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Bulletin of Mathematical Biology

, Volume 76, Issue 7, pp 1809–1834 | Cite as

Modeling and Analysis of a Density-Dependent Stochastic Integral Projection Model for a Disturbance Specialist Plant and Its Seed Bank

  • Eric Alan Eager
  • Richard Rebarber
  • Brigitte Tenhumberg
Original Article

Abstract

In many plant species dormant seeds can persist in the soil for one to several years. The formation of these seed banks is especially important for disturbance specialist plants, as seeds of these species germinate only in disturbed soil. Seed movement caused by disturbances affects the survival and germination probability of seeds in the seed bank, which subsequently affect population dynamics. In this paper, we develop a stochastic integral projection model for a general disturbance specialist plant-seed bank population that takes into account both the frequency and intensity of random disturbances, as well as vertical seed movement and density-dependent seedling establishment. We show that the probability measures associated with the plant-seed bank population converge weakly to a unique measure, independent of initial population. We also show that the population either persists with probability one or goes extinct with probability one, and provides a sharp criteria for this dichotomy. We apply our results to an example motivated by wild sunflower (Helianthus annuus) populations, and explore how the presence or absence of a “storage effect” impacts how a population responds to different disturbance scenarios.

Keywords

Disturbance specialist Seed bank Integral Projection Model Weak convergence Density dependence Storage effect 

Notes

Acknowledgments

We would like to thank Professors Diana Pilson and Steven Dunbar for useful discussions about this work, and the two anonymous referees for suggestions which greatly improved the paper.

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Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Eric Alan Eager
    • 1
  • Richard Rebarber
    • 2
  • Brigitte Tenhumberg
    • 3
  1. 1.University of Wisconsin - La CrosseLa CrosseUSA
  2. 2.Department of MathematicsUniversity of Nebraska–LincolnLincolnUSA
  3. 3.School of Biological SciencesUniversity of Nebraska–LincolnLincolnUSA

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