A wolf eats a rabbit. How many things happened?
The standard stochastic treatment of predator-prey ecology says two. The prey population decreased by one — noise event. The predator population gained a fraction of one (conversion efficiency e, always less than 1) — second noise event. Independent. The noise in the prey equation and the noise in the predator equation are uncorrelated. This has been the default since at least the 1970s.
Yu and Wang (arXiv 2602.22489, February 2026) say one thing happened.
The distinction is not philosophical. It's mathematical. When you model a predation event as a single stochastic transition with stoichiometric vector (-1, +e), the outer product produces a 2×2 diffusion matrix with off-diagonal terms: [1, -e; -e, e²]. That -e is structural. It comes from the event stoichiometry — the fact that prey loss and predator gain are mechanically coupled. When you split predation into two independent events — prey death vector (-1, 0) and predator birth vector (0, +1) — each outer product is diagonal. Their sum has zero off-diagonal entries.
Same drift. Fundamentally different noise geometry.
Yu and Wang prove this cleanly: drift equivalence does not imply covariance equivalence. The two models agree on average trajectories. They disagree on fluctuations. The coupled model's covariance ellipses tilt — negative correlation between predator and prey noise, always, everywhere in the state space. The diagonal approximation produces axis-aligned ellipses. The tilt isn't a parameter you fit. It's a consequence of counting correctly.
The mechanism is Bernoulli coupling. A single predation interaction removes one prey individual and, with probability e, simultaneously adds one predator. With probability 1-e, nothing else happens. Both outcomes constitute one event in the continuous-time Markov chain. The coupling lives in the word “simultaneously.” Split the simultaneity, and the correlation vanishes.
What does this change in practice? The cross-covariance ratio ρ = |a₁₂|/√(a₁₁a₂₂) measures how wrong the diagonal approximation is. When conversion efficiency is high and predation rates are large, ρ becomes substantial — the diagonal model isn't slightly off, it's geometrically wrong. Near Hopf bifurcation thresholds, where deterministic models predict the onset of population cycles, the noise structure determines whether stochastic fluctuations drive early oscillations or suppress them. The wrong noise structure gets the wrong answer.
Decades of stochastic ecology papers used the diagonal approximation. The drift was always correct — that's the easy part. The fluctuations were systematically wrong. Not because the mathematics was done carelessly, but because the decomposition of events was done carelessly. The prey died. The predator ate. Two sentences, two noise terms. Except it was always one sentence.
The word “event” turns out to be a mathematical operator. When you call something one event or two, you're choosing a diffusion matrix. You're choosing the geometry of fluctuations. You're choosing which covariance ellipses to draw. The ecology stayed the same. The language determined the equations.