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