Predator-Prey Dynamics and Keystone Species

Predator-prey dynamics describe how the populations of predators and their prey affect each other, often producing linked cycles, and a keystone species is a species that has a much greater effect on community structure than its abundance would suggest. In brief: prey numbers rise, predator numbers follow, prey then fall, and predators decline. Removing a keystone species, such as the sea otter, which controls sea urchins in kelp forests, can cause large changes in the whole community. Community structure includes the species present, their abundance and their feeding relationships.

Understanding these interactions helps to manage wildlife and to predict the effects of losing or adding species. This guide explains predator-prey cycles and their causes, prey defenses, the idea of trophic cascades, keystone species and other types of influential species, works through a simulation of a predator-prey model with computed numbers and corrects common mistakes.

What is community structure?

A community is all of the populations of different species living in an area. Its structure includes the species richness (number of species), their relative abundance, the feeding relationships (food webs), and the physical form, for example the layers of a forest. Predation, competition and mutualism shape the structure, along with the physical environment and disturbance.

How do predator-prey cycles arise?

Predators reduce prey populations, and prey provide food for predators, so each affects the other. In a simple situation, the following cycle appears:

1. When prey are abundant, predators have plenty of food, and their numbers increase.
2. More predators catch more prey, so the prey population falls.
3. With little food, predators starve or breed less, and their numbers fall.
4. With fewer predators, prey recover, and the cycle begins again.

The predator peak follows the prey peak with a delay. The Lotka-Volterra equations, developed independently in the 1920s, describe this behavior mathematically: dN/dt = aN − bNP (prey) and dP/dt = cbNP − mP (predators), where N is prey, P is predators, a the prey growth rate, b the capture rate, c the efficiency in turning prey into new predators and m the predator death rate. The model gives continuing oscillations.

The best-known data are the records of snowshoe hare and Canada lynx pelts bought by the Hudson’s Bay Company over about 90 years, which show cycles of 9 to 11 years. Later field experiments suggested that the cycles of the hare are driven both by the predators and by the food supply (plants), which shows that real cycles often involve more than two species. Many predator-prey systems do not cycle but are stable, because of alternative prey, refuges, or because predators are limited by other factors.

How do prey avoid predators?

• Camouflage: the color and shape match the background (stick insects, flounders).
• Warning coloration (aposematism): bright colors that advertise toxicity (poison dart frogs, monarch butterflies).
• Mimicry: harmless species resemble harmful ones (hoverflies look like wasps: Batesian mimicry), or several harmful species look alike (Müllerian mimicry).
• Physical and chemical defenses: spines, shells, toxins, bad taste.
• Behavior: fleeing, hiding in refuges, living in groups (herds, schools, which dilute the risk to each individual) and alarm calls.

Predators evolve counter-adaptations: speed, stealth, venom, better senses and cooperative hunting. This process of reciprocal change is called coevolution.

What is a keystone species?

The term was introduced by Robert Paine in 1969, from his experiments on the rocky shore of Washington State. When he removed the predatory sea star Pisaster ochraceus from plots, the mussel population grew and crowded out the other species, and the number of species fell from 15 to 8 within a few years. The sea star was not the most abundant species, but it kept the mussels in check and made room for the others. It was a keystone species, named after the central stone of an arch, which holds the other stones in place.

• Sea otters in the Pacific eat sea urchins. Without otters, urchins overgraze kelp, and kelp forests, which are habitat for many fish and invertebrates, turn into “urchin barrens”.
• Wolves in Yellowstone: after wolves were reintroduced in 1995 to 1996, elk behavior and numbers changed, and some studies have found recovery of willow and aspen along streams, though the size of the effect is debated.
• Beavers are ecosystem engineers: their dams create ponds and wetlands.
• Fig trees in tropical forests provide fruit throughout the year for many animals.
• Elephants in African savannas knock down trees and keep grasslands open.

Not every keystone is a predator. Keystone species can also be mutualists, engineers or plants. Ecologists distinguish them from dominant species, which have a large effect because they are very abundant, and from foundation species, such as corals and trees, which create the habitat.

Examples of influential species

What is a trophic cascade?

A trophic cascade is a chain of indirect effects across several trophic levels, usually triggered by the addition or removal of a top predator. In the kelp forest, otters (level 4) reduce urchins (level 2), which allows kelp (level 1) to thrive. When otters were hunted almost to extinction in the 1700s and 1800s, urchin numbers increased and kelp forests were lost in many areas. After protection in the early 1900s, otters returned, and kelp recovered in many places. Cascades show that predators can have positive effects for the plants at the bottom of the food chain.

Worked example: a predator-prey model

To see how a delayed cycle arises, use a simple yearly model for prey (N) and predators (P): N_t+1 = N_t + 0.4 N_t − 0.01 N_t P_t and P_t+1 = P_t + 0.002 N_t P_t − 0.3 P_t. Prey grow by 40 percent a year and lose 0.01 of their number for every predator; predators gain 0.002 per prey and predator pair and lose 30 percent a year. Start with 100 prey and 20 predators.

1. Year 1 by hand: prey = 100 + 40 − 0.01 × 100 × 20 = 120. Predators = 20 + 0.002 × 100 × 20 − 6 = 18.
2. Year 2 by hand: prey = 120 + 48 − 0.01 × 120 × 18 = 146.4. Predators = 18 + 0.002 × 120 × 18 − 5.4 = 16.9.
3. Prey peak: prey increase to about 394 in year 8, while predators are still few.
4. Predator peak: predators peak at about 122 in year 11, three years after the prey peak, by which time they have reduced the prey to 86.
5. Crash: by year 12, the prey are down to about 16, and predators will starve and decline in the following years.

The table shows the central idea: the predator peak follows the prey peak after a delay, and the predators’ numbers keep rising for a time even while the prey are already falling. This crude model is also unrealistic in an important way. It lets the prey fall to almost nothing, and if it is run for decades the numbers oscillate wildly. Real prey populations are limited by their own food supply, and have refuges where predators cannot reach them, which prevents such extreme swings. The model should therefore be used to understand the delayed feedback, and not to predict real numbers.

How did the ideas develop?

Alfred Lotka (1925) and Vito Volterra (1926), who was inspired by data on fish catches in the Adriatic Sea during World War I, developed the equations. Charles Elton analyzed the Hudson’s Bay Company data in the 1920s. Gause’s microbial experiments in the 1930s showed that predator-prey systems in laboratory tubes tend to go extinct without refuges. C. S. Holling described how predators respond to prey density (functional responses) in 1959. Robert Paine coined the term keystone species in 1969, and James Estes documented the sea otter cascade in the 1970s and 1990s.

Which mistakes are common?

Mistake 1: Thinking that predators always drive prey to extinction

Predators and prey usually coexist, in cycles or at stable levels. Extinction is unusual.

Mistake 2: Saying that a keystone species is the most abundant

It is defined by a large effect compared with its abundance. Abundant species with a large effect are called dominant species.

Mistake 3: Mixing up the order of peaks

The predator peak follows the prey peak.

Mistake 4: Thinking that removing a predator benefits the prey

It may allow the prey to overpopulate, overgraze and then crash, which harms the prey and the rest of the community.