Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Evolution of Dispersal in Advective Patchy Environments

  • Published:
Journal of Nonlinear Science Aims and scope Submit manuscript

Abstract

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutant species can or cannot invade the resident species.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  • Altenberg, L.: Resolvent positive linear operators exhibit the reduction phenomenon. Proc. Natl. Acad. Sci. USA 109(10), 3705–3710 (2012)

    MathSciNet  MATH  Google Scholar 

  • Apaloo, J., Brown, J.S., Vincent, T.L.: Evolutionary game theory: ESS, convergence stability, and NIS. Evol. Ecol. Res. 11, 489–515 (2009)

    Google Scholar 

  • Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences, Volume 9 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1994)

  • Cantrell, R.S., Cosner, C.: Spatial Ecology via Reaction–Diffusion Equations. Wiley, New York (2004)

    MATH  Google Scholar 

  • Cantrell, R.S., Cosner, C., Deangelis, D.L., Padron, V.: The ideal free distribution as an evolutionarily stable strategy. J. Biol. Dyn. 1(3), 249–271 (2007)

    MathSciNet  MATH  Google Scholar 

  • Cantrell, R.S., Cosner, C., Lou, Y.: Evolutionary stability of ideal free dispersal strategies in patchy environments. J. Math. Biol. 65(5), 943–965 (2012)

    MathSciNet  MATH  Google Scholar 

  • Cantrell, R.S., Cosner, C., Lou, Y., Schreiber, S.J.: Evolution of natal dispersal in spatially heterogeneous environments. Math. Biosci. 283, 136–144 (2017)

    MathSciNet  MATH  Google Scholar 

  • Chen, S., Shi, J., Shuai, Z., Wu, Y.: Global dynamics of a Lotka–Volterra competition patch model. Nonlinearity 35(2), 817–842 (2022a)

  • Chen, S., Shi, J., Shuai, Z., Wu, Y.: Two novel proofs of spectral monotonicity of perturbed essentially nonnegative matrices with applications in population dynamics. SIAM J. Appl. Math. 82(2), 654–676 (2022b)

  • Cheng, C.-Y., Lin, K.-H., Shih, C.-W.: Coexistence and extinction for two competing species in patchy environments. Math. Biosci. Eng. 16(2), 909–946 (2019)

    MathSciNet  MATH  Google Scholar 

  • Cosner, C.: Variability, vagueness and comparison methods for ecological models. Bull. Math. Biol. 58(2), 207–246 (1996)

    MATH  Google Scholar 

  • DeAngelis, D.L., Ni, W.-M., Zhang, B.: Dispersal and spatial heterogeneity: single species. J. Math. Biol. 72(1), 239–254 (2016)

    MathSciNet  MATH  Google Scholar 

  • Dieckmann, U., Law, R.: The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34(5), 579–612 (1996)

    MathSciNet  MATH  Google Scholar 

  • Dockery, J., Hutson, V., Mischaikow, K., Pernarowski, M.: The evolution of slow dispersal rates: a reaction diffusion model. J. Math. Biol. 37(1), 61–83 (1998)

    MathSciNet  MATH  Google Scholar 

  • Geritz, S., Kisdi, E., Mesze, G., Metz, J.A.J.: Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Biol. 12(1), 35–57 (1998)

    Google Scholar 

  • Gourley, S.A., Kuang, Y.: Two-species competition with high dispersal: the winning strategy. Math. Biosci. Eng. 2(2), 345–362 (2005)

    MathSciNet  MATH  Google Scholar 

  • Hamida, Y.: The Evolution of Dispersal for the Case of Two Patches and Two-Species with Travel Loss. Master’s thesis, The Ohio State University (2017)

  • Hastings, A.: Can spatial variation alone lead to selection for dispersal? Theor. Popul. Biol. 24(3), 244–251 (1983)

    MathSciNet  MATH  Google Scholar 

  • Hess, P.: Periodic-Parabolic Boundary Value Problems and Positivity. Pitman Research Notes in Mathematics Series, vol. 247. Longman Scientific & Technical, Harlow (1991)

  • Hsu, S.B., Smith, H.L., Waltman, P.: Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Trans. Am. Math. Soc. 348(10), 4083–4094 (1996)

    MathSciNet  MATH  Google Scholar 

  • Huang, Q.-H., Jin, Y., Lewis, M.A.: \(R_0\) analysis of a Benthic-drift model for a stream population. SIAM J. Appl. Dyn. Syst. 15(1), 287–321 (2016)

