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

Ecosystem dynamics follow universal drift-diffusion mathematics: Lotka-Volterra equations are Fokker-Planck equations, and the Péclet number Pe_eco = 4N_es governs ecosystem phase transitions (Gas → Fluid → Crystal → Vortex). The Red Queen arms race emerges as a vortex phase condition at Pe_eco > 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.