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Journal of Mathematical Biology

, Volume 55, Issue 1, pp 105–145 | Cite as

Plant interspecies competition for sunlight: a mathematical model of canopy partitioning

  • Andrew L. NevaiEmail author
  • Richard R. Vance
Article

Abstract

We examine the influence of canopy partitioning on the outcome of competition between two plant species that interact only by mutually shading each other. This analysis is based on a Kolmogorov-type canopy partitioning model for plant species with clonal growth form and fixed vertical leaf profiles (Vance and Nevai in J. Theor. Biol., 2007, to appear). We show that canopy partitioning is necessary for the stable coexistence of the two competing plant species. We also use implicit methods to show that, under certain conditions, the species’ nullclines can intersect at most once. We use nullcline endpoint analysis to show that when the nullclines do intersect, and in such a way that they cross, then the resulting equilibrium point is always stable. We also construct surfaces that divide parameter space into regions within which the various outcomes of competition occur, and then study parameter dependence in the locations of these surfaces. The analysis presented here and in a companion paper (Nevai and Vance, The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model, in review) together shows that canopy partitioning is both necessary and, under appropriate parameter values, sufficient for the stable coexistence of two hypothetical plant species whose structure and growth are described by our model.

Keywords

Canopy partitioning model Plant competition Light competition Mathematical model Stable coexistence Canopy structure model 

Mathematics Subject Classification (2000)

