Temperature falls with elevation at a fixed lapse rate (6.5 °C/km). A species' suitable band sits between two isotherms; as the mountain warms, both isotherms — and the band between them — move upslope by the same amount, while the band's own width in elevation stays fixed.
Because the mountain is cone-shaped, the land area inside an elevation band shrinks the higher it sits (a thin ring near the summit has far less area than the same-height ring near the base). Habitat area sets a carrying capacity that the population tracks with logistic growth. Once the band's lower edge is pushed past the true summit, no higher ground remains — the "escalator to extinction".
- T(h) = T₀ − warming − 6.5·h/1000
- Area(h₁,h₂) = π·(r(h₁)² − r(h₂)²), r(h) = R₀·(1 − h/H)
- dN/dt = r·N·(1 − N/K), K ∝ habitat area