Center for Spatial Information Science and Systems, George Mason University

Learning Ecological Cost Surfaces of Climate-Driven Range Shifts via Inverse Optimal Transport

Ishan Nagpal, Edison Academy Magnet School
Ziheng Sun, Center for Spatial Information Science and Systems, George Mason University

Resistance surfaces are usually assumed. We learn one from how 101 bird species actually moved between 1997–2002 and 2017–2022, by inverting an unbalanced optimal-transport model.

Accepted to AGU
Accepted to MIT URTC

The idea

Transporting μ(t0) straight to μ(obs) gives no learning signal because entropic OT fixes both marginals. Instead we transport toward the climate target under a learnable cost C(β) = d_geo + β1·d_clim + β2·d_elev and score the result against μ(obs), which is never seen in fitting.

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Explore a species

Pick one of the 33 held-out species from the unbiased set, or one of the 13 curated species.

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The learned cost surface

Viewed on its own, the learned elevation term is highest in two places: the western edge of the grid, where the land rises toward the Great Plains, and an interior chain that follows the Appalachians for about 1,100 km from northern Georgia to Maine. The model was given elevation as an input but no barrier map.

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How sure are we?

Held-out loss (km)

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r = 0: loss within 0.00% of the lowest value

Across an eightfold range of r, held-out loss changes by only about 0.45%, and it is lowest at r = 0.5, the smallest value tested. The data do not pin down the ratio (13-species fit).

held-out species won against each baseline

Uniform-cost OT
- Curated n=5
  5/5
- Unbiased n=33
  33/33
Climate-only
- Curated n=5
  5/5
- Unbiased n=33
  33/33
Climate velocity
- Curated n=5
  5/5
- Unbiased n=33
  30/33
Persistence
- Curated n=5
  3/5
- Unbiased n=33
  7/33

On an unbiased sample a no-change baseline wins 26 of 33, so species selection can inflate apparent skill.

Key numbers

held-out species: learned cost beats geography-only OT: 33/33
median Wasserstein reduction vs geography-only OT: 14.4%
median reduction on a later, unseen era: 19.7%
Appalachian band in the learned elevation term: ~1,100 km