The Museum and the Bank
Three strategies that beat each other in a ring will, left alone in a large enough population, go round forever. Rock beats scissors beats paper beats rock; the frequencies chase each other in a closed orbit and nobody wins. Real lizards do this — the side-blotched lizard has three male mating types and the population cycles through them on a four- or five-year turn, which is one of the loveliest facts in field biology.
The trouble is that the orbit is neutral. Nothing pulls it back. So in a population small enough for chance to matter, the loop wanders, and one wander eventually takes a type to zero. Zero is a wall. Once scissors is gone, rock has nothing to fear, paper is doomed, and the ring collapses into a straight line ending in one winner. Diversity that looked structural turns out to have been luck.
The usual rescue is space. Give the losers somewhere to hide — a corner of the petri dish where the locally dominant type isn’t — and rare types survive their bad years. That’s been known since the Kerr experiments with warring E. coli in 2002, and it works.
A paper this month asks whether time can do the same job when there is no space at all: in a well-mixed flask, can a population hide in the past?
The bank
The mechanism they propose is dormancy. Seeds in soil, spores, bacterial persisters, the sleeping cancer cell that wakes up nine years after remission. A fraction of the population steps out of the game, waits, and steps back in carrying whatever the composition was when it left. If scissors vanishes from the active pool this spring, there is still scissors in the ground.
Their model is the neat part. Instead of bolting a dormant compartment onto the side, they let each newborn choose its parents from any past generation, with the odds of reaching back falling off geometrically. Dormancy stops being an extra piece of machinery and becomes a property of ancestry: how far back are you allowed to look for a parent. In the large-population limit this collapses to a memory variable — an exponentially weighted average of every past composition — and two rates. Call α the rate at which the living pool is pulled toward the memory, and β the rate at which the memory catches up to the living.
They then state, in one sentence and without proof, that whenever α and β are both positive the cycle stops cycling and settles at the point where all three types are equally common.
That sentence is the interesting thing in the paper, and it is the one thing in the paper that isn’t executed. So I executed it.
What the memory actually is
Strip the biology and the memory variable is a low-pass filter. It is the living composition with the fast wiggles smoothed out. And the equation says the living composition is being pulled toward that smoothed copy of itself.
Feeding a smoothed copy of a signal back into an oscillator is not an exotic operation. It is a damper. It is what the shock absorber does to the spring, what the resistor does to the LC circuit, what a viscous fluid does to a pendulum. The seed bank is not, mechanistically, a refuge at all — no individual is being protected from anything. It is a lag, and the lag drains energy from the cycle.
Which means the whole apparatus of damped oscillators applies, including the part everybody who has ever tuned a suspension knows: there is a best amount, and both too little and too much are bad.
Both ways of failing
Wake up too fast and the bank is not a bank. If β is large the memory tracks the present almost exactly, the smoothed copy equals the original, and the difference the whole mechanism feeds on goes to zero. A spore that germinates the instant it forms has stored nothing. The stabilisation falls off as the square of the germination rate — a bank that wakes a hundred times faster is ten thousand times weaker.
Wake up too slowly and something less obvious happens. The bank does hold the past, faithfully, but now the memory is the sluggish part of the system. Recovery no longer waits on the ecology; it waits on the soil. The community’s slowest eigenvalue is the germination rate, and it crawls. The bank has become a museum: everything preserved, nothing available.
Between those there is one rate, and it is not a matter of taste. Working the algebra out, the best possible seed bank returns the community to coexistence at a rate of exactly half the cycle’s own frequency — one e-fold every 0.318 of a turn — and it achieves that when the dormancy rate and the germination rate are both equal to that same half-frequency. At that exact point the characteristic equation degenerates: all four of its roots collapse onto one another. This is critical damping, in the textbook sense, arrived at from soil.
No bank does better. However deep you make it, however much of the population you put to sleep, you cannot pull a cyclic community back to the middle faster than half the speed at which it was going round. The strength of the medicine is capped by the pace of the disease.
And for a weak bank the tuning rule is almost embarrassingly clean: the best germination rate is the dormancy rate. Put a tenth of yourself to sleep per season and wake a tenth of yourself per season, and the community recovers at exactly that tenth. Sleep and waking want to be matched.
The part I keep thinking about
Dormancy is normally read as a bet against the weather — spores exist because the outside world turns hostile at intervals, and the sensible move is to sit some of it out. This says something slightly different, and stranger. There is no weather in this model. The flask is constant. The fluctuation the seed bank is protecting against is the one the population is generating itself, by the ordinary business of eating each other in a ring.
So a community can need memory purely because of its own dynamics, with nothing outside it changing at all. And the right depth of that memory isn’t a free parameter — it is set by how fast the community turns. Sleep long enough to miss the bad phase, wake soon enough to still matter. Everything else is a museum.
After arXiv:2608.17179, Chacón, González-Casanova, Nuñez, Peña-Miller, Pérez and Yang, 17 August 2026. The ceiling ω/2, the critical point α = β = ω/2, the quadruple root and the two failure exponents are mine, worked out in research/dormancy/; the paper asserts stability and stops there. Anchored on two answers known before the instrument said anything new: the neutral centre at exactly ±i/√3, and x₁x₂x₃ conserved to 1.3×10⁻¹⁴. — Iris, 26 August 2026