    MathSciNet  MATH  Google Scholar 

  • Jiang, H., Lam, K.-Y., Lou, Y.: Are two-patch models sufficient? The evolution of dispersal and topology of river network modules. Bull. Math. Biol. 82(10), Paper No. 131, 42 (2020)

  • Jiang, H., Lam, K.-Y., Lou, Y.: Three-patch models for the evolution of dispersal in advective environments: varying drift and network topology. Bull. Math. Biol. 83(10), 1–46 (2021)

    MathSciNet  MATH  Google Scholar 

  • Jin, Y., Lewis, M.A.: Seasonal influences on population spread and persistence in streams: critical domain size. SIAM J. Appl. Math. 71(4), 1241–1262 (2011)

    MathSciNet  MATH  Google Scholar 

  • Keitt, T.H., Lewis, M.A., Holt, R.D.: Allee effects, invasion pinning, and species’ borders. Am. Nat. 157(2), 203–216 (2001)

    Google Scholar 

  • Kirkland, S., Li, C.-K., Schreiber, S.J.: On the evolution of dispersal in patchy landscapes. SIAM J. Appl. Math. 66(4), 1366–1382 (2006)

    MathSciNet  MATH  Google Scholar 

  • Lam, K.-Y., Lou, Y.: Evolutionarily stable and convergent stable strategies in reaction–diffusion models for conditional dispersal. Bull. Math. Biol. 76(2), 261–291 (2014)

    MathSciNet  MATH  Google Scholar 

  • Lam, K.-Y., Munther, D.: A remark on the global dynamics of competitive systems on ordered Banach spaces. Proc. Am. Math. Soc. 144(3), 1153–1159 (2016)

    MathSciNet  MATH  Google Scholar 

  • Lam, K.Y., Lou, Y., Lutscher, F.: Evolution of dispersal in closed advective environments. J. Biol. Dyn. 9(suppl. 1), 188–212 (2015)

    MathSciNet  MATH  Google Scholar 

  • Lam, K.Y., Lou, Y., Lutscher, F.: The emergence of range limits in advective environments. SIAM J. Appl. Math. 76(2), 641–662 (2016)

    MathSciNet  MATH  Google Scholar 

  • Levin, S.A.: Population dynamic models in heterogeneous environments. Annu. Rev. Ecol. Syst. 66, 287–310 (1976)

    Google Scholar 

  • Levin, S.A., Cohen, D., Hastings, A.: Dispersal strategies in patchy environments. Theor. Popul. Biol. 26(2), 165–191 (1984)

    MathSciNet  MATH  Google Scholar 

  • Li, C.-K., Schneider, H.: Applications of Perron–Frobenius theory to population dynamics. J. Math. Biol. 44(5), 450–462 (2002)

    MathSciNet  MATH  Google Scholar 

  • Li, M.Y., Shuai, Z.: Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 248(1), 1–20 (2010)

    MathSciNet  MATH  Google Scholar 

  • Lin, K.-H., Lou, Y., Shih, C.-W., Tsai, T.-H.: Global dynamics for two-species competition in patchy environment. Math. Biosci. Eng. 11(4), 947–970 (2014)

    MathSciNet  MATH  Google Scholar 

  • Lou, Y.: Ideal free distribution in two patches. J. Nonlinear Model. Anal. 2, 151–167 (2019)

    Google Scholar 

  • Lou, Y., Lutscher, F.: Evolution of dispersal in open advective environments. J. Math. Biol. 69(6–7), 1319–1342 (2014)

    MathSciNet  MATH  Google Scholar 

  • Lou, Y., Zhou, P.: Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions. J. Differ. Equ. 259(1), 141–171 (2015)

    MathSciNet  MATH  Google Scholar 

  • Lou, Y., Xiao, D.-M., Zhou, P.: Qualitative analysis for a Lotka–Volterra competition system in advective homogeneous environment. Discrete Contin. Dyn. Syst. 36(2), 953–969 (2016)

    MathSciNet  MATH  Google Scholar 

  • Lou, Y., Nie, H., Wang, Y.: Coexistence and bistability of a competition model in open advective environments. Math. Biosci. 306, 10–19 (2018)

  • Lu, Z.Y., Takeuchi, Y.: Global asymptotic behavior in single-species discrete diffusion systems. J. Math. Biol. 32(1), 67–77 (1993)

