[1] Allwright, J.:Reaction-diffusion on a time-dependent interval:refining the notion of 'critical length'. Commun. Contemp. Math. (2022). https://doi.org/10.1142/S021919972250050X. In press [2] Averill, I., Lou, Y., Munther, D.:On several conjectures from evolution of dispersal. J. Biol. Dyn. 6, 117-130 (2012) [3] Berestycki, H., Diekmann, O., Nagelkerke, C.J., Zegeling, P.A.:Can a species keep pace with a shifting climate? Bull. Math. Biol. 71, 399-429 (2009) [4] Cantrell, R.S., Cosner, C.:Spatial Ecology Via Reaction-Diffusion Equations. Wiley Series in Mathematical and Computational Biology. Wiley, Chichester (2003) [5] Cantrell, R.S., Cosner, C., DeAngelis, D.L., Padron, V.:The ideal free distribution as an evolutionarily stable strategy. J. Biol. Dyn. 1, 249-271 (2007) [6] Cantrell, R.S., Cosner, C., Lou, Y.:Evolution of dispersal and the ideal free distribution. Math. Biosci. Eng. 7, 17-36 (2010) [7] Diekmann, O.:A beginner's guide to adaptive dynamics. Banach Center Publ. 63, 47-86 (2004) [8] Dockery, J., Hutson, V., Mischaikow, K., Pernarowski, M.:The evolution of slow disperal rates:a reaction-diffusion model. J. Math. Biol. 37, 61-83 (1998) [9] Evans, L.C.:Partial Differential Equations, 2nd edn. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence, RI (2010) [10] Fretwell, S.D., Lucas, H.L.:On territorial behavior and other factors influencing habitat distribution in birds. Acta. Biotheor. 19, 16-36 (1969) [11] Gan, W., Shao, Y., Wang, J., Xu, F.:Global dynamics of a general competitive reaction-diffusion-advection system in one dimensional environments. Nonlinear Anal. Real World Appl. 66, 103523 (2022) [12] Hao, W., Lam, K.-Y., Lou, Y.:Ecological and evolutionary dynamics in advective environments:critical domain size and boundary conditions. Discrete Contin. Dyn. Syst. Ser. B 26, 367-400 (2021) [13] Hastings, A.:Can spatial variation alone lead to selection for dispersal? Theor. Popul. Biol. 24, 244-251 (1983) [14] Hsu, S.B., Smith, H.L., Waltman, P.:Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Trans. Amer. Math. Soc. 348, 4083-4094 (1996) [15] Kierstead, H., Slobodkin, L.B.:The size of water masses containing plankton blooms. J. Mar. Res. 12, 141-147 (1953) [16] Lam, K.-Y., Lou, Y.:Introduction to Reaction-Diffusion Equations:Theory and Applications to Spatial Ecology and Evolutionary Biology. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Cham (2022) [17] Lam, K.-Y., Munther, D.:A remark on the global dynamics of competitive systems on ordered Banach spaces. Proc. Am. Math. Soc. 144, 1153-1159 (2016) [18] Lewis, M.A., Hillen, T., Lutscher, F.:Spatial dynamics in ecology. In:Lewis, M.A., Keener, J., Maini, P., Chaplain, M. (eds.) Mathematical Biology. IAS/Park City Math. Ser., Vol. 14, pp. 27-45. Amer. Math. Soc., Providence, RI (2009) [19] Lou, Y., Lutscher, F.:Evolution of dispersal in open advective environments. J. Math. Biol. 69, 1319-1342 (2014) [20] Lou, Y., Zhao, X.-Q., Zhou, P.:Global dynamics of a Lotka-Volterra competition-diffusion-advection system in heterogeneous environments. J. Math. Pures Appl. 121, 47-82 (2019) [21] Lou, Y., Zhou, P.:Evolution of dispersal in advective homogeneous environment:the effect of boundary conditions. J. Differential Equations 259, 141-171 (2015) [22] Ludwig, D., Aronson, D.G., Weinberger, H.F.:Spatial patterning of the spruce budworm. J. Math. Biol. 8, 217-258 (1979) [23] Lutscher, F., Lewis, M.A., McCauley, E.:Effects of heterogeneity on spread and persistence in rivers. Bull. Math. Biol. 68, 2129-2160 (2006) [24] Mckenzie, H.W., Jin, Y., Jacobsen, J., Lewis, M.A.:R0 analysis of a spatiotemporal model for a stream population. SIAM J. Appl. Dyn. Syst. 11, 567-596 (2012) [25] Parmesan, C., Yohe, G.:A globally coherent fingerprint of climate change impacts across natural systems. Nature 421, 37-42 (2003) [26] Potapov, A.B., Lewis, M.A.:Climate and competition:the effect of moving range boundaries on habitat invasibility. Bull. Math. Biol. 66, 975-1008 (2004) [27] Qin, W., Zhou, P.:A review on the dynamics of two species competitive ODE and parabolic systems. J. Appl. Anal. Comput. 12, 2075-2109 (2022) [28] Shigesada, N., Kawasaki, K.:Biological Invasions:Theory and Practice. Oxford Series in Ecology and Evolution. Oxford University Press, Oxford, New York, Tokyo (1997) [29] Skellam, J.G.:Random dispersal in theoretical populations. Biometrika 38, 196-218 (1951) [30] Speirs, D.C., Gurney, W.S.C.:Population persistence in rivers and estuaries. Ecology 82, 1219-1237 (2001) [31] Tang, D., Chen, Y.M.:Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments. J. Differential Equations 269, 1465-1483 (2020) [32] Tang, D., Zhou, P.:On a Lotka-Volterra competition-diffusion-advection system:homogeneity vs heterogeneity. J. Differential Equations 268, 1570-1599 (2020) [33] Vasilyeva, O., Lutscher, F.:Population dynamics in rivers:analysis of steady states. Can. Appl. Math. Q. 18, 439-469 (2010) [34] Wang, Y., Xu, Q., Zhou, P.:Evolution of dispersal in advective homogeneous environments:inflow vs outflow. Submitted [35] Xu, F., Gan, W., Tang, D.:Population dynamics and evolution in river ecosystems. Nonlinear Anal. Real World Appl. 51, 102983 (2020) |