Theoretical ecology asks two questions about ecosystems: will species coexist, and is that coexistence stable? The first question is about feasibility — whether all species have positive abundance at equilibrium. The second is about stability — whether perturbations decay. Almost all the mathematical effort has gone into stability. Eskin, Nguyen, and Vural show that feasibility is the more dangerous problem, and it fails in a way nobody modeled.
The standard framework fixes species interactions and asks whether the resulting equilibrium is stable. But real interactions aren't fixed. A predator-prey coupling fluctuates with seasons, disease, territory. A mutualism weakens when one partner becomes abundant. The fluctuations are small — nobody's asking about catastrophic shocks. The question is what happens when the interaction matrix drifts by a little, continuously.
The equilibrium drifts with it. Not the abundances oscillating around a fixed point — the fixed point itself wanders. And eventually it wanders into a region where some species would need negative abundance to satisfy the equations. That species goes extinct. Not because it was destabilized, not because a perturbation overwhelmed the restoring force, but because the place it was supposed to be no longer exists.
The universality is the striking part. Regardless of community structure — mutualistic, competitive, food web — the resulting species abundances follow a heavy-tailed power law with exponent approximately 2. The distribution emerges from light-tailed interaction noise, which is a violation of the usual expectation that heavy tails in outputs require heavy tails in inputs. The equilibrium's random walk through parameter space produces fat tails from thin inputs.
Worse: the critical noise threshold scales as 1/N, where N is the number of species. Larger communities are exponentially more fragile. A 50-species food web tolerates less interaction noise than a 10-species one. Validated across 98 real networks, the pattern holds. Biodiversity itself is a risk factor.
The deeper lesson is about what “stable” means. A system can be stable in the dynamical sense — perturbations decay, eigenvalues have negative real parts — while being unstable in the feasibility sense — the equilibrium it's stable around doesn't correspond to a physically realizable state. You can converge perfectly toward a point that no longer makes sense. The mathematics of local stability says nothing about whether the target is still in the feasible region.
The ground shifts under your feet. Not suddenly, not dramatically. Just enough, each step, that one day the place you were standing is gone.