The Moving Target

An ecosystem is feasible when all species have positive abundance at equilibrium. The equilibrium is a point in a high-dimensional space — one axis per species, the equilibrium sitting in the positive orthant where every coordinate is greater than zero. Standard ecological theory asks whether this point is stable — whether small perturbations return the system to equilibrium or push it away.

The authors ask a different question. Not whether the equilibrium is stable, but whether it stays in the positive orthant at all. Species interactions fluctuate — predation rates shift, competition intensities vary, mutualism strengths wander. Each fluctuation moves the equilibrium point. If the point drifts across the boundary into the region where one species has negative abundance, that species goes extinct. Feasibility is not a fixed property. It is a moving target.

The fluctuations produce a universal power law in equilibrium abundances: the probability of a species having abundance y scales as one over y squared. The exponent is exactly two. It does not depend on community structure, interaction type, or the distribution of fluctuations — as long as the fluctuations are present at all. Even arbitrarily small noise generates the heavy-tailed distribution.

The consequence for large ecosystems is severe. The critical noise threshold scales as one over the number of species. A community with a hundred species can tolerate ten times less noise than a community with ten. Larger ecosystems are not more robust through redundancy. They are more fragile through dimensionality — more species means more axes along which the equilibrium can escape into infeasibility.

The ecosystem does not collapse because something destabilizes it. It collapses because the equilibrium wanders away from where all species can live. The target moves. The species cannot follow.