Dispersal Success

  • Frithjof Lutscher
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 49)


In this chapter, we present techniques for approximating the steady-state profile and the dominant eigenvalue of an IDE on a bounded domain. The approximations are based on the idea that only partial information about dispersal may be available, corresponding to two different mark-recapture experiments. The approximations are surprisingly good when dispersal is symmetric but less reliable when dispersal is asymmetric.


  1. Cobbold, C., Lewis, M., Lutscher, F., & Roland, J. (2005). How parasitism affects critical patch size in a host–parasitoid system: Application to forest tent caterpillar. Theoretical Population Biology, 67(2), 109–125.CrossRefGoogle Scholar
  2. Cobbold, C., & Lutscher, F. (2014). Mean occupancy time: Linking mechanistic movement models, population dynamics and landscape ecology to population persistence. Journal of Mathematical Biology, 68(3), 549–579.MathSciNetCrossRefGoogle Scholar
  3. Fagan, W., & Lutscher, F. (2006). Average dispersal success: Linking home range, dispersal and metapopulation dynamics to reserve design. Ecological Applications, 16(2), 820–828.CrossRefGoogle Scholar
  4. Kot, M., & Phillips, A. (2015). Bounds for the critical speed of climate-driven moving-habitat models. Mathematical Biosciences, 262, 65–72.MathSciNetCrossRefGoogle Scholar
  5. Latore, J., Gould, P., & Mortimer, A. (1998). Spatial dynamics and critical patch size of annual plant populations. Journal of Theoretical Biology, 190, 277–285.CrossRefGoogle Scholar
  6. Lockwood, D., Hastings, A., & Botsford, L. (2002). The effects of dispersal patterns on marine reserve: Does the tail wag the dog? Theoretical Population Biology, 61, 297–309.CrossRefGoogle Scholar
  7. Lutscher, F., & Lewis, M. (2004). Spatially-explicit matrix models. A mathematical analysis of stage-structured integrodifference equations. Journal of Mathematical Biology, 48, 293–324.MathSciNetCrossRefGoogle Scholar
  8. Lutscher, F., Pachepsky, E., & Lewis, M. (2005). The effect of dispersal patterns on stream populations. SIAM Review, 47(4), 749–772.MathSciNetCrossRefGoogle Scholar
  9. Reimer, J., Bonsall, M., & Maini, P. (2016). Approximating the critical patch-size of integrodifference equations. Bulletin of Mathematical Biology, 78, 72–109.MathSciNetCrossRefGoogle Scholar
  10. Rinnan, D. S. (2017). The dispersal success and persistence of populations with asymmetric dispersal. Theoretical Ecology, 11(1), 55–69.CrossRefGoogle Scholar
  11. Van Kirk, R., & Lewis, M. (1997). Integrodifference models for persistence in fragmented habitats. Bulletin of Mathematical Biology, 59(1), 107–137.CrossRefGoogle Scholar
  12. Zhou, Y., & Kot, M. (2013). Life on the move: Modeling the effects of climate-driven range shifts with integrodifference equations. In Dispersal, individual movement and spatial ecology (pp. 263–292). Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Frithjof Lutscher
    • 1
  1. 1.Mathematics and StatisticsUniversity of OttawaOttawaCanada

Personalised recommendations