Skip to main content
SpringerLink
Log in

Dispersal-mediated coexistence of indirect competitors in source-sink metacommunities

  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

The source-sink dynamics is a major hypothesis to explain dispersal-mediated coexistence of locally exclusive competitors. We study Lotka-Volterra diffusive models of indirect competition in patchy metacommunities. In a model of exploitative competition, we numerically show that the effect of resource movement on the coexistence depends on demographic factors that create source-sink structures and that the dispersal rate of the superior competitor need not be higher than that of the inferior to promote dispersal-mediated coexistence. In a model of apparent competition, we analytically prove that dispersal can make coexistence possible even if any patches are sinks for the inferior resource species. The requirement for this coexistence is the lower dispersal rate of the inferior competitor. We conclude that dispersal among patches can be a mechanism to save inferior indirect competitors from regional extinction and that the level of spatial heterogeneity need not be so high to reverse the competitive rankings among patches.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Abrams and W.G. Wilson, Coexistence of competitors in metacommunities due to spatial variation in resource growth rates; does R* predict the outcome of competition? Ecol. Lett.,7, (2004) 929–940.

    Article  Google Scholar 

  2. F.R. Adler and J. Mosquera, Is space necessary? Interference competition and limits to biodiversity, Ecology,81, (2000) 3226–3232.

    Article  Google Scholar 

  3. P. Amarasekare, Competitive coexistence in spatially structured environments: a synthesis. Ecol. Lett.,6, (2003) 1109–1122.

    Article  Google Scholar 

  4. P. Amarasekare, M.F. Hoopes, N. Mouquet and M. Holyoak, Mechanisms of coexistence in competitive metacommunities. Am. Nat.,164, (2004) 310–326.

    Article  Google Scholar 

  5. P. Amarasekare and R.M. Nisbet, Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species. Am. Nat.,158, (2001) 572–584.

    Article  Google Scholar 

  6. R.A. Armstrong and R. McGehee, Competitive exclusion. Am. Nat.,115, (1980) 151–170.

    Article  MathSciNet  Google Scholar 

  7. B.M. Bolker and S.W. Pacala, Spatial moment equations for plant communities: understanding spatial strategies and the advantages of short dispersal. Am. Nat.,153, (1999) 575–602.

    Article  Google Scholar 

  8. J.H. Brown and A. Kodric-Brown, Turnover rates in insular biogeography: effect of immigration on extinction. Ecology,58, (1977) 445–449.

    Article  Google Scholar 

  9. V. Calcagno, N. Mouquet, P. Jarne and P. David, Coexistence in a metacommunity: the competition-colonization trade-off is not dead. Ecol. Lett.,9, (2006) 897–907.

    Article  Google Scholar 

  10. R.S. Cantrell and C. Cosner, On the effects of spatial heterogeneity on the persistence of interacting species. J. Math. Biol.,37, (1998) 103–145.

    Article  MATH  MathSciNet  Google Scholar 

  11. J.M. Chase, P. Amarasekare, K. Cottenie, A. Gonzalez, R.D. Holt, M. Holyoak, M.F. Hoopes, M.A. Leibold, M. Loreau, N. Mouquet, J.B. Shurin and D. Tilman, Competing theories for competitive metacommunities. Metacommunities: Spatial Dynamics and Ecological Communities, (M. Holyoak, M.A. Leibold and R.D. Holt eds.), Chicago University Press, Chicago, 2005, 335–354.

    Google Scholar 

  12. P. Chesson, Coexistence of competitors in spatially and temporally varying environments: a look at the combined effects of different sorts of variability. Theor. Popul. Biol.,28, (1985) 263–287.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Chesson, General theory of competitive coexistence in spatially-varying environments. Theor. Popul. Biol.,58, (2000) 211–237.

    Article  MATH  Google Scholar 

  14. P. Chesson, Mechanisms of maintenance of species diversity. Annu. Rev. Ecol. Syst.,31, (2000) 343–366.

    Article  Google Scholar 

  15. U. Dieckmann, R. Law and J.A.J. Metz (eds.), The Geometry of Ecological Interactions: Simplifying Spatial Complexity, Cambridge University Press, Cambridge, 2000.

