<p>This paper presents a class of stochastic predation models and the dynamical behaviour is analyzed, including the unique existence of global positive solutions, boundedness of solutions, the mean persistence and extinction of interacting populations by theories of stochastic differential equations. The results show that stochastic perturbations have important effects on the dynamical behaviour of the considered system. Smaller combined perturbations for the interacting populations guarantee the mean persistence of predator and prey populations. Meanwhile, moderate perturbations for the interacting populations may ensure the population mean persistence while predator conversion rate is relatively high. However, moderate perturbations to predators could lead to extinction of interacting populations when predator conversion rate is relatively low. Predator and prey populations will become extinct when combined perturbations to the interacting populations are relatively high. Finally, all the theoretical results are verified by numerical simulations. The conclusions of this paper may be applied in biological control and the biodiversity conservation, and provide some theoretical suggestions for experimental biology.</p>