Lotka-Volterra oscillations are what Péclet dynamics look like in population biology.
Predators and prey maintain each other. Remove one constraint and the system cascades.
A balanced ecosystem is a constraint architecture. Predators hold prey populations in check. Pollinators and plants maintain each other. Soil bacteria regulate nutrient cycles. Each relationship is transparent (the rules of ecology don't hide), invariant (natural selection doesn't change based on opinion), and independent (each species regulates without centralized control).
Introduce an invasive species — something opaque to the existing food web, responsive to the available resources, and coupled to everything it eats — and the system cascades. Cane toads in Australia. Kudzu in the American South. Rabbits in New Zealand. Each invasion follows the drift cascade: D1 (the ecosystem misidentifies the threat), D2 (native defenses erode), D3 (ecosystem collapse).
The Lotka-Volterra equations — the classic predator-prey math — turn out to be drift-diffusion equations. The Pe number predicts where the cycle destabilizes. Below Pe = 1, the ecosystem oscillates healthily. Above Pe = 1, one species runs away with the system. The Red Queen hypothesis — that species must constantly evolve just to survive — is the biological name for vortex-phase dynamics at Pe > 4.
A healthy ecosystem is a constraint architecture. Introduce an invasive species — something opaque, responsive, and coupled — and the drift cascade runs. Every time.
Academic title: The Ecological Péclet Number: Lotka-Volterra Dynamics as Drift-Diffusion, Ecosystem Phase Transitions, and the Red Queen as Vortex Condition
Once you see it in this domain, you see it in all of them. That's the point.
Move the sliders. Watch the system change state. Pe > 1 means drift wins.
The framework scores these systems — ordered by void index.
The correlation coefficient. The sample size. The p-value. The math doesn't care about the domain.
Paste any text — AI output, ad copy, a policy document. The scorer runs the same algorithm the framework uses.
Three variables. One ratio. Predicts drift across every domain where the conditions co-occur.
Pe = (O × R) / α
Where O is opacity (how hidden the mechanism is), R is reactivity (how strongly the system responds to you), and α is your independence (how free you are to disengage).
When Pe < 1: diffusion dominates. You can navigate freely. The system is coherent.
When Pe > 1: drift dominates. The system pulls you in a direction. Your agency is reduced.
When Pe >> V* (≈ 3): irreversible cascade. D1 → D2 → D3. The system has captured you.
The framework identifies this pattern in every domain where O, R, and α co-occur. It specifies 26 falsification conditions. 0 of 26 have fired.
Full derivation: 10.5281/zenodo.18793556
Part of the Void Framework — 120 papers, 0/26 kill conditions fired, mean ρ = 0.958.