We investigate how a spatial barrier influences the spread of an invading species via numerical analysis of a free boundary model, which is known to exhibit successful spreading like a traveling wave in homogeneous environments with population growth described by either a bistable function (incorporating Allee effect) or a monostable function. The barrier is represented by a region where the environment becomes hostile.
Our numerical simulations show that, there exists a critical barrier length and a critical level of hostility, so that below the critical values, the species can successfully spread across the barriers, otherwise, the invasion is blocked.
We also incorporate temporal environmental variation by introducing periodic changes in the growth rate. The results indicate that stronger fluctuations tend to promote invasion, while slower temporal variation reduces the spreading ability.
A comparison between the bistable and monostable cases shows that, the bistable case allows invasion across the barrier more easily, suggesting that the presence of an Allee effect may enhance the likelihood of successful spread.