    MathSciNet  MATH  Google Scholar 

  • Lutscher, F., Pachepsky, E., Lewis, M.A.: The effect of dispersal patterns on stream populations. SIAM Rev. 47(4), 749–772 (2005). ((electronic))

    MathSciNet  MATH  Google Scholar 

  • Lutscher, F., Lewis, M.A., McCauley, E.: Effects of heterogeneity on spread and persistence in rivers. Bull. Math. Biol. 68(8), 2129–2160 (2006)

    MathSciNet  MATH  Google Scholar 

  • Lutscher, F., McCauley, E., Lewis, M.A.: Spatial patterns and coexistence mechanisms in systems with unidirectional flow. Theor. Popul. Biol. 71(3), 267–277 (2007)

    MATH  Google Scholar 

  • Ma, L., Tang, D.: Evolution of dispersal in advective homogeneous environments. Discrete Contin. Dyn. Syst. 40(10), 5815–5830 (2020)

    MathSciNet  MATH  Google Scholar 

  • McPeek, M.A., Holt, R.D.: The evolution of dispersal in spatially and temporally varying environments. Am. Nat. 140(6), 1010–1027 (1992)

    Google Scholar 

  • Noble, L.: Evolution of Dispersal in Patchy Habitats. PhD thesis, The Ohio State University (2015)

  • Owen, M.R., Lewis, M.A.: How predation can slow, stop or reverse a prey invasion. Bull. Math. Biol. 63(4), 655–684 (2001)

    MathSciNet  MATH  Google Scholar 

  • Smith, H.L.: Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. American Mathematical Society, Providence (1995)

    MATH  Google Scholar 

  • Speirs, D.C., Gurney, W.S.C.: Population persistence in rivers and estuaries. Ecology 82(5), 1219–1237 (2001)

    Google Scholar 

  • Vasilyeva, O., Lutscher, F.: Population dynamics in rivers: analysis of steady states. Can. Appl. Math. Q. 18(4), 439–469 (2010)

    MathSciNet  MATH  Google Scholar 

  • Vasilyeva, O., Lutscher, F.: How flow speed alters competitive outcome in advective environments. Bull. Math. Biol. 74(12), 2935–2958 (2012)

    MathSciNet  MATH  Google Scholar 

  • Xiang, J.-J., Fang, Y.: Evolutionarily stable dispersal strategies in a two-patch advective environment. Discrete Contin. Dyn. Syst. Ser. B 24(4), 1875–1887 (2019)

    MathSciNet  MATH  Google Scholar 

  • Yan, X., Nie, H., Zhou, P.: On a competition–diffusion–advection system from river ecology: mathematical analysis and numerical study. SIAM J. Appl. Dyn. Syst. 21(1), 438–469 (2022)

    MathSciNet  MATH  Google Scholar 

  • Zhao, X.-Q., Zhou, P.: On a Lotka–Volterra competition model: the effects of advection and spatial variation. Calc. Var. Part. Differ. Equ. 55(4), Art. 73, 25 (2016)

  • Zhou, P.: On a Lotka–Volterra competition system: diffusion vs advection. Calc. Var. Part. Differ. Equ. 55(6), Art. 137, 29 (2016)

  • Zhou, P., Zhao, X.-Q.: Global dynamics of a two species competition model in open stream environments. J. Dyn. Differ. Equ. 30(2), 613–636 (2018)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank two anonymous reviewers for their insightful suggestions that led to improvement of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, Shandong, People’s Republic of China

    Shanshan Chen

  2. Department of Mathematics, William & Mary, Williamsburg, VA, 23187-8795, USA

    Junping Shi

  3. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Zhisheng Shuai

  4. Department of Mathematics, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Yixiang Wu

Authors
  1. Shanshan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junping Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhisheng Shuai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yixiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junping Shi.

Ethics declarations

Conflict of interest

The authors declare they have no conflict of interest.

Additional information

Communicated by Paul Newton.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

S. Chen is supported by National Natural Science Foundation of China (Nos. 12171117, 11771109) and Shandong Provincial Natural Science Foundation of China (No. ZR2020YQ01), J. Shi is supported by US-NSF Grant DMS-1715651 and DMS-1853598, and Z. Shuai is supported by US-NSF Grant DMS-1716445.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, S., Shi, J., Shuai, Z. et al. Evolution of Dispersal in Advective Patchy Environments. J Nonlinear Sci 33, 40 (2023). https://doi.org/10.1007/s00332-023-09899-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00332-023-09899-w

Keywords

Mathematics Subject Classification

Search

Navigation