    Google Scholar 

  16. I.A. Hanski and M.E. Gilpin, Metapopulation dynamics: brief history and conceptual domain. Biol. J. Linn. Soc,42, (1991) 3–16.

    Article  Google Scholar 

  17. I.A. Hanski and M.E. Gilpin (eds.), Metapopulation Biology: Ecology, Genetics, and Evolution. Academic Press, San Diego, 1997

    MATH  Google Scholar 

  18. A. Hastings, Disturbance, coexistence, history, and competition for space. Theor. Popul. Biol.,18, (1980) 363–373.

    Article  MATH  MathSciNet  Google Scholar 

  19. R.D. Holt, Predation, apparent competition, and the structure of prey communities. Theor. Popul. Biol.,12, (1977) 197–229.

    Article  MathSciNet  Google Scholar 

  20. R.D. Holt, Spatial heterogeneity, indirect interactions, and coexistence of prey species. Am. Nat.,124, (1984) 377–406.

    Article  Google Scholar 

  21. R.D. Holt, Population dynamics in two-patch environments: some anomalous consequences of optimal habitat selection. Theor. Popul. Biol.,28, (1985) 181–208.

    Article  MATH  MathSciNet  Google Scholar 

  22. R.D. Holt, Ecology at the mesoscale: the influence of regional processes on local communities. Species Diversity in Ecological Communities: Historical and Geographical Perspectives, (R.E. Ricklefs and D. Schulter eds.), University of Chicago Press, Chicago, 1993, 77–88.

    Google Scholar 

  23. R.D. Holt, J. Grover and D. Tilman, Simple rules for interspecific dominance in systems with exploitative and apparent competition. Am. Nat.,144, (1994) 741–771.

    Article  Google Scholar 

  24. M. Holyoak and S.P. Lawler, The role of dispersal in predator-prey metapopulation dynamics. J. Anim. Ecol.,65, (1996) 640–652.

    Article  Google Scholar 

  25. M. Holyoak and S.P. Lawler, Persistence of an extinction-prone predator-prey interaction through metapopulation dynamics. Ecology,77, (1996) 1867–1879.

    Article  Google Scholar 

  26. M. Holyoak, M.A. Leibold and R.D. Holt editors, Metacommunities: Spatial Dynamics and Ecological Communities. Chicago University Press, Chicago, 2005.

    Google Scholar 

  27. M. Holyoak, M.A. Leibold, N. Mouquet, R.D. Holt, M.F. Hoopes, Metacommunities. A framework for large-scale community ecology. Metacommunities: Spatial Dynamics and Ecological Communities, (M. Holyoak, M.A. Leibold and R.D. Holt, eds.), Chicago University Press, Chicago, 2005, 35–67.

    Google Scholar 

  28. M.F. Hoopes, R.D. Holt and M. Holyoak, The effects of spatial processes on two species interactions. Metacommunities: Spatial Dynamics and Ecological Communities, (M. Holyoak, M.A. Leibold and R.D. Holt eds), Chicago University Press, Chicago, 2005, 35–67.

    Google Scholar 

  29. H.S. Horn and R.H. MacArthur, Competition among fugitive species in a harlequin environment. Ecology,53, (1972) 749–752.

    Article  Google Scholar 

  30. S.B. Hsu, S.P. Hubbell and P. Waltman, Competing predators. SIAM J. Appl. Math.,35, (1978) 617–625.

    Article  MATH  MathSciNet  Google Scholar 

  31. S.B. Hsu, S.P. Hubbell and P. Waltman, A contribution to the theory of competing predators. Ecol. Monog.,48, (1978) 337–349.

    Article  Google Scholar 

  32. Y. Iwasa and J. Roughgarden, Interspecific competition among metapopulations with spacelimited subpopulations. Theor. Popul. Biol.,30, (1986) 194–214.

    Article  MATH  MathSciNet  Google Scholar 

  33. K. Kishimoto, Coexistence of any number of species in the Lotka-Volterra competitive system over two patches. Theor. Popul. Biol.,38, (1990) 149–158.

