Thursday 03 Oct 2013: Modeling and mathematical analysis of a disturbance specialist plant and its seed bank
Prof Richard Rebarber - University of Nebraska
ESI Trevithick Room (AV Link to XFi Seminar B) 16:00-17:00
In many plant species dormant seeds can persist in the soil for one or more years. The formation of these seed banks is especially important for disturbance specialist plants, since for these species seeds germinate only in disturbed soil. In particular, disturbances alter the depth distribution of seeds in the seed bank, burying some seeds deep in the soil where survival is high (and germination rates are low), and relocating other seeds closer to the soil surface where germination rates are high (but survival is low). For instance, seeds can be moved from lower seed depths to the surface through digging activities by mammals. In this talk we consider disturbances that occur in an unpredictable fashion, so that the disturbance is described by a random variable. We describe 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. For these systems the population cannot converge to an asymptotic population, since the population vector is also a random variable. We can, however, 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 provide a sharp criteria for this dichotomy. We apply our results to an example motivated by wild sunflower (Helianthus annuus) populations.