Abstract
The population dynamics for predator and prey environments have been studied extensively, and several major mathematical models have been introduced to quantify this. The situation becomes more complex, however, when the prey incorporates preservation strategies for survival. One of the most interesting approaches here is the use of mimicry of prey which are unacceptable to the predator, to avoid being consumed. Here we develop a Markov chain model of interactions between a predator and a prey population comprising unpalatable models, general mimics and specific mimics. This incorporates a simple stochastic procedure for the predator, enabling modifiable behavior to be modeled. We calculate equilibrium consumption probabilities and introduce a fitness measure for each type of prey. Finally, by taking into account the population size of each type of prey, we extend the previously reported notion of a predator benefit function for this more complex situation and provide various mathematical forms of optimal benefit for the predator under selected scenarios of biological importance.
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