The Periodical Population Dynamics of Lottery Models Including the Effect of Undeveloped Seeds

  • Shigehide Iwata
  • Ryusuke Kon
  • Yasuhiro Takeuchi

Summary

The mechanism that promotes coexistence of species has not been completely clarified yet. We propose that the amount of nutrient can be one of the factors that promote coexistence of species. Plant species have to reproduce seeds to produce descendants. Even if plant species do reproduce seeds, it is not ensured that every seed will bud. The amount of seeds that can bud successfully depends on the amount of nutrient: if the nutrient is scarce, then every seed cannot bud, but if the nutrient is rich, then every seed can bud. We also assume that the amount of seeds reproduced by one plant individual depends on the amount of nutrient.We show that, in this situation, the population dynamics of plants exhibits a complex behavior, which promotes coexistence of species.

Keywords

Space nutrient reproduction function effective availability undeveloped seed 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chesson, P., Warner, R. R.: Environmental variability promotes coexistence in lottery competitive system. Am. Nat., 117, 923–943 (1981).CrossRefMathSciNetGoogle Scholar
  2. 2.
    Chesson, P.: The stabilizing effect of a random environment. J. Math. Biol., 15, 1–36 (1982).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chesson, P., Huntly, N.: The roles of harsh and fluctuating conditions in the dynamics of ecological communities. Am. Nat., 150, 519–553 (1997).CrossRefGoogle Scholar
  4. 4.
    Comins, H. N., Noble, I. R.: Dispersal, variability and transient niches: Species coexistence in a uniformly variable environment. Am. Nat., 126, 706–723 (1985).CrossRefGoogle Scholar
  5. 5.
    Dewi, S., Chesson, P.: The age-structured lottery model. Theor. Popul. Biol., 117, 923–943 (1981).Google Scholar
  6. 6.
    Hatfield, J. S., Scheibling, R. E.: Diffusion analysis and stationary distribution of the twospecies lottery competition model. Theor. Popul. Biol., 36, 251–266 (1989).MATHCrossRefGoogle Scholar
  7. 7.
    Huisman, J., Weissing, F. J.: Biodiversity of plankton by species oscillations and chaos. Nature., 402, 407–410 (1999).CrossRefGoogle Scholar
  8. 8.
    Lambers, H., Chapin III, F. S., Pons, T. L.: Plant Physiological Ecology. Springer-Verlag, New York (1998).Google Scholar
  9. 9.
    Laurie, H., Mustart, P. J., Cowling, R. M.: A shared niche? The case of the species pair, Protea obtusifolia Leucadendron meridianum. Oikos., 79, 127–136 (1997).CrossRefGoogle Scholar
  10. 10.
    Muko, S., Iwasa, Y.: Species coexistence by permanent spatial heterogeneity in a lottery model. Theor. Popul. Biol., 57, 273–284 (2000).MATHCrossRefGoogle Scholar
  11. 11.
    Muko, S., Iwasa, Y.: Incomplete mixing promotes species coexistence in a lottery model with permanent spatial heterogeneity. Theor. Popul. Biol., 64, 359–368 (2003).MATHCrossRefGoogle Scholar
  12. 12.
    Neuhauser, C., Pacala, W.: An explicitly spatial version of the Lotka–Volterra model with interspecific competition. Ann. Appl. Probab., 9, 1226–1259 (1999).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Shigehide Iwata
    • 1
  • Ryusuke Kon
    • 2
  • Yasuhiro Takeuchi
    • 3
  1. 1.Graduate School of Science and Technology, Shizuoka UniversityJohoku 3-5-2Japan
  2. 2.Faculty of MathematicsKyushu UniversityHakozaki 6-10-1Japan
  3. 3.Department of Systems Engineering, Faculty of EngineeringShizuoka UniversityJohoku 3-5-2Japan

Personalised recommendations