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

Abstract

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].

Keywords:

• Integrodifference pioneer-climax system
• spreading speeds
• travelling waves
• linear selection

Mathematics Subject Classifications:

• 92D25
• 37N25
• 39A70

Acknowledgments

The authors are grateful to the referees for their careful reading and valuable comments which improve our original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors were supported by National Natural Science Foundation of China [grant numbers 11601386, 11701415], and Y. Zhang is partially supported by Research Project of Tianjin Municipal Education Commission [grant number 2022ZD014].