Joint Impact of Advection and Diffusion on the Predator–Prey Coexistence in an Open Flow

• Shixia Xin ^[1] ; Hua Nie ^[1] ; Hongying Shu ^[1]
  1. [1] Shaanxi Normal University

     Shaanxi Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01151-4
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we examine a predator–prey model with general reaction functions in open advective environments, where the predator and prey may employ distinct movement strategies. Using the coefficients of diffusion and advection as varying parameters, we conduct a quantitative analysis on the critical advection rates, which distinguish the different dynamics of this predator–prey system, to explore the joint impact of advection and diffusion on the invasion and coexistence of predators and prey in an open flow. It turns out that the dynamics may switch many times between a successful or failed invasion, coexistence or generalist predator take-over as the advection and diffusion rates of predators and prey vary, which suggests that both diffusion and advection play a crucial role in shaping the dynamics of the predator–prey system.

• Referencias bibliográficas
  • 1. Anholt, B.R.: Density dependence resolves the stream drift paradox. Ecology 76, 2235–2239 (1995)
  • 2. Cantrell, R.S., Cosner, C.: Spatial ecology via reaction-diffusion equations, wiley series in mathematical and computational biology. John...
  • 3. Courant, R., Hilbert, D.: Methods of mathematical physics. Wiley-Interscience, New York (1953)
  • 4. He, X.Q., Ni, W.M.: The effects of diffusion and spatial variation in Lotka-Volterra competitiondiffusion system I: heterogeneity vs. homogeneity....
  • 5. Hershey, A.E., Pastor, J., Peterson, B.J., Kling, G.W.: Stable isotopes resolve the drift paradox for baetis mayflies in an arctic river....
  • 6. Hilker, F.M., Lewis, M.A.: Predator-prey systems in streams and rivers. Theor. Ecol. 3, 175–193 (2010)
  • 7. Jin, Y., Peng, R., Shi, J.P.: Population dynamics in river networks. J. Nonlinear Sci. 29, 2501–2545 (2019)
  • 8. Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Uspehi Matem. Nauk. 3, 3–95 (1948)
  • 9. Lam, K.Y., Lou, Y., Lutscher, F.: Evolution of dispersal in closed advective environments. J. Biol. Dyn. 9, 188–212 (2015)
  • 10. Lam, K.Y., Lou, Y., Lutscher, F.: The emergence of range limits in advective environments. SIAM J. Appl. Math. 76, 641–662 (2016)
  • 11. Lou, Y., Lutscher, F.: Evolution of dispersal in open advective environments. J. Math. Biol. 69, 1319– 1342 (2014)
  • 12. Lou, Y., Xiao, D.M., Zhou, P.: Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment. Discrete...
  • 13. Lou, Y., Zhou, P.: Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions. J. Differ. Equ. 259,...
  • 14. Lutscher, F., Seo, G.: The effect of temporal variability on persistence conditions in rivers. J. Theoret. Biol. 283, 53–59 (2011)
  • 15. Ma, L., Tang, D.: Evolution of dispersal in advective homogeneous environments. Discrete Contin. Dyn. Syst. Ser. B 40, 5815–5830 (2020)
  • 16. Mckenzie, H.W., Jin, Y., Jacobsen, J., Lewis, M.A.: R0 analysis of a spatiotemporal model for a stream population. SIAM J. Appl. Dyn....
  • 17. Meng, Y., Lin, Z.G., Pedersen, M.: On a competition model in stream environments: the effects of seasonal pulses and advection. J. Differ....
  • 18. Nie, H., Hsu, S.B., Grover, J.P.: Algal competition in a water column with excessive dioxide in the atmosphere. J. Math. Biol. 72, 1845–1892...
  • 19. Nie, H., Wang, B., Wu, J.H.: Invasion analysis on a predator-prey system in open advective environments. J. Math. Biol. 81, 1429–1463...
  • 20. Speirs, D.C., Gurney, W.S.C.: Population persistence in rivers and estuaries. Ecology 82, 1219–1237 (2001)
  • 21. Tang, D., Chen, Y.M.: Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments. J. Differ....
  • 22. Vasilyeva, O., Lutscher, F.: Population dynamics in rivers: analysis of steady states. Can. Appl. Math. Q. 18, 439–469 (2010)
  • 23. Vasilyeva, O., Lutscher, F., Lewis, M.A.: Analysis of spread and persistence for stream insects with winged adult stages. J. Math. Biol....
  • 24. Wang, J.F., Nie, H.: Invasion dynamics of a predator-prey system in closed advective environments. J. Differ. Equ. 318, 298–322 (2022)
  • 25. Wang, Y., Shi, J.P.: Persistence and extinction of population in reaction-diffusion-advection model with weak Allee effect growth. SIAM...
  • 26. Wang, Y., Shi, J.P., Wang, J.F.: Persistence and extinction of population in reaction-diffusion-advection model with strong Allee effect...
  • 27. Xin, S.X., Li, L.C., Nie, H.: The effect of advection on a predator-prey model in open advective environments. Commun. Nonlinear Sci....
  • 28. Zhou, P., Tang, D., Xiao, D.M.: On Lotka-Volterra competitive parabolic systems: exclusion, coexistence and bistability. J. Differ. Equ....
  • 29. Zhou, P., Zhao, X.Q.: Global dynamics of a two species competition model in open stream environments. J. Dynam. Differ. Equ. 30, 613–636...