糖心TV

Speaker: Sergei Petrovskiy (Leicester)

Title:  Nonlinear Waves and Pattern Formation in the problems of Biological Invasion and Biological Control

Abstract:

Biological invasions are currently regarded as a major threat to biodiversity and agriculture all over the world. Apparent importance of this issue has brought to life various strategies of invasive species management. The concept of biological control is based on the assumption that the impact of certain biological or environmental factors can slow down or block the spread of harmful species. Several such factors have been identified earlier. In this talk, we consider how the rate of invasion and the whole pattern of spread can possibly be affected by the impact of predation.

Mathematically, the system is described by two nonlinear partial differential equations of diffusion-reaction type. We first try to treat the problem analytically. Under some additional constraints, we obtain its exact solution. Having considered the solution properties, we show that predation can block or even reverse the invasive species spread provided the population growth is damped by the strong Allee effect. We then study the problem by means of extensive numerical experiments in one and two spatial dimensions and show that the impact of predation can change the whole pattern of spread: in a certain parameter range, invasion can take place not via the intuitively expected circular continuous population front but via motion and interaction of separate patches. The population density appears to be on the order of carrying capacity inside the patches and it is virtually zero between the patches. Remarkably, a similar pattern of spread can be seen in data field observations. We then show that this phenomenon of patchy invasion takes place "at the edge of extinction." Moreover, we show that the regime of patchy invasion in two spatial dimensions actually takes place when the species go extinct in the corresponding 1-D system.