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Hamilton also went on to model predation in two-dimensions, using a lion as an example. Movements that Hamilton proposed would lower an individual's domain of danger were largely based on the theory of marginal predation. This theory states that predators attack the closest prey, who are typically on the outside of an aggregation. [1]
EcoSim is an individual-based predator-prey ecosystem simulation in which agents can evolve. It has been designed to investigate several broad ecological questions, as well as long-term evolutionary patterns and processes such as speciation and macroevolution.
The aim of Huffaker’s 1958 experiment was to “shed light upon the fundamental nature of predator–prey interaction” [2] and to “establish an ecosystem in which a predatory and a prey species could continue living together so that the phenomena associated with their interactions could be studied in detail”. [3]
Examples include predator-prey competition and host-parasite co-evolution, as well as mutualism. Evolutionary game models have been created for pairwise and multi-species coevolutionary systems. [58] The general dynamic differs between competitive systems and mutualistic systems.
The Lotka–Volterra predator-prey model makes a number of assumptions about the environment and biology of the predator and prey populations: [5] The prey population finds ample food at all times. The food supply of the predator population depends entirely on the size of the prey population.
The form is similar to the Lotka–Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential. For the competition equations, the logistic equation is the basis.
Predators receive a reproductive payoff, e, for consuming prey, and die at rate u. Making predation pressure a function of the ratio of prey to predators contrasts with the prey-dependent Lotka–Volterra equations, where the per capita effect of predators on the prey population is simply a function of the magnitude of the prey population g(N).
At low prey densities, the search time is long. Since the predator spends most of its time searching, it eats every prey item it finds. As prey density increases, the predator is able to capture the prey faster and faster. At a certain point, the rate of prey capture is so high, that the predator doesn't have to eat every prey item it encounters.