    Article  MATH  Google Scholar 

  34. J.M. Kneitel and J.M. Chase, Trade-offs in community ecology: linking spatial scales and species coexistence. Ecol. Lett.,7, (2004) 69–80.

    Article  Google Scholar 

  35. A.L. Koch, Competitive coexistence of two predators utilizing the same prey under constant environmental conditions. J. Theor. Biol.,44, (1974) 387–395.

    Article  Google Scholar 

  36. V.A. Kostitzin, Biologie Mathématique. Collection Armand Colin: Paris, Translated in English by T.H. Savory in 1939. Mathematical Biology. Harrap and Co., London, 1937.

    Google Scholar 

  37. M.A. Leibold, M. Holyoak, N. Mouquet, P. Amarasekare, J.M. Chase, M.F. Hoopes, R.D. Holt, J.B. Shurin, R. Law, D. Tilman, M. Loreau and A. Gonzalez, The metacommunity concept: a framework for multi-scale community ecology. Ecol. Lett.,7, (2004) 601–613.

    Article  Google Scholar 

  38. J. Leon and D. Tumpson, Competition between two species for two complementary or substitutable resources. J. Theor. Biol.,50, (1975) 185–201.

    Article  Google Scholar 

  39. S.A. Levin, Dispersion and population interactions. Am. Nat.,108, (1974) 207–228.

    Article  Google Scholar 

  40. R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am.,15, (1969) 237–240.

    Google Scholar 

  41. R. Levins, Extinction. Some Mathematical Problems in Biology, (M. Gerstenhaber, ed.), American Mathematical Society: Providence RI. 1970, 75–107.

    Google Scholar 

  42. R. Levins and D. Culver, Regional coexistence of species and competition between rare species. Proc. Natl. Acad. Sci. USA,68, (1971) 1246–1248.

    Article  MATH  Google Scholar 

  43. N. Mouquet, M.F. Hoopes and P. Amarasekare, The world is patchy and heterogeneous! Trade-off and source-sink dynamics in competitive metacommunities. Metacommunities: Spatial Dynamics and Ecological Communities, (M. Holyoak, M.A. Leibold and R.D. Holt, eds.), Chicago University Press, Chicago, 2005, 237–262.

    Google Scholar 

  44. N. Mouquet and M. Loreau, Coexistence in metacommunities: the regional similarity hypothesis. Am. Nat.,159, (2002) 420–426.

    Article  Google Scholar 

  45. N. Mouquet and M. Loreau, Community patterns in source-sink metacommunities. Am. Nat.,162, (2003) 544–557.

    Article  Google Scholar 

  46. N. Mouquet, T.E. Miller, T. Daufresne and J.M. Kneitel, Consequences of varying regional heterogeneity in source-sink metacommunities, Oikos,113, (2006) 481–488.

    Article  Google Scholar 

  47. S. Muko and Y. Iwasa, Species coexistence by permanent spatial heterogeneity in a lottery model. Theor. Popul. Biol.,57, (2000) 273–284.

    Article  MATH  Google Scholar 

  48. S. Muko and Y. Iwasa, Incomplete mixing promotes species coexistence in a lottery model with permanent spatial heterogeneity. Theor. Popul. Biol.,64, (2003) 359–368.

    Article  MATH  Google Scholar 

  49. D.J. Murrell and R. Law, Heteromyopia and the spatial coexistence of similar competitors. Ecol. Lett.,6, (2003) 48–59.

    Article  Google Scholar 

  50. T. Namba, Emigration of a population and stability of a prey-predator system. Bull. Assoc. Nat. Sci. Senshu Univ.,11, (1993) 9–20.

    Google Scholar 

  51. T. Namba and C. Hashimoto, Dispersal-mediated coexistence of competing predators. Theor. Popul. Biol.,66, (2004) 53–70.

    Article  MATH  Google Scholar 

  52. T. Namba, A. Umemoto and E. Minami, The Effects of Habitat Fragmentation on Persistence of Source-Sink Metapopulations in Systems with Predators and Prey or Apparent Competitors. Theor. Popul. Biol.,56, (1999) 123–137.

