Effects of the probability of a predator catching prey on predator-prey system stability
2011
Lee, S.H., National Institute for Mathematical Sciences, Daejeon, Republic of Korea
To understand the effect of the probability of a predator catching prey, P∧catch, on the stability of the predator-prey system, a spatially explicit lattice model consisting of predators, prey, and grass was constructed. The predators and prey randomly move on the lattice space, and the grass grows according to its growth probability. When a predator encounters prey, the predator eats the prey in accordance with the probability P∧catch. When a prey encounters grass, the prey eats the grass. The predator and prey give birth to offspring according to a birth probability after eating prey or grass, respectively. When a predator or prey is initially introduced or newly born, its health state is set at a high given value. This health state decreases by one with every time step. When the state of an animal decreases to less than zero, the individual dies and is removed from the system. Population densities for predator and prey fluctuated significantly according to P∧catch. System stability was characterized by the standard deviation φ of the fluctuation. The simulation results showed that φ for predators increased with an increase of P∧catch; φ for prey reached a maximum at P∧catch = 0.4; and φ for grass fluctuated little regardless of P∧catch. These results were due to the tradeoff between P∧catch and the predator-prey encounter rate, which represents the degree of interaction between predator and prey and the average population density, respectively.
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