Predation and Community Effects

In the early 1960s Robert Paine began keeping the sea star Pisaster ochraceus out of one patch of rocky shore at Mukkaw Bay, Washington. By his 1966 report, the patch held 8 species instead of 15. Taking a predator away made the community poorer. How can a species that eats others keep more of them around?

This lesson builds a model of how a predator and its prey change each other’s numbers, works it with numbers, then reads three field studies and asks how far each one reaches.

The idea: eating couples two populations

In population growth each population changed by its own births and deaths. Predation ties two populations together. A predator is a consumer that kills and eats other organisms, its prey. Every prey eaten is a death in one population and, after some delay, part of a birth in the other. So the prey’s growth rate depends on how many predators there are, and the predators’ growth rate depends on how many prey there are.

A slow thermostat shows what this coupling does. If the furnace responds to how cold the room was a while ago, the room swings past the set point both ways. Predators respond to prey through births, which take time, so predators lag behind prey.

Predators also act on species they never touch. A trophic level is a feeding position in a food chain: plants, herbivores, carnivores. A predator’s effect can pass down through several levels, or shift competition among its prey.

The Lotka-Volterra cycle and what it leaves out

Alfred Lotka, in his 1925 book Elements of Physical Biology, and Vito Volterra, in a 1926 paper in Nature, reached the same pair of equations independently. With N prey and P predators:

dN/dt = rN - aNP dP/dt = eaNP - mP

Here r is the prey’s per capita growth rate without predators (per day), a is the attack rate (the fraction of prey each predator catches per day), e is new predators made per prey eaten, and m is the predators’ per capita death rate (per day).

The assumptions are strong. Without predators the prey grow exponentially, with no carrying capacity. Without prey the predators decline exponentially. Each predator’s intake rises in proportion to prey numbers with no handling time (the time spent catching and eating each prey), so a predator never gets full. Populations are well mixed, with no age structure, no space and constant parameters.

An isocline is the set of numbers at which one population stops changing. Prey stop changing when births equal losses, rN = aNP, which happens when P = r/a. Predators stop changing when eaN = m, which happens when N = m/(ea). Where the two lines cross is the equilibrium:

N = m/(ea) P = r/a**

Notice the swap: the prey equilibrium is set by the predator’s parameters, and the predator equilibrium by the prey’s. A faster-breeding prey raises the number of predators.

Worked problem. These numbers are made up for illustration: r = 1 per day, a = 0.01 per predator per day, e = 0.1 predators per prey eaten, m = 0.5 per day. Today there are N = 400 prey and P = 50 predators.

1. Prey rate. Prey births are rN = 1 x 400 = 400 prey per day. Prey eaten are aNP = 0.01 x 400 x 50 = 200 prey per day. So dN/dt = 400 - 200 = +200 prey per day.
2. Predator rate. Predator production is eaNP = 0.1 x 200 = 20 predators per day. Predator deaths are mP = 0.5 x 50 = 25 predators per day. So dP/dt = 20 - 25 = -5 predators per day.
3. Equilibrium. N* = 0.5 / (0.1 x 0.01) = 0.5 / 0.001 = 500 prey. P* = 1 / 0.01 = 100 predators. Check: at (500, 100), prey births are 500 and prey eaten are 0.01 x 500 x 100 = 500, so dN/dt = 0; predator production is 0.1 x 500 = 50 and deaths are 0.5 x 100 = 50, so dP/dt = 0.
4. Period. Near the equilibrium the cycle takes about 2 pi / square root of (rm) = 6.283 / square root of 0.5 = 6.283 / 0.707 = 8.89 days. This is a small-amplitude approximation, not the period of the larger orbit that passes through (400, 50).
5. Read the state. Prey are below N* = 500, so each predator eats too little to replace itself and predators fall. Predators are below P* = 100, so prey births outrun losses and prey rise. Predators will keep falling until prey pass 500; the predator low comes after the prey have started climbing.

That last step is the lag: prey peak first, and predators peak later.

• prey isocline: P = r/a
• predator isocline: N = m/(ea)
• orbit through the start
• start
• equilibrium (N*, P*)

Start prey N 400 Start predators P 50 Predator death rate m 0.5 per day

Equilibrium N* = m/(ea)

500

Equilibrium P* = r/a

100

Period of this orbit, in this sketch (integrated from the equations)

—

Near-equilibrium period 2π/√(rm)

—

• prey N
• predators P
• prey peak
• predator peak

Pick a start to see its orbit.

In this sketch: prey grow exponentially without predators (no self-limitation), each predator’s intake rises in proportion to prey numbers with no handling time, the populations are well mixed with no age structure, and r = 1 per day, a = 0.01 per predator per day and e = 0.1 predators per prey eaten stay fixed, and the model is continuous, so values below 1 are not real individuals. Units on the plot are individuals and days from the lesson’s illustration, not data on any real species.

The rule to keep: in the classical model every start sits on its own closed, neutral orbit, so the start sets the amplitude, and predators peak after prey.

