Co-extinctions reduce the robustness of planetary life to catastrophe. Response of global diversity to environmental change: progressive, monotonic increase (‘planetary heating’; left panel) or decrease (‘planetary cooling’; right panel) trajectories in local temperature. Species either go extinct based only on their tolerance to environmental conditions (‘environmental tolerance’ scenarios = blue curves), or where species go extinct not only when unable to cope with changed environmental conditions, but also following the depletion of their essential resources (‘co-extinction’ scenarios = magenta curves). Solid lines represent mean values, and shaded areas indicate the system boundaries (minimum-maximum) arising from 1000 randomly parametrized models (see Methods for details). Dotted lines show the decline in ‘tardigrade’ (extremophile) species richness in the environmental tolerance (blue) and in the co-extinction scenario (magenta) for both temperature trajectories.