The Lotka–Volterra predator-prey model with foraging-predation risk trade-offs
The Lotka-Volterra predator-prey model is one of the earliest and, perhaps, the best known example used to explain why predators can indefinitely coexist with their prey. The population cycles resulting from this model can be found in every ecology textbook. Dr. Vlastimil Krivan, a mathematical ecologist at the Biology Center at Ceske Budejovice, shows that adaptive behavior of prey and predators can destroy these cycles and stabilize population dynamics at an equilibrium.
The Lotka-Volterra predator-prey model is one of the earliest and, perhaps, the best known example used to explain why predators can indefinitely coexist with their prey. The population cycles resulting from this model (Figure A) can be found in every ecology textbook. Dr. Vlastimil Krivan, a mathematical ecologist at the Biology Center at Ceske Budejovice, shows that adaptive behavior of prey and predators can destroy these cycles and stabilize population dynamics at an equilibrium (Figure B).
The classical predator-prey model assumes that interaction strength is fixed, which means that coefficients describing interactions between prey and predators do not change in time. However, there is increasing evidence that individuals adjust their activity levels to maximize their Darwinian fitness. For example, a high predation risk due to large predator numbers leads to prey behaviors that make them less vulnerable. They can either move to a refuge or become vigilant. However, such avoidance behaviors usually also decrease animal opportunities to forage which leads to the so called foraging-predation risk trade-off. The present article shows that such a trade-off can have a strong bearing on population dynamics. In fact, while the classical Lotka-Volterra model has isoclines that are straight lines, the foraging-predation risk trade-off leads to prey (predator) isoclines with vertical (horizontal) segments. Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey models showed that such isoclines have stabilizing effect on population dynamics because they limit maximum possible fluctuations in prey and predator populations. The present article shows that not only population fluctuations are limited, but they can even be completely eliminated. "Although mathematical models are caricatures of the real world, they can indicate the major mechanisms that regulate biodiversity," says V. Krivan.
Krivan, V. 2007. The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs. American Naturalist 170: 771-782.