The classical cycles have an odd property: they are neutral. Each starting point sits on its own closed orbit, so the amplitude is set by where the system starts, and a disturbance pushes it onto a different orbit. There is no single cycle that the system returns to. Add prey self-limitation, as in the logistic model, and the oscillations damp toward the equilibrium. Add a handling time, so predators get full, and the model can instead settle onto one cycle whose size does not depend on the start.

Real data rarely fit the classical model. The famous hare and lynx cycle comes from fur-trade records, which count trapping as much as animals. In the 1950s Carl Huffaker could keep predatory and plant-eating mites coexisting on oranges only when he made the arena patchy, a story taken up in movement and spatial populations. And rapid evolution of prey defenses can reshape cycles, as Takehito Yoshida and colleagues found with rotifers and algae, the subject of mutualism, parasitism and coevolution.

Paine’s shore and the keystone

At Mukkaw Bay, Pisaster ate mussels, barnacles, chitons, limpets and snails. Paine kept it out of a patch of shore, with an adjacent control, and surveyed both along line transects. In the removal patch richness fell from 15 to 8 species in the 1966 paper. The control did not lose species in the same way.

The mechanism was competition for space, a resource on a rocky shore as limiting as light in a forest (see competition). Mussels are strong competitors for rock. With Pisaster eating them, space kept opening for weaker competitors. Without it, mussels spread and the others lost their footing. Pisaster raised richness by freeing space, not by eating species that harmed the rest.

A keystone species has an effect on its community that is disproportionately large relative to its abundance. Keystone predation is the process seen here: a consumer that preferentially eats a strong competitor indirectly benefits the weaker ones. The memorial to Paine in PNAS dates the keystone term to a short note he published in 1969, three years after the paper and six after the removal began. Keep the three dates apart. And because the definition is about effect relative to abundance, the most common or dominant species is not a keystone by default.

Cascades through killing and through fear

A trophic cascade is an indirect predator effect that extends through several trophic levels: predator to herbivore to plant.

The sea otter case comes from a comparison. James Estes and John Palmisano surveyed islands in the western Aleutians, Alaska, where otters had returned after fur hunting and islands where they had not. In their 1974 paper, islands with many otters had few sea urchins and dense kelp, and islands without otters had many urchins and little kelp. No one removed otters. The contrast fits a cascade but leaves room for other differences among the islands.

A cascade can also run through behavior. In enclosures in a Connecticut old field, Andrew Beckerman, Maria Uriarte and Oswald Schmitz (1997) kept grasshoppers with no spiders, with hunting spiders, or with spiders whose mouthparts were glued so they could not kill. Grasshopper densities did not differ significantly among treatments. Yet with either kind of spider, grasses were damaged less and herbs more, because grasshoppers changed where and what they ate. The plant effect came from fear rather than death, and not every plant benefited.

Landscape-scale cascades are harder to pin down. Wolves were reintroduced to the park in the mid-1990s, and willow recovery has often been credited to them. Kristin Marshall, Thompson Hobbs and David Cooper (2013) ran a ten-year factorial experiment at four small-stream sites on the northern range, crossing fences that excluded browsers such as elk with simulated beaver dams, which raised July water tables by 33 cm on average. Reducing browsing alone did not restore the willow communities to their 2-metre recovery criterion. Wolves were never an experimental treatment. A 2024 extension of the experiment to about two decades, and published disagreement over how willow recovery should be measured, leave the park-wide question open.

How far one system generalizes

Paine had one removal patch and one control: a strong local experiment and a weak basis for a law. A 2025 review by Anthony Gillis and colleagues found 25 publications that explicitly manipulated predators to test keystone predation, of which 10 reported consistent support. Their search relied on the term itself, so it could miss studies that used other words, and a vote count is not an estimate of how often keystone predation occurs.

Sea-star wasting disease killed Pisaster along much of the Pacific coast from 2013. Monica Moritsch and Peter Raimondi (2018) found that sea-star counts at monitoring sites could recover while biomass, a proxy for predation potential, stayed below 40% of its pre-outbreak level at most sites outside North Central California, because recovering populations were made of small stars. Near Monterey, Joshua Smith and colleagues (2025) reported that mussels grew larger and spread lower on the shore after Pisaster collapsed, and they inferred that eating more mussels contributed in part to a local rise in sea otters.

Design problem

Paine had one removal patch and an adjacent control. Design a study that tests whether keystone predation by Pisaster generalizes across the coast. Say what you would measure, how you would replicate, and what result would count against generality.

One way to do it

Choose many sites that differ in wave exposure and mussel recruitment, since both could change how fast mussels take space. At each site assign several plots to removal or control at random. Survey every plot before removal and each year for several years after (a before-after-control-impact design), so a change can be separated from what was already happening.

Fix the list of taxa you count before you start, so richness means the same thing everywhere. Measure mussel cover in every plot: if removal lowers richness, mussel cover should rise first, which tests the mechanism.

Use the sea-star wasting die-off from 2013 as a natural experiment, comparing shores that lost most of their Pisaster with shores that lost fewer, while noting that the die-off was not randomly assigned.

Expect context dependence. If richness falls where mussel recruitment is high and changes little where it is low, keystone predation is real but conditional, which fits the Gillis review, where of 25 manipulations 10 gave consistent support, 7 were context-dependent and 8 gave none.