Intrinsic Uncertainty in Ecological Catastrophe

Abstract The dynamics of spatial pattern in a prey-predator system is studied by applying the lattice model of position-fixed reaction. Each lattice site may be empty, or occupied by a single prey or predator individual. This system exhibits a phase transition between a phase where both prey and predator survive, and a phase where predators are extinct. If the system is situated in the vicinity of the phase boundary, a kind of catastrophe is observed, such as the abrupt increase of prey or the extinction of predator. This catastrophe is brought about by very small disturbances; for example, the prey population abruptly increases, even though the reproduction rate of prey slightly decreases. Such a paradox is not explained by the Lotka-Volterra equation, but comes from the spatial pattern change of predator (indirect effect). It is, therefore, found that the catastrophe has both properties of phase transition and indirect effect. If such a catastrophe occurs in real ecosystems, it is hopeless to determine the origin of the catastrophe.