  The potential of extreme environmental change driven by a destabilized
climate system is an alarming prospect for humanity. But the intricate, subtle
ways Earth's climate couples to social and economic systems raise the question
of when more incremental climate change signals the need for alarm. Questions
about incremental sensitivity are particularly crucial for human systems that
are organized by optimization. Optimization is most valuable in resolving
complex interactions among multiple factors, however, those interactions can
obscure coupling to underlying drivers such as environmental degradation. Here,
using Multi-Objective Land Allocation as an example, we show that model
features that are common across non-convex optimization problems drive
hypersensitivities in climate-induced degradation--loss response. We show that
catastrophic losses in human systems can occur well before catastrophic climate
collapse. We find punctuated insensitive/hypersensitive degradation--loss
response, which we trace to the contrasting effects of environmental
degradation on subleading, local versus global optima (SLO/GO). We argue that
the SLO/GO response we identify in land-allocation problems traces to features
that are common across non-convex optimization problems more broadly. Given the
broad range of human systems that rely on non-convex optimization, our results
therefore suggest that substantial social and economic risks could be lurking
in a broad range in human systems that are coupled to the environment, even in
the absence of catastrophic changes to the environment itself.
