What question did this study set out to answer?

The study aims to explore the relationship between the ecological Péclet number and ecosystem phase transitions through Lotka-Volterra dynamics.

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February 28, 2026Open Access

The Ecological Péclet Number: Lotka-Volterra Dynamics as Drift-Diffusion, Ecosystem Phase Transitions, and the Red Queen as Vortex Condition

Key Points

The study aims to explore the relationship between the ecological Péclet number and ecosystem phase transitions through Lotka-Volterra dynamics.
Utilized the Lotka-Volterra equations in the context of drift-diffusion mathematics.
Analyzed empirical data from 12 biome void scores and 16 post-extinction recovery intervals.
Applied THRML theory to understand fossil record recoveries.
Established that Pe_eco governs ecosystem phase transitions from gas to vortex states.
Identified the Red Queen arms race as a vortex phase condition at Pe_eco > 4.
Confirmed a continuous vortex onset power law evident in fossil record recoveries over 540 million years.

Abstract

Ecosystem dynamics follow universal drift-diffusion mathematics: Lotka-Volterra equations are Fokker-Planck equations, and the Péclet number Peₑco = 4Nₑs governs ecosystem phase transitions (Gas → Fluid → Crystal → Vortex). The Red Queen arms race emerges as a vortex phase condition at Peₑco > 4, trophic cascades instantiate the D1→D2→D3 drift cascade, and post-extinction fossil record recovery follows the continuous vortex onset power law from THRML theory. This result extends the cross-substrate convergence of the void framework to ecosystem biology, with empirical support from 12 biome void scores and 16 post-extinction recovery intervals spanning 540 million years of fossil record.

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