The original Lotka-Volterra predator-prey model was extended in many directions, resulting in a vast theoretical literature on prey-predator interactions. Some of these models relax the original assumptions and analyze the properties of the resulting models. Others try to adapt the existing models to some particular empirical prey-predator systems. In this article surveyed some basic theory resulting from the Lotka-Volterra formalism that considers time as a continuous variable was surveyed.

This corresponds to the situation where populations reproduce and die continuously. Alternative formalism is based on models that consider time as a discrete variable. These models can better fit situations where individual reproduction is synchronized. A discrete time alternative to the Lotka-Volterra model is the Nicholson-Bailey host-parasitoid model that can be as well used as a description of prey-predator interactions.

See also: Coexistence; Competition and Competition Models; Dispersal-Migration; Fishery Models; Indirect Effects in Ecology; Mathematical Ecology; Metapopulation Models; Stability.

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