simulated_locations_min = min(vapply(simulated_tracks, nrow, integer(1))),
  simulated_locations_max = max(vapply(simulated_tracks, nrow, integer(1)))
)
#>   observed_locations observed_steps simulated_tracks simulated_locations_min
#> 1                823            822               99                     823
#>   simulated_locations_max
#> 1                     823

The table below is the scorecard from the empirical workflow in Nicosia (2026). It is included as provenance for the precomputed simulation ensemble.

red_deer_gmov$article_scorecard
#>        Pillar      Metric     Observed P_Value       Result
#> 1 1. Topology Wasserstein 5.323038e+03    0.68 NOT REJECTED
#> 2 2. Dynamics   MSD (ISE) 3.229350e+10    0.04     REJECTED
#> 3 3. Behavior   Sinuosity 8.052233e-03    0.17 NOT REJECTED

The article reports a pattern of partial generative realism: the fitted iSSA reproduces broad space-use and path straightness, but shows a detectable mismatch in displacement dynamics.

Observed and simulated trajectories

The observed trajectory is shown in orange. A subset of the 99 simulated trajectories is shown in blue to keep the plot readable.

plot_sims <- simulated_tracks[seq_len(25)]
plot_sims_df <- do.call(
  rbind,
  Map(
    function(track, id) {
      data.frame(sim_id = id, x_ = track$x_, y_ = track$y_)
    },
    plot_sims,
    seq_along(plot_sims)
  )
)

ggplot2::ggplot() +
  ggplot2::geom_path(
    data = plot_sims_df,
    ggplot2::aes(x = x_, y = y_, group = sim_id),
    color = col_sim,
    alpha = 0.45,
    linewidth = 0.25
  ) +
  ggplot2::geom_path(
    data = observed_track,
    ggplot2::aes(x = x_, y = y_),
    color = col_obs,
    linewidth = 0.8
  ) +
  ggplot2::coord_equal() +
  ggplot2::theme_minimal() +
  ggplot2::theme(
    panel.grid.minor = ggplot2::element_blank(),
    panel.grid.major = ggplot2::element_line(color = "grey90", linewidth = 0.3)
  ) +
  ggplot2::labs(
    x = "Easting (m)",
    y = "Northing (m)",
    title = "Observed and simulated red deer trajectories",
    subtitle = "Observed track in orange; 25 simulated tracks in blue"
  )

Run the gmov diagnostics

The call below validates the same supplied simulation ensemble with the current gmov diagnostics. The UD diagnostic uses an empirical grid approximation to the utilization distribution. The MSD diagnostic uses lagged MSD curves. These implementation details are documented in the package help pages, and numerical values can differ from the prototype diagnostics used in the article.

deer_validation <- validate_ssf_generative(
  observed = observed_track,
  simulated = simulated_tracks,
  metrics = c("ud", "msd", "sinuosity"),
  ud_args = list(grid_size = 20),
  msd_args = list(max_lag = 80)
)

deer_validation
#> gmov generative validation
#> Observed locations: 823 
#> Simulated tracks: 99 
#> Validation pillars: Emergent space use, Diffusion behavior, Path structure 
#> 
#> # A tibble: 3 × 7
#>   pillar             metric    diagnostic                      observed
#>   <chr>              <chr>     <chr>                              <dbl>
#> 1 Emergent space use ud        mean observed-simulated grid W1 5.29e+ 3
#> 2 Diffusion behavior msd       MSD integrated squared error    4.12e+15
#> 3 Path structure     sinuosity absolute straightness deviation 8.05e- 3
#>   discrepancy p_value alternative
#>         <dbl>   <dbl> <chr>      
#> 1    5.29e+ 3    0.96 greater    
#> 2    4.12e+15    0.06 greater    
#> 3    1.51e- 2    0.17 greater

The printed object gives a compact diagnostic scorecard with one row per validation pillar. The same information is also available as a tidy tibble for downstream work.

