Spatiotemporal complexity of biological invasion in a space- and time-discrete predator–prey system with the strong Allee effect

Understanding dynamical complexity of alien species invasion is an important and timely issue as it is believed that identification of possible invasion scenarios may result in a more effective invasive species management and control. To address this issue, mathematical modeling is widely recognized as a convenient theoretical tool as it often helps to reveal generic tendencies in a situation when it would hardly be possible otherwise. However, although much attention has been paid to spatially continuous models of biological invasion, spatially discrete models have remained outside of the mainstream. Meanwhile, species habitat is often distinctly patchy or even fragmented, and then spatially discrete models seems to be the most appropriate modeling framework. In this paper, we consider invasion scenarios in a spaceand time-discrete system described by a coupled map lattice. The alien species is assumed to be affected by the strong Allee effect and by a specialist predator. We first consider the stage of species introduction and obtain analytical conditions to distinguish between invasion success and invasion failure. We then focus on species spatial spread. By means of extensive computer simulations, we identify the main scenarios of species spread (e.g. patchy invasion and multiple traveling bands) and reveal the corresponding structure of the parameter space. Counter-intuitively, we have found that alien species can invade over the whole domain even in the case when its local persistence would not be possible. 2011 Elsevier B.V. All rights reserved.