Lotka-Volterra Equations

The Lotka-Volterra equations are a pair of first order, nonlinear differential equations frequently used to describe the dynamics of a biological system in which two species interact, one as a predator and the other as its prey. The equations were proposed independently by the American mathematician and chemist Alfred Lotka in 1910, in the context of chemical reaction dynamics, and by the Italian mathematician Vito Volterra in 1926, who developed them specifically to explain observed fluctuations in fish catches in the Adriatic Sea following the reduction of fishing during the First World War. The model predicts that predator and prey populations will oscillate in a cyclical pattern, with the prey population rising, followed by a rise in the predator population that in turn drives the prey population back down, and the equations remain a foundational model in mathematical biology despite the simplifying assumptions on which they rest, such as unlimited food for the prey and no environmental carrying capacity.