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

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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.

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References

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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. Barot, S., Gignoux, J.: Mechanisms promoting plant coexistence: can all the proposed processes be reconciled? OIKOS 106, 185–192 (2004)

  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

    Article  Google Scholar 

  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)

  10. Courant, R.: Differential and integral calculus. Interscience, New York (1936) (reprinted 1964)

  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

    Article  Google Scholar 

  12. Gause, G.F.: The struggle for existence. Dover, New York (1934) (reprinted 1971)

  13. Grace, J.B., Tilman, D. (eds.): Perspectives on plant competition. Academic, New York (1990)

  14. Hardin G. (1960). The competitive exclusion principle. Science 131: 1292–1297

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  17. Hirsch, M.W., Smale, S., Devaney, R.L.: Differential equations, dynamical systems, and an introduction to chaos. Academic, San Diego (2004)

  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

    Article  MATH  MathSciNet  Google Scholar 

  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

    Article  Google Scholar 

  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. 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. Hutchinson G.E. (1961). The paradox of the plankton. Am. Nat. 85: 137–145

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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)

  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)

  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

    Article  Google Scholar 

  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. Law R. and Dieckmann U. (2000). A dynamical system for neighborhoods in plant communities. Ecology 81: 2137–2148

    Google Scholar 

  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. Nevai, A.L., Vance, R.R.: The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model (in review)

  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

    Article  Google Scholar 

  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)

  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

    MATH  Google Scholar 

  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: 57–72

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    MathSciNet  Google Scholar 

  37. Porté A. and Bartelink H.H. (2002). Modelling mixed forest growth: a review of models for forest management. Ecol. Mod. 150: 141–188

    Article  Google Scholar 

  38. Shmida A. and Ellner S. (1984). Coexistence of plant species with similar niches. Vegetatio 58: 29–55

    Google Scholar 

  39. Stoll P. and Prati D.L. (2001). Intraspecific aggregation alters competitive interactions in experimentals plant communities. Ecology 82: 319–327

    Google Scholar 

  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

    Article  Google Scholar 

  41. Thornley, J.H.M., Johnson, I.: Plant and crop modelling—a mathematical approach to plant and crop physiology. Clarendon Press, Oxford (1990)

  42. Tilman, D.: Resource competition and community structure. Princeton University Press, Princeton (1982)

  43. Tilman, D.: Plant strategies and the dynamics and structure of plant communities. Princeton University Press, Princeton (1988)

  44. Vance R.R. (1985). The stable coexistence of two competitors for one resource. Am. Nat. 126: 72–86

    Article  Google Scholar 

  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)

  46. Weissing F. and Huisman J. (1994). Growth and competition in a light gradient. J. Theor. Biol. 168: 323–336

    Article  Google Scholar 

  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

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, 90095-1555, USA

    Andrew L. Nevai

  2. Mathematical Biosciences Institute, The Ohio State University, 231 West 18th Ave, Columbus, OH, 43210, USA

    Andrew L. Nevai

  3. Department of Ecology and Evolutionary Biology, University of California, 621 Charles E. Young Drive South, Los Angeles, CA, 90095-1606, USA

    Richard R. Vance

Authors
  1. Andrew L. Nevai
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  2. Richard R. Vance
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Correspondence to Andrew L. Nevai.

Additional information

A. L. Nevai was supported in part by the National Institutes of Health, National Research Service Award (T32-GM008185) from the National Institute of General Medical Sciences (NIGMS).

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Nevai, A.L., Vance, R.R. Plant interspecies competition for sunlight: a mathematical model of canopy partitioning. J. Math. Biol. 55, 105–145 (2007). https://doi.org/10.1007/s00285-007-0073-y

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