What is a dynamic equilibrium?
A system is a set of parts linked by flows of energy and matter, such as a lake, a forest or the climate. A system is in dynamic equilibrium when its parts keep changing, but its overall state stays roughly steady, because inputs balance outputs.
Example: a lake gets water from rain and rivers, and loses water by evaporation and outflow. Each day the level rises and falls a little, but over years it stays about the same. Numbers of animals, the amount of carbon in a forest and the Earth's average temperature behave in the same way.
A static equilibrium has no change at all (a rock sitting still). Natural systems are almost never static.
Negative feedback: the system corrects itself
Negative feedback happens when a change causes effects that reduce the change. It keeps the system stable, like a thermostat.
- Predator and prey: more rabbits → more food for foxes → more foxes → more rabbits eaten → rabbit numbers fall.
- Carbon dioxide and plants: more CO₂ in the air can speed up plant growth, which takes more CO₂ out of the air.
- Body temperature: you get hot → you sweat → you cool down.
In the 3D model this is the valley: wherever you push the ball, the slope pushes it back to the bottom.
Positive feedback: the change grows
Positive feedback happens when a change causes effects that increase the change. It moves the system away from its starting state. ("Positive" does not mean "good".)
- Ice–albedo: warming melts ice → darker sea and land are exposed → they absorb more sunlight → more warming → more melting.
- Permafrost: warming thaws frozen soil → it releases methane and CO₂ → more warming.
- Forest dieback: fewer trees → less water put back into the air → less rain → more trees die.
- Soil erosion: less plant cover → more erosion → poorer soil → even fewer plants.
In the 3D model this is the hilltop: the further the ball moves, the faster it goes.
Tipping points
A tipping point is a threshold. Below it, negative feedback brings the system back. Beyond it, positive feedback takes over and the system moves to a new equilibrium with different features.
- Clear lake → green, algae-filled lake after too many nutrients (eutrophication).
- Coral reef → seaweed reef after warming, bleaching and loss of grazing fish.
- Rainforest → savanna after large-scale clearing and drying.
- Ice sheets in Greenland and West Antarctica: past a certain warming they may keep melting even if temperatures stop rising.
Tipping points are dangerous because changes can be sudden, hard to predict and very hard or impossible to reverse: pushing the ball back over the ridge needs a much bigger effort. This is why scientists use the precautionary principle and try to keep well away from thresholds.
Diversity and resilience
Resilience is the ability of a system to absorb a disturbance and return to its earlier state. Stability (or resistance) is how little it changes in the first place.
Systems with high diversity (many species, many feeding links, varied genes and habitats) are usually more resilient:
- If one species declines, another can do the same job (pollination, grazing, decomposition).
- Complex food webs give predators other prey to switch to.
- Genetic variety means some individuals survive disease or drought.
Simple systems such as monoculture farms or plantations are less resilient: one pest or one drought can wipe them out. Large population size, quick regrowth and connected habitats also help resilience. Human actions like pollution, habitat loss and climate change make the valley shallower, so a smaller push can tip the system.
Try it: find the tipping point
In the free-play step, keep diversity at 3 and raise the push one step at a time. Write down the first push that tips the ball. Now set diversity to 6 and repeat. The tipping push is bigger. That is resilience in action. You can also try it at home: roll a marble in a bowl (negative feedback), then balance it on an upside-down bowl (positive feedback).
Key formulas and definitions
- Dynamic equilibrium: inputs = outputs (on average)
- Negative feedback: change → effect that reduces the change → stability
- Positive feedback: change → effect that increases the change → runaway
- Tipping point: threshold where positive feedback takes over → new equilibrium
- More diversity → deeper 'valley' → more resilience
Worked examples
1. A lake gains 500 m³ of water a day from rivers and 50 m³ from rain. It loses 420 m³ through outflow. How much must evaporate each day for the level to stay steady?
Inputs = 500 + 50 = 550 m³. Outputs must also be 550, so evaporation = 550 − 420 = 130 m³ a day.
2. Is this negative or positive feedback? Warming thaws permafrost, which releases methane, which causes more warming.
Positive feedback: the effect (more methane) increases the original change (warming).
3. Explain why a mixed natural forest recovers from a pest attack better than a plantation of one tree species.
In a mixed forest the pest attacks only some species; other species keep doing the same jobs, predators of the pest are present, and genetic variety means some trees resist. In a plantation every tree is the same, so the pest can spread through all of them.
4. A fishery's catch is cut after a coral reef turns into a seaweed reef, but the coral does not return. Use the idea of a tipping point to explain why.
The reef has passed a tipping point and settled in a new equilibrium. Seaweed now shades out young coral and few grazers are left, so positive feedback keeps the seaweed state in place. Removing the original cause is not enough to push it back.
Common mistakes
- Thinking "positive feedback" means a good effect. It only means the change gets bigger.
- Saying equilibrium means nothing changes. In a dynamic equilibrium things change all the time; only the average stays steady.
- Thinking a system always returns once the cause is removed. After a tipping point it may stay in the new state.
- Confusing resilience (bouncing back) with stability or resistance (not changing much in the first place).