Alternative Stable State

An alternative stable state (or alternative stable regime) is one of two or more locally asymptotically stable equilibrium configurations—characterized by contrasting species assemblages, functional guild dominance, and internal biogeochemical feedback loops—that a single ecosystem or community can occupy under identical external abiotic conditions. Introduced as a formal mathematical concept in population and community ecology by Richard C. Lewontin (1969), expanded into ecosystem resilience theory by Crawford S. ("Buzz") Holling (1973) and Robert M. May (1977), and synthesized empirically across aquatic and terrestrial biomes by Marten Scheffer et al. (1993, 2001), the theory of alternative stable states explains why gradual, continuous changes in external environmental drivers (such as nutrient loading, climate warming, or harvesting pressure) can trigger abrupt, nonlinear regime shifts across the biosphere that are difficult or impossible to reverse simply by restoring the driver to its pre-collapse value.

Nonlinear Positive Feedbacks and the S-Shaped Equilibrium Curve

In a linear or weakly nonlinear ecosystem without strong internal positive feedbacks, the equilibrium ecosystem state X* (such as vegetation biomass, coral cover, or water clarity) varies as a smooth, single-valued monotonic function of an external environmental control parameter E (such as phosphorus loading, mean annual rainfall, or grazing intensity). Conversely, when a community contains a strong self-reinforcing positive feedback—such as mutual facilitation by a foundation species, predator-prey saturation (Holling Type III functional response), or priority-effect preemption in the Competitive Lotka-Volterra Equations (α₁₂ α₂₁ > 1)—the differential equation dX / dt = f(X, E) folds back into an S-shaped equilibrium manifold over an intermediate range of the external driver E ∈ (F₁, F₂).

A canonical minimally parameterized differential equation used by Robert M. May (1977) and Marten Scheffer (2001) to model bistable ecosystem dynamics (such as lake turbidity or overgrazed vegetation) is:

dX / dt = a − b X + ( r X^p ) / ( h^p + X^p )

where a represents the external environmental loading rate, −b X represents linear loss or flushing, and the Hill-function term r X^p / (h^p + X^p) with exponent p > 1 (typically p = 2 or 4) represents sigmoidal internal recycling or positive feedback with half-saturation threshold h.

Saddle-Node (Fold) Bifurcations, Basins of Attraction, and Hysteresis

Within the bistable parameter window F₁ < E < F₂, setting dX / dt = 0 yields three equilibria at the same environmental value E:

• Two Locally Stable Equilibria (X_lower* and X_upper*): Along the lower and upper branches of the S-curve, the Jacobian derivative ∂f / ∂X < 0. Each stable branch sits at the bottom of a basin of attraction (visualized as a valley in a potential energy landscape V(X) where dX / dt = −∂V / ∂X).
• One Unstable Interior Threshold (X_saddle*): Along the middle dashed branch of the S-curve, ∂f / ∂X > 0. This unstable equilibrium forms the watershed boundary (separatrix or ridge) separating the two basins of attraction.

This geometry generates two distinct pathways for an abrupt regime shift:

1. State Perturbation (Pulse Disturbance Across the Basin Boundary): While the external environment E remains fixed inside (F₁, F₂), a large exogenous shock (such as a hurricane, wildfire, disease outbreak, or fish kill) pushes the state variable X across the unstable saddle threshold X_saddle*, causing the ecosystem to roll into the alternative basin of attraction. Holling's ecological resilience is defined as the width and depth of the current basin of attraction (*|X** − X_saddle*|).
2. Parameter Forcing Across a Fold Bifurcation (Tipping Point) and Hysteresis: As chronic external forcing gradually increases E toward the upper saddle-node (fold) bifurcation point F₂, the basin of attraction of the current state shrinks toward zero width. The instant E exceeds F₂, the current stable equilibrium collides with the unstable saddle branch and annihilates; the ecosystem undergoes a rapid collapse to the alternative branch. To reverse this collapse and restore the original state, it is not sufficient to reduce the environmental driver back to just below F₂; instead, the driver must be reduced all the way back to the lower fold bifurcation point F₁ < F₂. This path dependence between forward collapse (F₂) and backward recovery (F₁) is termed ecological hysteresis.

Shallow Lakes: Clear-Water Macrophytes vs. Turbid Phytoplankton

Synthesized by Marten Scheffer et al. (1993), shallow temperate lakes (mean depth <3 meters, such as Lake Veluwe in the Netherlands) exhibit textbook hysteresis along a gradient of dissolved orthophosphate (PO₄^3-) and nitrate (NO₃^-) loading:

