Travelling waves and speed selection for the integrodifference pioneer-climax competition system

This is the authors' abstract. We don't add key points for this paper.

We present a general integrodifference pioneer-climax competition system and study the invasion dynamics of the system in both monotone and nonmonotone cases. For the parameter regions in which the system is monotone, we establish the existence of the spreading speed and travelling waves and show that the minimum wave speed is linearly selected if the overall dispersal of the invasive species is larger than that of the native one. For the parameter regions in which the system is nonmonotone, we estimate the spreading speed by constructing suitable auxiliary systems and prove the existence of travelling waves by the fixed point theorem and upper-lower solution method. We apply our theoretical results to an integrodiffference pioneer-climax system which is a spatial version of the model recently studied by Gilbertson and Kot [Theor. Ecol., 14(2021), 501-523].