92D25 34C23 34D23 92C80 92D40 

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References

  1. 1.
    Aikman D.P. and Benjamin L.R. (1994). A model for plant and crop growth, allowing for competition for light by the use of potential and restricted projected crown zone areas. Ann. Bot. 73: 185–194 CrossRefGoogle Scholar
  2. 2.
    Anten N.P.R. and Hirose T. (1998). Biomass allocation and light partitioning among dominant and subordinate individuals in Xanthium canadense stands. Ann. Bot. 82: 665–674 CrossRefGoogle Scholar
  3. 3.
    Anten N.P.R. and Hirose T. (2001). Limitations on photosynthesis of competing individuals in stands and the consequences for canopy structure. Oecologia 129: 186–196 CrossRefGoogle Scholar
  4. 4.
    Anten N.P.R. and Hirose T. (2003). Interspecific differences in structural and physiological characteristics in a tall-grass meadow and consequences for carbon gain. Ecology 84: 955–968 CrossRefGoogle Scholar
  5. 5.
    Armstrong R.A. and McGehee R. (1980). Competitive exclusion. Am. Nat. 115: 151–170 CrossRefMathSciNetGoogle Scholar
  6. 6.
    Barnes P.W., Beyschlag W., Ryel R., Flint S.D. and Caldwell M.M. (1990). Plant competition for light analyzed with a multispecies canopy model. III Influence of canopy structure in Mixtures and Monocultures of Wheat and Wild Oat. Oecologia 82: 560–566 Google Scholar
  7. 7.
    Barot, S., Gignoux, J.: Mechanisms promoting plant coexistence: can all the proposed processes be reconciled? OIKOS 106, 185–192 (2004)Google Scholar
  8. 8.
    Bolker B.M. and Pacala S.W. (1999). Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal. Am. Nat. 153: 575–602 CrossRefGoogle Scholar
  9. 9.
    Bunker, D.E., Stark, S.C.: Carson, W.P.: Competition for light between plant species with complex canopies: using invasibility criteria to predict competitive outcomes. (2007) (in preparation)Google Scholar
  10. 10.
    Courant, R.: Differential and integral calculus. Interscience, New York (1936) (reprinted 1964)Google Scholar
  11. 11.
    Ellsworth D.S. and Reich P.B. (1993). Canopy structure and vertical patterns of photosynthesis and related leaf traits in a deciduous forest. Oecologia 96: 169–178 CrossRefGoogle Scholar
  12. 12.
    Gause, G.F.: The struggle for existence. Dover, New York (1934) (reprinted 1971)Google Scholar
  13. 13.
    Grace, J.B., Tilman, D. (eds.): Perspectives on plant competition. Academic, New York (1990)Google Scholar
  14. 14.
    Hardin G. (1960). The competitive exclusion principle. Science 131: 1292–1297 CrossRefGoogle Scholar
  15. 15.
    Hikosaka K., Sudoh S. and Hirose T. (1999). Light acquisition and use by individuals competing in a dense stand of an annual herb. Xanthium canadense. Oecologia 118: 388–396 CrossRefGoogle Scholar
  16. 16.
    Hirose T. and Werger M.J.A. (1995). Canopy structure and photon flux partitioning among species in a herbaceous plant community. Ecology 76: 466–474 CrossRefGoogle Scholar
  17. 17.
    Hirsch, M.W., Smale, S., Devaney, R.L.: Differential equations, dynamical systems, and an introduction to chaos. Academic, San Diego (2004)Google Scholar
  18. 18.
    Hsu S.B., Hubbell S. and Waltman P. (1977). A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms. SIAM J. Appl. Math. 32: 366–383 zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Hubbell S.P., Foster R.B., Harms K.E., Condit R., Wechsler B., Wright S.J., Loo de Lao S., O’Brien and S.T. (1999). Light-gap disturbances, recruitment limitation, and tree diversity in a neotropical forest. Science 283: 554–557 CrossRefGoogle Scholar
  20. 20.
    Huisman J., Jonker R.R., Zonneveld C. and Weissing F.J. (1999). Competition for light between phytoplankton species: experimental tests of mechanistic theory. Ecology 80: 211–222 Google Scholar
  21. 21.
    Huston, M.A., DeAngelis, D.L.: Competition and coexistence: the effects of resource transport and supply rates. Am. Nat. 144, 954–977 (1994)Google Scholar
  22. 22.
    Hutchinson G.E. (1961). The paradox of the plankton. Am. Nat. 85: 137–145 CrossRefGoogle Scholar
  23. 23.
    Hutchinson B.A., Matt D.R., McMillen R.T., Gross L.J., Tajchman S.J. and Norman J.M. (1986). The architecture of a deciduous forest canopy in eastern Tennessee. J. Ecol. 74: 635–646 CrossRefGoogle Scholar
  24. 24.
    Just, W., Nevai, A.L.: A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight. MBI Technical Report No. 59 (in review)Google Scholar
  25. 25.
    Klausmeier, C.A., Tilman, D.: Spatial models of competition. In: Sommer, U., Worm, B. (eds.) Competition and coexistence. pp. 43–78. Springer, Heidelberg (2002)Google Scholar
  26. 26.
    Kohyama T. (1993). Size-structured tree populations in gap-dynamic forest—the forest architecture hypothesis for the stable coexistence of species. J. Ecol. 81: 131–143 CrossRefGoogle Scholar
  27. 27.
    Kolmogorov A.N. (1936). Sulla teoria di Volterra della lotta per l’esistenza. Giornale dell Istituto Italiano Degli Attuari 7: 74–80 Google Scholar
  28. 28.
    Law R. and Dieckmann U. (2000). A dynamical system for neighborhoods in plant communities. Ecology 81: 2137–2148 Google Scholar
  29. 29.
    Monsi M. and Saeki T. (1953). Über den Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung für die Stoffproduktion. Jap. J. Bot. 14: 22–52 Google Scholar
  30. 30.
    Nevai, A.L., Vance, R.R.: The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model (in review)Google Scholar
  31. 31.
    Pacala S.W., Canham C.D., Saponara J., Kone R.K., Ribbens E. and Silander J.A. (1996). Forest models defined by field measurements: estimation, error analysis and dynamics. Ecol. Monogr. 66: 1–43 CrossRefGoogle Scholar
  32. 32.
    Pacala, S.W., Levin, S.A.: Biologically generated spatial pattern and the coexistence of competing species. In: Tilman, D., Kareiva, P. (eds.) Spatial ecology, pp. 185–203. Princeton University Press, Princeton (1997)Google Scholar
  33. 33.
    Pakes A.G. and Maller R.A. (1990). Mathematical ecology of plant species competition: a class of deterministic models for binary mixtures of plant genotypes. Cambridge University Press, Cambridge zbMATHGoogle Scholar
  34. 34.
    Passarge J., Hol S., Escher M. and Huisman J. (2006). Competition for nutrients and light: stable coexistence, alternative stable states, or competitive exclusion?. Ecol. Monogr. 76: 57–72CrossRefGoogle Scholar
  35. 35.
    Pennings S.C. and Callaway R.M. (1992). Salt marsh plant zonation: the relative importance of competition and physical factors. Ecology 73: 681–690 CrossRefGoogle Scholar
  36. 36.
    Perry L.G., Neuhauser C. and Galatowitsch S.M. (2003). Founder control and coexistence in a simple model of asymmetric competition for light. J. Theor. Biol. 222: 425–436 MathSciNetGoogle Scholar
  37. 37.
    Porté A. and Bartelink H.H. (2002). Modelling mixed forest growth: a review of models for forest management. Ecol. Mod. 150: 141–188 CrossRefGoogle Scholar
  38. 38.
    Shmida A. and Ellner S. (1984). Coexistence of plant species with similar niches. Vegetatio 58: 29–55 Google Scholar
  39. 39.
    Stoll P. and Prati D.L. (2001). Intraspecific aggregation alters competitive interactions in experimentals plant communities. Ecology 82: 319–327 Google Scholar
  40. 40.
    Stomp M., Huisman J., de Jongh F., Veraart A.J., Gerla D., Rijkeboer M., Ibelings B.W., Wollenzien U.I.A. and Stal L.J. (2004). Adaptive divergence in pigment composition promotes phytoplankton biodiversity. Nature 432: 104–107 CrossRefGoogle Scholar
  41. 41.
    Thornley, J.H.M., Johnson, I.: Plant and crop modelling—a mathematical approach to plant and crop physiology. Clarendon Press, Oxford (1990)Google Scholar
  42. 42.
    Tilman, D.: Resource competition and community structure. Princeton University Press, Princeton (1982)Google Scholar
  43. 43.
    Tilman, D.: Plant strategies and the dynamics and structure of plant communities. Princeton University Press, Princeton (1988)Google Scholar
  44. 44.
    Vance R.R. (1985). The stable coexistence of two competitors for one resource. Am. Nat. 126: 72–86 CrossRefGoogle Scholar
  45. 45.
    Vance, R.R., Nevai, A.L.: Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning. J. Theor. Biol. (2007) (to appear)Google Scholar
  46. 46.
    Weissing F. and Huisman J. (1994). Growth and competition in a light gradient. J. Theor. Biol. 168: 323–336 CrossRefGoogle Scholar
  47. 47.
    Zavala M.A. and Bravo de la Parra R. (2005). A mechanistic model of tree competition and facilitation for Mediterranean forests: scaling from leaf physiology to stand dynamics. Ecol. Mod. 188: 76–92 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Mathematical Biosciences InstituteThe Ohio State UniversityColumbusUSA
  3. 3.Department of Ecology and Evolutionary BiologyUniversity of CaliforniaLos AngelesUSA

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