Lotka–Volterra equations Mathematical models of competition, devised in the 1920s by A. J. Lotka and V. Volterra, between resource-limited species living in the same space with the same environmental requirements. They have been modified subsequently to simulate simple predator–prey interactions. The competition model predicts that coexistence of such species populations is impossible; one is always eliminated, as was verified experimentally by G. F. Gause. The predation model predicts cyclic fluctuations of predator and prey populations. Reduction of predator numbers allows prey to recuperate, which in turn stimulates the population growth of the predator. Increasing predator numbers depress the prey population, leading eventually to a reduction in the predator population. This was also tested experimentally by Gause in 1934 and more recently and more convincingly by S. Utida in 1950 and 1957. See also competitive exclusion principle.

Lotka-Volterra equations Mathematical models of competition between resource-limited species living in the same space with the same environmental requirements. They have been modified subsequently to simulate simple predator–prey interactions. The competition model predicts that coexistence of such species populations is impossible: one is always eliminated, as was verified experimentally by G. F. Gause. The predation model predicts cyclic fluctuations of predator and prey populations. Reduction of predator numbers allows prey to recuperate, which in turn stimulates the population growth of the predator. Increasing predator numbers depress the prey population, leading eventually to a reduction in the predator population. This was also tested experimentally by Gause (1934) and more recently and more convincingly by S. Utida (1950, 1957). See also COMPETITIVE EXCLUSION PRINCIPLE.

Lotka-Volterra equations Mathematical models of competition between resource-limited species living in the same space with the same environmental requirements. They have been modified subsequently to simulate simple predator-prey interactions. The competition model predicts that coexistence of such species populations is impossible; one is always eliminated, according to the competitive-exclusion principle. The predation model predicts cyclic fluctuations of predator and prey populations. Reduction of predator numbers allows prey to recuperate, which in turn stimulates the population growth of the predator. Increasing predator numbers depress the prey population, leading eventually to a reduction in the predator population.