Source
Scheffer & Carpenter (2003), LIT-726, read in NOTE-571. The 2001 Nature paper it restates, LIT-720, is unread.
What was actually shown
Scheffer & Carpenter (LIT-726) review the theory and the evidence.
- Theory. Alternative attractors exist when a feedback is strong enough to make more than one basin of attraction at the same external conditions. As conditions change, a basin can shrink to nothing (a bifurcation), and returning needs a reversal past a second bifurcation: hysteresis.
- What field data can and cannot show. Jumps in time series, multimodal distributions and two-branched relationships to a driver all fit the theory. Each is also produced by a driver that itself jumps, or by a threshold that is not a bifurcation. Such data “can never be conclusive”.
- What experiments can show. They can show different end states from different starting states under the same conditions, a lasting shift after a temporary perturbation (temporary fish removal turning lakes clear), and hysteresis (charophytes in Lake Veluwe as phosphorus rose and fell).
- The confound. A long return time looks like a new stable state. Biomanipulated Lake Zwemlust stayed clear for six years and then slipped back.
- Feedback alone is not enough. “Positive feedbacks only lead to alternative attractors if they are sufficiently strong.”
What this does not say
- Not that alternative states are rare. The review documents many cases and holds that they are part of the expected range of behaviour.
- Not that persistence is irrelevant. A state that regenerates itself over generations is evidence; one that simply has not yet decayed is not.
- Not a recipe for large systems. The experiments that discriminate are hard to run on oceans, and on organizations.
Connections
- Reef recovery (THEORY-128). Hughes et al. found the algal state on Great Barrier Reef plots vanished within 30 days once the cages excluding fishes were reopened. By this standard it was a reversible response, not a move between attractors. The review’s Caribbean account is of resilience eroded slowly by fishing, nutrients and the loss of Diadema.
- Self-reinforcing disorders (THEORY-058) says disorders persist because their symptom networks maintain themselves and so outlast their triggers. Outlasting a trigger is one of the hints this account calls inconclusive. No relation is declared; the network account would need hysteresis or initial-state evidence to meet this standard.
- Presupposes resilience (THEORY-132). The test takes Holling’s picture as given: a system’s states fall into basins of attraction, and resilience is how large the basin is. Hysteresis and lasting shifts after a temporary push are evidence of more than one basin. Without that picture the test has nothing to detect (ADR-029).
Note of 2026-10-27: a third route to abrupt change
Ashwin et al. 2012 (LIT-1654, read in NOTE-1215) add a third route to abrupt change without alternative stable states, beside a stepwise driver and a threshold: a smooth but fast driver acting on a system with one globally stable equilibrium, tipping at a threshold “not associated with any basin boundary” (§3.3, p. 13). That supports this account’s caution. Where the frozen system is bistable (their §4), an outcome that depends on the rate along one parameter path is a kind of history dependence, near what this account counts as diagnostic; the paper does not discuss evidence.