Escalator to Extinction: Mountain Reserve Climate Tracking

Climate & Reserve

Warming rate 2.0 °C/decade

Reserve upper boundary 1800 m

Species thermal tolerance ±2.0 °C

Simulation speed 8 yr/s

Live Readouts

Band inside reserve — species tracking safely

Years elapsed

0 yr

Comfort band

1231–1846 m

Population (protected reserve)

1000 birds

How it works

Air temperature falls with altitude at the environmental lapse rate L ≈ 6.5 °C/km. A species has an optimal temperature T_opt and tolerates ±τ around it, so at any moment it can only live inside one elevation band:

T(h) = T0(t) − L·h
Comfort band:  h ∈ [ (T0(t) − Topt − τ)/L ,  (T0(t) − Topt + τ)/L ]
T0(t) = T0(0) + warmingRate · (t / 10 yr)

As global warming raises the base temperature T0(t), the whole band slides upslope at a fixed width — this is the "escalator to extinction" documented for tropical mountain birds and alpine plants. The reserve boundary, drawn once on a map, does not move with it. Habitat area on a conical mountain shrinks toward the summit:

radius(h) = R0·(1 − h/Hpeak)
Protected area(h_lo,h_hi) = π·[ radius(h_lo)² − radius(h_hi)² ],  clamped to the reserve's upper limit

Population follows logistic growth toward the carrying capacity implied by that protected area, and declines whenever the comfort band is pushed above the reserve boundary or off the mountain entirely:

dN/dt = r·N·(1 − N/K)      if K > 0  (protected habitat exists)
dN/dt = −0.3·N              if K = 0  (band is outside protection)

Warming rate — how fast T0(t) rises; higher values push the band upslope faster than most reserves were designed for.
Reserve upper boundary — how far up the mountain legal protection extends. Set it to the peak (3000 m) and the species can track warming indefinitely; set it low and the band eventually climbs past the fence.
Thermal tolerance — a wider τ gives a thicker, more resilient band; a narrow specialist runs out of mountain sooner.
Once the band's lower edge passes the summit, there is no cooler ground left at any elevation — the mountain itself runs out, regardless of reserve policy.

Species population Thermal comfort band Reserve boundary

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