summary(deer_validation)
#> # A tibble: 3 × 6
#>   metric    statistic_name      observed_statistic discrepancy_statistic p_value
#>   <chr>     <chr>                            <dbl>                 <dbl>   <dbl>
#> 1 ud        mean observed-simu…           5.29e+ 3              5.29e+ 3    0.96
#> 2 msd       MSD integrated squ…           4.12e+15              4.12e+15    0.06
#> 3 sinuosity absolute straightn…           8.05e- 3              1.51e- 2    0.17
#> # ℹ 1 more variable: alternative <chr>

Visual diagnostics

The default gmov plots are intentionally simple package diagnostics. They are not exact reproductions of the custom figures prepared for the article. Their purpose is to give a stable visual summary for any gmov_generative object; article-specific figure layouts can still be built from the returned tidy objects when needed. The package plots use the same basic visual coding as the article workflow: blue for simulated quantities and orange for the observed track or observed statistic.

The UD diagnostic compares the observed grid utilization distribution to the simulated grid utilization distributions using the 1-Wasserstein distance between empirical grid masses.

plot(deer_validation, metric = "ud")

The MSD diagnostic compares the observed lagged displacement curve to the simulation envelope. This targets temporal organization of movement, not only the final spatial footprint.

plot(deer_validation, metric = "msd")

The sinuosity diagnostic compares the observed straightness index with the distribution of straightness indices from simulated trajectories.

plot(deer_validation, metric = "sinuosity")

Article-style dashboard

For presentations or reports, the same diagnostics can be displayed as a compact multi-panel dashboard. This figure keeps the generic gmov diagnostics but arranges them in a layout closer to the article workflow: trajectory panel on the left, diagnostic panels on the right.

plot_gmov_dashboard(
  deer_validation,
  observed = observed_track,
  simulated = simulated_tracks,
  n_simulations = 25
)

Reproducing the model-fitting workflow with amt

The precomputed ensemble above was produced from the red deer and forest objects distributed with amt. The modelling workflow is summarized here rather than evaluated during vignette building, because it depends on a working amt installation and can take longer than a typical package vignette build.

The empirical workflow used the following steps:

  1. Load the red deer relocation data and the forest raster distributed with amt.
  2. Resample the trajectory to a 6-hour interval with a 30-minute tolerance.
  3. Convert the resampled trajectory to steps.
  4. Generate 25 available steps for each observed step.
  5. Extract the binary forest covariate for used and available steps.
  6. Add movement-kernel terms for step length, log step length, and cosine of turning angle.
  7. Fit the iSSA with the conditional logistic regression formula shown above.
  8. Simulate replicate trajectories from the fitted model.
  9. Pass the observed trajectory and simulated trajectories to validate_ssf_generative().

Once the simulation output is a list of track-like objects, the validation step is the same as in this vignette: call validate_ssf_generative() with the observed track, simulated tracks, and selected metrics, then inspect summary() and plot() outputs.

Interpretation

The red deer example illustrates why generative validation is useful even when a fitted iSSA is plausible at the one-step scale. The model can generate trajectories that occupy broadly similar regions of space while still failing to reproduce the temporal structure of displacement. In the article workflow, this appears as a mismatch in the MSD pillar, while the broad space-use and sinuosity pillars are not rejected.

In practice, the diagnostics should be read together. A single p-value is not a complete model assessment. Instead, the pattern across pillars helps identify which aspect of generative realism is plausible and which aspect may require a better movement kernel, additional behavioural states, temporal structure, or landscape constraints.

References

Avgar, T., Potts, J. R., Lewis, M. A., and Boyce, M. S. (2016). Integrated step selection analysis: bridging the gap between resource selection and animal movement. Methods in Ecology and Evolution, 7, 619-630. https://doi.org/10.1111/2041-210X.12528

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

Signer, J., Fieberg, J., and Avgar, T. (2019). Animal movement tools (amt): R package for managing tracking data and conducting habitat selection analyses. Ecology and Evolution, 9, 880-890. https://doi.org/10.1002/ece3.4823