REM sleep propensity — the drive to enter REM — follows a non-monotonic curve across humans, rats, and mice. As time in non-REM sleep accumulates, REM propensity rises. This much is expected: pressure builds. But past a peak, additional non-REM time causes REM propensity to decline. The system overshoots its own readiness. A sleep architecture that delays REM too long doesn't just postpone it — it weakens the drive that would have produced it. The pressure builds, peaks, and then the window closes.
In tumor immunology, chemotherapy that eliminates sensitive cancer cells releases resistant subpopulations from competitive suppression. Moderate immune pressure maintains equilibrium — the sensitive majority suppresses the resistant minority through competition for resources. But escalating treatment past the suppressive threshold doesn't achieve more control. It achieves less, by removing the very competitors that were keeping resistant cells marginal.
Both systems exhibit non-monotonic response to accumulated pressure. More is not more. There is a peak, and beyond it, the accumulated input undermines its own effect.
The sleep case is elegant because the non-monotonicity is conserved across three species with radically different sleep architectures. Mice sleep polyphasically — many short bouts. Humans sleep in a single consolidated block. Rats fall between. Yet all three show the same propensity curve: rise, peak, decay. The underlying mechanism — whatever converts non-REM duration into REM drive — saturates and then reverses, regardless of how the organism packages its sleep. The curve is more fundamental than the architecture it drives.
The tumor case is tragic for the same reason. The non-monotonicity is structural, not contingent on the specific cancer or drug. Any treatment that selectively eliminates the majority population will release minority populations from competitive suppression. The peak — maximum tumor control — occurs at moderate treatment intensity. Beyond that peak, escalation produces the opposite of its intent.
The principle: pressure systems with internal competition overshoot. When the pressure's effect depends on an ecosystem of responders — sleep stages competing for expression, tumor subpopulations competing for resources — the response curve must have a peak. Before the peak, more pressure helps. After the peak, more pressure reverses. The art is finding the peak and staying there, which requires understanding that the system you're pressuring has its own internal dynamics that your pressure is rearranging.