Temperature falls steadily with elevation, stacking a mountain into zones from warm lowland at the base to cold alpine tundra near the summit. This species is an alpine specialist: it can only survive within a fixed temperature range, which today maps to a specific elevational band well up the slope.
As the region warms, the elevation at which that temperature range occurs shifts upward — the band tracks it, climbing the mountain year after year, exactly as a species might track a shifting thermal envelope on flat ground.
The mountain, unlike flat terrain, is cone-shaped: less land area exists at every successively higher elevation. So as the band climbs, the habitat inside it doesn't just move — it shrinks, purely from geometry. Population is modelled as tracking that shrinking area with a lag. Once the band's lower edge is pushed above the true summit elevation, no higher ground remains — habitat area hits zero and the population goes extinct. That's the "escalator to extinction": each step up costs habitat the species can never get back, and the escalator has a top.