University of Wisconsin - La Crosse, La Crosse, WI, USA,
Bull Math Biol. 2014 Jul;76(7):1809-34. doi: 10.1007/s11538-014-9978-y. Epub 2014 Jun 11.
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.
在许多植物物种中，休眠种子可以在土壤中存活一到几年。这些种子库的形成对干扰专性植物尤为重要，因为这些物种的种子仅在受干扰的土壤中发芽。干扰引起的种子移动会影响种子库中种子的生存和发芽概率，从而影响种群动态。在本文中，我们为一种一般的干扰专性植物-种子库种群开发了一个随机积分投影模型，该模型考虑了随机干扰的频率和强度，以及垂直种子移动和密度依赖的幼苗建立。我们证明与植物-种子库种群相关的概率测度弱收敛到一个唯一的测度，与初始种群无关。我们还表明，种群要么以概率 1 持续存在，要么以概率 1 灭绝，并为此二分法提供了一个尖锐的标准。我们将我们的结果应用于一个受野生向日葵（Helianthus annuus）种群启发的例子，并探讨了“存储效应”的存在与否如何影响种群对不同干扰场景的反应。