• Clear-Water Macrophyte State: At low to moderate nutrient loading, submerged vascular macrophytes (Potamogeton pectinatus, Myriophyllum) and charophyte green algae (Chara spp.) carpet the lake bottom. Macrophytes stabilize the clear-water state through four synergistic feedbacks: (1) damping wind-driven wave shear stress to prevent benthic sediment resuspension; (2) absorbing luxury PO₄^3- and NO₃^- from the water column; (3) secreting allelopathic polyphenols that inhibit cyanobacteria; and (4) providing daytime structural refuge for large herbivorous cladoceran zooplankton (Daphnia magna) against planktivorous fish (Abramis brama, Rutilus rutilus), allowing Daphnia to graze down phytoplankton at night.
• Turbid Phytoplankton State: When chronic nutrient loading pushes phytoplankton and epiphytic periphyton density past the light-attenuation threshold of submerged macrophytes—or when a herbicide pulse or winter ice kill destroys the macrophyte bed—submerged plants die back. Without macrophytes, Daphnia lose their refuge and are decimated by benthivorous/planktivorous fish, wind waves and foraging fish resuspend phosphorus-rich benthic mud (internal eutrophication), and dense blooms of cyanobacteria (Microcystis, Planktothrix) shade the bottom so deeply that macrophyte seedlings cannot re-establish even if external PO₄^3- inputs are substantially reduced. Restoring the clear-water state requires either extreme nutrient reduction below F₁ or food-web biomanipulation (removing 75–85% of planktivorous fish to trigger a trophic cascade that restores Daphnia grazing and water clarity).

Caribbean Coral-to-Macroalgal Phase Shifts

Across Caribbean coral reefs during the 1980s and 1990s (Terence P. Hughes, 1994; Peter J. Mumby et al., 2007), chronic overfishing of herbivorous parrotfishes (Scarus, Sparisoma) and surgeonfishes (Acanthurus) eroded the grazing resilience of reefs dominated by Acropora palmata and Orbicella annularis, while coral cover remained high solely due to grazing by a single remaining echinoid species, the long-spined black sea urchin (Diadema antillarum). When a waterborne pathogen eradicated >95% of Diadema antillarum across the Caribbean in 1983–1984 and Hurricanes Allen and Joan damaged branching corals, fast-growing fleshy macroalgae (Dictyota, Lobophora, Sargassum) overgrew the reef substrate. Once mature macroalgal mats establish, they become unpalatable to juvenile grazing fishes, trap fine sediment, and chemically/physically block the settlement of planktonic coral planula larvae, locking the reef into a persistent macroalgal alternative stable state.

Tropical Forest–Savanna Bistability

Using global satellite tree-cover distributions across Africa, South America, and Australia, Marina Hirota et al. (2011) and A. Carla Staver, Sally Archibald, and Simon A. Levin (2011) demonstrated that across a broad intermediate rainfall band (1,000 to 2,500 mm mean annual precipitation), terrestrial landscapes exhibit a bimodal frequency distribution of tree cover, clustering tightly around either closed-canopy tropical forest (>60% tree cover) or open grassy savanna (~10–20% tree cover) with a scarcity of intermediate woodland states (~40% tree cover). This bistability is maintained by the grass–fire feedback: in open savannas, high light availability supports productive C₄ grasses that cure in the dry season and fuel frequent surface fires (every 1–5 years) that kill fire-sensitive forest tree saplings ("Gulliver syndrome"). Conversely, once tree cover crosses a percolation threshold of ~40–45%, the closed forest canopy shades out C₄ grass fuel and maintains high sub-canopy humidity, excluding fire and stabilizing the forest state against tipping points in the climate system.

Because an ecosystem approaching a fold bifurcation (E → F₂) experiences a progressive flattening of its potential basin, the dominant eigenvalue λ of the linearized system approaches zero from below (λ → 0⁻). As proven by Hermann Haken (1977) and applied to ecological time series by Marten Scheffer et al. (2009) and Stephen R. Carpenter et al. (2011), this critical slowing down produces three generic, model-independent statistical early-warning signals in high-frequency ecological monitoring data (including indicator species abundances) prior to a regime shift:

1. Slower Recovery Rate from Perturbations: The return rate |λ| after small natural disturbances decreases linearly toward zero as the tipping point approaches.
2. Rising Temporal Lag-1 Autocorrelation (ρ₁ → 1): Because the state variable X(t) retains memory of prior stochastic fluctuations longer, its lag-1 autocorrelation ρ₁ = exp(λ Δt) increases toward unity.
3. Rising Variance and Flickering (σ_X² = σ_ε² / (1 − ρ₁²)): Identical background environmental noise (σ_ε²) generates progressively larger amplitude fluctuations in X(t), accompanied by skewness and bimodal "flickering" between the two basins immediately prior to transition.

1. Holling, C. S. (1973). Resilience and stability of ecological systems. Annual Review of Ecology and Systematics, 4(1), 1–23. https://doi.org/10.1146/annurev.es.04.110173.000245
2. May, R. M. (1977). Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature, 269(5628), 471–477. https://doi.org/10.1038/269471a0
3. Scheffer, M., Carpenter, S., Foley, J. A., Folke, C., & Walker, B. (2001). Catastrophic shifts in ecosystems. Nature, 413(6856), 591–596. https://doi.org/10.1038/35098000
4. Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V., Held, H., van Nes, E. H., Rietkerk, M., & Sugihara, G. (2009). Early-warning signals for critical transitions. Nature, 461(7260), 53–59. https://doi.org/10.1038/nature08227