The Lotka-Volterra equations describe the dynamics of biological systems in which two species interact, typically a predator and its prey. Developed by Alfred J. Lotka and Vito Volterra in the early 20th century, these mathematical models illustrate how the populations of each species affect one another over time. In the model, the prey population grows exponentially in the absence of predators, while the predator population relies on the prey for food. As the prey population increases, the predator population also rises, but eventually, over-predation can lead to a decline in prey, which in turn affects the predators, creating a cyclical pattern.