Feasibility as a moving target: Fluctuating species interactions lead to universal power law in equilibrium abundances

TL;DR

This paper demonstrates that fluctuations in species interactions cause equilibrium displacements leading to a universal power law distribution in species abundances, revealing new insights into ecosystem fragility and stability.

Contribution

It introduces a theoretical framework showing universal power law behavior in equilibrium abundances due to interaction fluctuations and empirically validates this with real ecological data.

Findings

Power law distribution with exponent ~2 in species abundances.

Larger communities are more fragile to noise-induced feasibility loss.

Derived critical noise threshold scales as N^{-1}."

Abstract

Theoretical ecology has traditionally equated persistence with the stability of a fixed equilibrium point. Here we argue that the primary threat to ecosystem persistence need not be the loss of stability, but instead the escape of the stable equilibrium to a negative orthant. In a realistic setting, fluctuations in interactions do not merely disturb abundances about an equilibrium but can displace the equilibrium point itself. We theoretically and empirically analyze such displacements of the equilibrium point in a complex community. Theoretically, we find that light-tailed fluctuations in species interactions, no matter how small, lead to a heavy-tailed power law $P(y)=1/y^\alpha$ for the equilibrium abundance $y$ of a species. Remarkably, the exponent $\alpha=2$ is a universal value independent of interaction structure, community size, and species. Empirically, our analysis of 34 species reveals a power law signal for most, with a median exponent $\alpha \sim2.56$. Next, we derive a formula for the critical noise, $\sigma_c$, beyond which the community experiences feasibility loss ``with near certainty''. We find that $\sigma_c(N)\sim N^{-1}$, implying that larger communities are significantly more fragile to noise induced feasibility loss. Lastly, we define and calculate biologically measurable analytical metrics for both global and species-specific feasibility escape rates, and implement these metrics in dynamic simulations of 98 real world mutualistic and food web networks, to successfully predict their fragility.