English: Stability properties for a small network of two pollinators (shown) and two plants (not shown). (a) Attraction basins (valleys) of alternative stable states (balls) are separated by thresholds (dashed curves). Initially, the only alternative to pristine state 1 is fully collapsed state 2 (a.I). When conditions change, two additional, partially collapsed states appear (states 3 and 4). The initial, pristine state loses resilience after state 3 appears (a.II and a.III). Eventually, the threshold towards state 3 approaches the pristine state so closely that a critical transition towards this state becomes inevitable (a.III and a.IV). (b) Alternative stable states, saddle points (yellow dots) and hilltops (grey dots) are surrounded by areas in which the landscape's slope, and thus the rate at which abundances change, is nearly zero (indicated in orange). Higher speeds are found further away from these points. The direction of slowest recovery changes substantially before future state 3 appears (yellow arrow, b.I and b.II). After state 3 appears, the system slows down in the direction of the saddle point on the approaching threshold (b.II and b.III). (c) Slow recovery from a perturbation towards the saddle point (c.I) as opposed to the much faster recovery from an equally large perturbation in another direction (c.II).