    Article  MATH  Google Scholar 

  53. A. Okubo and S.A. Levin, Diffusion and Ecological Problems: Modern Perspectives (Interdisciplinary Applied Mathematics). Springer-Verlag, New York, 2001.

    Google Scholar 

  54. S.W. Pacala and M. Rees, Models suggesting field experiments to test two hypotheses explaining successional diversity. Am. Nat.,152, (1998) 729–737.

    Article  Google Scholar 

  55. S.W. Pacala, and J. Roughgarden. Spatial heterogeneity and interspecific competition. Theor. Popul. Biol.,21, (1982) 92–113.

    Article  MATH  MathSciNet  Google Scholar 

  56. H.R. Pulliam, Sources, sinks, and population regulation. Am. Nat.,132, (1988) 652–661.

    Article  Google Scholar 

  57. H.R. Pulliam and B.J. Danielson, Sources, sinks, and habitat selection: a landscape perspective on population dynamics. Am. Nat.,137, (1991) S50-S66.

    Article  Google Scholar 

  58. A. Schneeberger and V.A.A. Jansen, The estimation of dispersal rates using the covariance of local populations. Ecol. Modell.,196, (2006) 434–446.

    Article  Google Scholar 

  59. N. Shigesada and K. Kawasaki, Biological Invasions: Theory and Practice (Oxford Series in Ecology and Evolution). Oxford University Press, Oxford, New York, 1997.

    Google Scholar 

  60. A. Shmida and R.H. Whittaker, Pattern and biological microsite effects in two shrub communities, Southern California. Ecology,62, (1981) 234–251.

    Article  Google Scholar 

  61. R. Snyder and P. Chesson, Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity. Ecol. Lett.,6, (2003) 301–309.

    Article  Google Scholar 

  62. F.M. Stewart and B.R. Levin, Partitioning of resources and the outcome of interspecific competition: a model and some general considerations. Am. Nat.,107, (1973) 171–198.

    Article  Google Scholar 

  63. Y. Takeuchi, Diffusion-mediated persistence in two-species competition Lotka-Volterra model. Math. Biosci.,95, (1989) 65–83.

    Article  MATH  MathSciNet  Google Scholar 

  64. D. Tilman, Resources: a graphical-mechanistic approach to competition and predation. Am. Nat.,116, (1980) 362–393.

    Article  Google Scholar 

  65. D. Tilman, Resource Competition and Community Structure. Princeton University Press, Princeton, 1982.

    Google Scholar 

  66. D. Tilman, Competition and biodiversity in spatially structured habitats. Ecology,75, (1994) 2–16.

    Article  Google Scholar 

  67. D. Tilman and P. Kareiva, eds., Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Princeton University Press, Princeton, 1997.

    Google Scholar 

  68. D. Tilman, R.M. May, C.L. Lehman and M.A. Nowak, Habitat destruction and the extinction debt. Nature,371, (1994) 65–66.

    Article  Google Scholar 

  69. A.R. Watkinson and W.J. Sutherland, Sources, sinks and pseudo-sinks. J. Anim. Ecol.,64, (1995) 126–130.

    Article  Google Scholar 

  70. D.S. Wilson, Complex interactions in metacommunities with implications for biodiversity and higher levels of selection. Ecology,73, (1992) 1984–2000.

    Article  Google Scholar 

  71. D.W. Yu and H.B. Wilson, The competition-colonization trade-off is dead; long live the competition-colonization trade-off. Am. Nat.,158, (2001) 49–63.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biological Science, Graduate School of Science, Osaka Prefecture University, Daisen-cho 2-1, Sakai-ku, 590-0035, Sakai, Japan

    Toshiyuki Namba

Authors
  1. Toshiyuki Namba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Toshiyuki Namba.

About this article

Cite this article

Namba, T. Dispersal-mediated coexistence of indirect competitors in source-sink metacommunities. Japan J. Indust. Appl. Math. 24, 39–55 (2007). https://doi.org/10.1007/BF03167506

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03167506

Key words

Search

Navigation