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Functional responses measure the trophic interactions between species, taking into account the density and behavior of the interacting species. In predator-prey interactions, the prey preference of the predator and the antipredator behavior of the prey together determine the feeding rate of the predator and the survival rate of the prey. Consequently, the behavior dependent functional responses make it possible to establish dynamic ecological models providing insight, among others, into the coexistence of predator and prey species and the efficiency of agents in biological pest control. In this paper the derivation methods of functional responses are reviewed. Basically, there are three classes of such methods: heuristic, stochastic and deterministic ones. All of them can take account of the behavior of the predator and prey. There are three main stochastic methods for the derivation of functional responses: renewal theory, Markov chain and the Wald equality-based method. All these methods assume that during the foraging process the prey densities do not change, which provides a mathematical basis for heuristic derivation. There are two deterministic methods using differential equations. The first one also assumes that during the foraging process the prey densities do not change, while the second one does not use that assumption. These derivation methods are appropriate to handle the behavior dependent functional responses, which is essential in the derivation of ecological games, when the payoff of prey and predator depends on the strategies of the prey and predator at the same time.

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